gemseo_pymoo / problems / analytical

# knapsack module¶

Knapsack problem.

This module implements the Knapsack problem.

In its simplest form, it states that:

Given a set of items, each with a given weight and value, determine the number of each item to include in a collection so that the total weight is less than or equal to a given weight capacity and the total value is as large as possible.

\begin{split}\begin{aligned} \text{maximize the total knapsack value } & \sum_{i=1}^{n} value_i * x_i \\ \text{with respect to the design variables }&x_i \\ \text{subject to the general constraints } & \sum_{i=1}^{n} weight_i * x_i \leq capacity_weight\\ & \sum_{i=1}^{n} x_i \leq capacity_items\\ \text{subject to the search domain } & x_i \in \mathbb{N} \end{aligned}\end{split}

Multiple variations of the Knapsack problem can be achieved depending on the inputs provided.

Moreover, a multi-objective version of this problem is also available, in which the following new objective function is added to previous formulation:

\begin{split}\begin{aligned} \text{minimize the number of items carried } & \sum_{i=1}^{n} x_i \\ \end{aligned}\end{split}
class gemseo_pymoo.problems.analytical.knapsack.Knapsack(values, weights, items_ub=None, binary=True, capacity_weight=None, capacity_items=None, initial_guess=None)[source]

Generic knapsack optimization problem.

Different variations can be achieved:

• 0/1 or Binary Knapsack problem:

Given a set of $$n$$ items, each with a weight $$w_i$$ and a value $$v_i$$, and a knapsack with a maximum weight capacity $$W$$. Choose which items to pack in order to maximize the total knapsack value while respecting its weight capacity.

• Unbounded Knapsack problem:

With respect to the Binary variant, it removes the restriction that there is only one of each item. This can be achieved by setting the attribute binary to False, which will remove the upper bound of the design variables.

• Bounded Knapsack problem:

With respect to the Binary variant, it specifies an upper bound for each item. This can be achieved by providing an array items_ub with the upper bound relative to each item.

Moreover, an additional constraint regarding the total number of items can be added. This is achieved through the attribute capacity_items and will limit the number of items that fit into the knapsack.

The constructor.

Initialize the Knapsack OptimizationProblem by defining the DesignSpace and the objective and constraint functions.

The number of items in the problem is deduced from the values array.

Parameters:
• values (ndarray) – The items’ values.

• weights (ndarray) – The items’ weights.

• items_ub (ndarray | None) – The items’ upper bounds. If None, an unlimited number of each item is allowed.

• binary (bool) –

If True, the upper bound of design variables is set to 1.

By default it is set to True.

• capacity_weight (float | None) – The knapsack weight capacity. If None, the knapsack will have an unlimited weight capacity.

• capacity_items (int | None) – The knapsack number of items capacity. If None, the knapsack will accept an unlimited total number of items.

• initial_guess (ndarray | None) – The initial guess for the optimal solution. If None, the initial guess will be an empty knapsack (0, 0, …, 0).

Raises:

ValueError – Either if the provided arrays do not have the same length or if no capacity is provided.

AggregationFunction

alias of EvaluationFunction

class ApproximationMode(value)

Bases: StrEnum

The approximation derivation modes.

capitalize()

Return a capitalized version of the string.

More specifically, make the first character have upper case and the rest lower case.

casefold()

Return a version of the string suitable for caseless comparisons.

center(width, fillchar=' ', /)

Return a centered string of length width.

Padding is done using the specified fill character (default is a space).

count(sub[, start[, end]]) int

Return the number of non-overlapping occurrences of substring sub in string S[start:end]. Optional arguments start and end are interpreted as in slice notation.

encode(encoding='utf-8', errors='strict')

Encode the string using the codec registered for encoding.

encoding

The encoding in which to encode the string.

errors

The error handling scheme to use for encoding errors. The default is ‘strict’ meaning that encoding errors raise a UnicodeEncodeError. Other possible values are ‘ignore’, ‘replace’ and ‘xmlcharrefreplace’ as well as any other name registered with codecs.register_error that can handle UnicodeEncodeErrors.

endswith(suffix[, start[, end]]) bool

Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.

expandtabs(tabsize=8)

Return a copy where all tab characters are expanded using spaces.

If tabsize is not given, a tab size of 8 characters is assumed.

find(sub[, start[, end]]) int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

format(*args, **kwargs) str

Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces (‘{’ and ‘}’).

format_map(mapping) str

Return a formatted version of S, using substitutions from mapping. The substitutions are identified by braces (‘{’ and ‘}’).

index(sub[, start[, end]]) int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

isalnum()

Return True if the string is an alpha-numeric string, False otherwise.

A string is alpha-numeric if all characters in the string are alpha-numeric and there is at least one character in the string.

isalpha()

Return True if the string is an alphabetic string, False otherwise.

A string is alphabetic if all characters in the string are alphabetic and there is at least one character in the string.

isascii()

Return True if all characters in the string are ASCII, False otherwise.

ASCII characters have code points in the range U+0000-U+007F. Empty string is ASCII too.

isdecimal()

Return True if the string is a decimal string, False otherwise.

A string is a decimal string if all characters in the string are decimal and there is at least one character in the string.

isdigit()

Return True if the string is a digit string, False otherwise.

A string is a digit string if all characters in the string are digits and there is at least one character in the string.

isidentifier()

Return True if the string is a valid Python identifier, False otherwise.

Call keyword.iskeyword(s) to test whether string s is a reserved identifier, such as “def” or “class”.

islower()

Return True if the string is a lowercase string, False otherwise.

A string is lowercase if all cased characters in the string are lowercase and there is at least one cased character in the string.

isnumeric()

Return True if the string is a numeric string, False otherwise.

A string is numeric if all characters in the string are numeric and there is at least one character in the string.

isprintable()

Return True if the string is printable, False otherwise.

A string is printable if all of its characters are considered printable in repr() or if it is empty.

isspace()

Return True if the string is a whitespace string, False otherwise.

A string is whitespace if all characters in the string are whitespace and there is at least one character in the string.

istitle()

Return True if the string is a title-cased string, False otherwise.

In a title-cased string, upper- and title-case characters may only follow uncased characters and lowercase characters only cased ones.

isupper()

Return True if the string is an uppercase string, False otherwise.

A string is uppercase if all cased characters in the string are uppercase and there is at least one cased character in the string.

join(iterable, /)

Concatenate any number of strings.

The string whose method is called is inserted in between each given string. The result is returned as a new string.

Example: ‘.’.join([‘ab’, ‘pq’, ‘rs’]) -> ‘ab.pq.rs’

ljust(width, fillchar=' ', /)

Return a left-justified string of length width.

Padding is done using the specified fill character (default is a space).

lower()

Return a copy of the string converted to lowercase.

lstrip(chars=None, /)

Return a copy of the string with leading whitespace removed.

If chars is given and not None, remove characters in chars instead.

static maketrans()

Return a translation table usable for str.translate().

If there is only one argument, it must be a dictionary mapping Unicode ordinals (integers) or characters to Unicode ordinals, strings or None. Character keys will be then converted to ordinals. If there are two arguments, they must be strings of equal length, and in the resulting dictionary, each character in x will be mapped to the character at the same position in y. If there is a third argument, it must be a string, whose characters will be mapped to None in the result.

partition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing the original string and two empty strings.

removeprefix(prefix, /)

Return a str with the given prefix string removed if present.

If the string starts with the prefix string, return string[len(prefix):]. Otherwise, return a copy of the original string.

removesuffix(suffix, /)

Return a str with the given suffix string removed if present.

If the string ends with the suffix string and that suffix is not empty, return string[:-len(suffix)]. Otherwise, return a copy of the original string.

replace(old, new, count=-1, /)

Return a copy with all occurrences of substring old replaced by new.

count

Maximum number of occurrences to replace. -1 (the default value) means replace all occurrences.

If the optional argument count is given, only the first count occurrences are replaced.

rfind(sub[, start[, end]]) int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

rindex(sub[, start[, end]]) int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

rjust(width, fillchar=' ', /)

Return a right-justified string of length width.

Padding is done using the specified fill character (default is a space).

rpartition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string, starting at the end. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing two empty strings and the original string.

rsplit(sep=None, maxsplit=-1)

Return a list of the words in the string, using sep as the delimiter string.

sep

The delimiter according which to split the string. None (the default value) means split according to any whitespace, and discard empty strings from the result.

maxsplit

Maximum number of splits to do. -1 (the default value) means no limit.

Splits are done starting at the end of the string and working to the front.

rstrip(chars=None, /)

Return a copy of the string with trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

split(sep=None, maxsplit=-1)

Return a list of the words in the string, using sep as the delimiter string.

sep

The delimiter according which to split the string. None (the default value) means split according to any whitespace, and discard empty strings from the result.

maxsplit

Maximum number of splits to do. -1 (the default value) means no limit.

splitlines(keepends=False)

Return a list of the lines in the string, breaking at line boundaries.

Line breaks are not included in the resulting list unless keepends is given and true.

startswith(prefix[, start[, end]]) bool

Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.

strip(chars=None, /)

Return a copy of the string with leading and trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

swapcase()

Convert uppercase characters to lowercase and lowercase characters to uppercase.

title()

Return a version of the string where each word is titlecased.

More specifically, words start with uppercased characters and all remaining cased characters have lower case.

translate(table, /)

Replace each character in the string using the given translation table.

table

Translation table, which must be a mapping of Unicode ordinals to Unicode ordinals, strings, or None.

The table must implement lookup/indexing via __getitem__, for instance a dictionary or list. If this operation raises LookupError, the character is left untouched. Characters mapped to None are deleted.

upper()

Return a copy of the string converted to uppercase.

zfill(width, /)

Pad a numeric string with zeros on the left, to fill a field of the given width.

The string is never truncated.

CENTERED_DIFFERENCES = 'centered_differences'

The centered differences method used to approximate the Jacobians by perturbing each variable with a small real number.

COMPLEX_STEP = 'complex_step'

The complex step method used to approximate the Jacobians by perturbing each variable with a small complex number.

FINITE_DIFFERENCES = 'finite_differences'

The finite differences method used to approximate the Jacobians by perturbing each variable with a small real number.

class DifferentiationMethod(value)

Bases: StrEnum

The differentiation methods.

capitalize()

Return a capitalized version of the string.

More specifically, make the first character have upper case and the rest lower case.

casefold()

Return a version of the string suitable for caseless comparisons.

center(width, fillchar=' ', /)

Return a centered string of length width.

Padding is done using the specified fill character (default is a space).

count(sub[, start[, end]]) int

Return the number of non-overlapping occurrences of substring sub in string S[start:end]. Optional arguments start and end are interpreted as in slice notation.

encode(encoding='utf-8', errors='strict')

Encode the string using the codec registered for encoding.

encoding

The encoding in which to encode the string.

errors

The error handling scheme to use for encoding errors. The default is ‘strict’ meaning that encoding errors raise a UnicodeEncodeError. Other possible values are ‘ignore’, ‘replace’ and ‘xmlcharrefreplace’ as well as any other name registered with codecs.register_error that can handle UnicodeEncodeErrors.

endswith(suffix[, start[, end]]) bool

Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.

expandtabs(tabsize=8)

Return a copy where all tab characters are expanded using spaces.

If tabsize is not given, a tab size of 8 characters is assumed.

find(sub[, start[, end]]) int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

format(*args, **kwargs) str

Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces (‘{’ and ‘}’).

format_map(mapping) str

Return a formatted version of S, using substitutions from mapping. The substitutions are identified by braces (‘{’ and ‘}’).

index(sub[, start[, end]]) int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

isalnum()

Return True if the string is an alpha-numeric string, False otherwise.

A string is alpha-numeric if all characters in the string are alpha-numeric and there is at least one character in the string.

isalpha()

Return True if the string is an alphabetic string, False otherwise.

A string is alphabetic if all characters in the string are alphabetic and there is at least one character in the string.

isascii()

Return True if all characters in the string are ASCII, False otherwise.

ASCII characters have code points in the range U+0000-U+007F. Empty string is ASCII too.

isdecimal()

Return True if the string is a decimal string, False otherwise.

A string is a decimal string if all characters in the string are decimal and there is at least one character in the string.

isdigit()

Return True if the string is a digit string, False otherwise.

A string is a digit string if all characters in the string are digits and there is at least one character in the string.

isidentifier()

Return True if the string is a valid Python identifier, False otherwise.

Call keyword.iskeyword(s) to test whether string s is a reserved identifier, such as “def” or “class”.

islower()

Return True if the string is a lowercase string, False otherwise.

A string is lowercase if all cased characters in the string are lowercase and there is at least one cased character in the string.

isnumeric()

Return True if the string is a numeric string, False otherwise.

A string is numeric if all characters in the string are numeric and there is at least one character in the string.

isprintable()

Return True if the string is printable, False otherwise.

A string is printable if all of its characters are considered printable in repr() or if it is empty.

isspace()

Return True if the string is a whitespace string, False otherwise.

A string is whitespace if all characters in the string are whitespace and there is at least one character in the string.

istitle()

Return True if the string is a title-cased string, False otherwise.

In a title-cased string, upper- and title-case characters may only follow uncased characters and lowercase characters only cased ones.

isupper()

Return True if the string is an uppercase string, False otherwise.

A string is uppercase if all cased characters in the string are uppercase and there is at least one cased character in the string.

join(iterable, /)

Concatenate any number of strings.

The string whose method is called is inserted in between each given string. The result is returned as a new string.

Example: ‘.’.join([‘ab’, ‘pq’, ‘rs’]) -> ‘ab.pq.rs’

ljust(width, fillchar=' ', /)

Return a left-justified string of length width.

Padding is done using the specified fill character (default is a space).

lower()

Return a copy of the string converted to lowercase.

lstrip(chars=None, /)

Return a copy of the string with leading whitespace removed.

If chars is given and not None, remove characters in chars instead.

static maketrans()

Return a translation table usable for str.translate().

If there is only one argument, it must be a dictionary mapping Unicode ordinals (integers) or characters to Unicode ordinals, strings or None. Character keys will be then converted to ordinals. If there are two arguments, they must be strings of equal length, and in the resulting dictionary, each character in x will be mapped to the character at the same position in y. If there is a third argument, it must be a string, whose characters will be mapped to None in the result.

partition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing the original string and two empty strings.

removeprefix(prefix, /)

Return a str with the given prefix string removed if present.

If the string starts with the prefix string, return string[len(prefix):]. Otherwise, return a copy of the original string.

removesuffix(suffix, /)

Return a str with the given suffix string removed if present.

If the string ends with the suffix string and that suffix is not empty, return string[:-len(suffix)]. Otherwise, return a copy of the original string.

replace(old, new, count=-1, /)

Return a copy with all occurrences of substring old replaced by new.

count

Maximum number of occurrences to replace. -1 (the default value) means replace all occurrences.

If the optional argument count is given, only the first count occurrences are replaced.

rfind(sub[, start[, end]]) int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

rindex(sub[, start[, end]]) int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

rjust(width, fillchar=' ', /)

Return a right-justified string of length width.

Padding is done using the specified fill character (default is a space).

rpartition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string, starting at the end. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing two empty strings and the original string.

rsplit(sep=None, maxsplit=-1)

Return a list of the words in the string, using sep as the delimiter string.

sep

The delimiter according which to split the string. None (the default value) means split according to any whitespace, and discard empty strings from the result.

maxsplit

Maximum number of splits to do. -1 (the default value) means no limit.

Splits are done starting at the end of the string and working to the front.

rstrip(chars=None, /)

Return a copy of the string with trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

split(sep=None, maxsplit=-1)

Return a list of the words in the string, using sep as the delimiter string.

sep

The delimiter according which to split the string. None (the default value) means split according to any whitespace, and discard empty strings from the result.

maxsplit

Maximum number of splits to do. -1 (the default value) means no limit.

splitlines(keepends=False)

Return a list of the lines in the string, breaking at line boundaries.

Line breaks are not included in the resulting list unless keepends is given and true.

startswith(prefix[, start[, end]]) bool

Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.

strip(chars=None, /)

Return a copy of the string with leading and trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

swapcase()

Convert uppercase characters to lowercase and lowercase characters to uppercase.

title()

Return a version of the string where each word is titlecased.

More specifically, words start with uppercased characters and all remaining cased characters have lower case.

translate(table, /)

Replace each character in the string using the given translation table.

table

Translation table, which must be a mapping of Unicode ordinals to Unicode ordinals, strings, or None.

The table must implement lookup/indexing via __getitem__, for instance a dictionary or list. If this operation raises LookupError, the character is left untouched. Characters mapped to None are deleted.

upper()

Return a copy of the string converted to uppercase.

zfill(width, /)

Pad a numeric string with zeros on the left, to fill a field of the given width.

The string is never truncated.

CENTERED_DIFFERENCES = 'centered_differences'
COMPLEX_STEP = 'complex_step'
FINITE_DIFFERENCES = 'finite_differences'
NO_DERIVATIVE = 'no_derivative'
class ProblemType(value)

Bases: StrEnum

The type of problem.

capitalize()

Return a capitalized version of the string.

More specifically, make the first character have upper case and the rest lower case.

casefold()

Return a version of the string suitable for caseless comparisons.

center(width, fillchar=' ', /)

Return a centered string of length width.

Padding is done using the specified fill character (default is a space).

count(sub[, start[, end]]) int

Return the number of non-overlapping occurrences of substring sub in string S[start:end]. Optional arguments start and end are interpreted as in slice notation.

encode(encoding='utf-8', errors='strict')

Encode the string using the codec registered for encoding.

encoding

The encoding in which to encode the string.

errors

The error handling scheme to use for encoding errors. The default is ‘strict’ meaning that encoding errors raise a UnicodeEncodeError. Other possible values are ‘ignore’, ‘replace’ and ‘xmlcharrefreplace’ as well as any other name registered with codecs.register_error that can handle UnicodeEncodeErrors.

endswith(suffix[, start[, end]]) bool

Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.

expandtabs(tabsize=8)

Return a copy where all tab characters are expanded using spaces.

If tabsize is not given, a tab size of 8 characters is assumed.

find(sub[, start[, end]]) int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

format(*args, **kwargs) str

Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces (‘{’ and ‘}’).

format_map(mapping) str

Return a formatted version of S, using substitutions from mapping. The substitutions are identified by braces (‘{’ and ‘}’).

index(sub[, start[, end]]) int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

isalnum()

Return True if the string is an alpha-numeric string, False otherwise.

A string is alpha-numeric if all characters in the string are alpha-numeric and there is at least one character in the string.

isalpha()

Return True if the string is an alphabetic string, False otherwise.

A string is alphabetic if all characters in the string are alphabetic and there is at least one character in the string.

isascii()

Return True if all characters in the string are ASCII, False otherwise.

ASCII characters have code points in the range U+0000-U+007F. Empty string is ASCII too.

isdecimal()

Return True if the string is a decimal string, False otherwise.

A string is a decimal string if all characters in the string are decimal and there is at least one character in the string.

isdigit()

Return True if the string is a digit string, False otherwise.

A string is a digit string if all characters in the string are digits and there is at least one character in the string.

isidentifier()

Return True if the string is a valid Python identifier, False otherwise.

Call keyword.iskeyword(s) to test whether string s is a reserved identifier, such as “def” or “class”.

islower()

Return True if the string is a lowercase string, False otherwise.

A string is lowercase if all cased characters in the string are lowercase and there is at least one cased character in the string.

isnumeric()

Return True if the string is a numeric string, False otherwise.

A string is numeric if all characters in the string are numeric and there is at least one character in the string.

isprintable()

Return True if the string is printable, False otherwise.

A string is printable if all of its characters are considered printable in repr() or if it is empty.

isspace()

Return True if the string is a whitespace string, False otherwise.

A string is whitespace if all characters in the string are whitespace and there is at least one character in the string.

istitle()

Return True if the string is a title-cased string, False otherwise.

In a title-cased string, upper- and title-case characters may only follow uncased characters and lowercase characters only cased ones.

isupper()

Return True if the string is an uppercase string, False otherwise.

A string is uppercase if all cased characters in the string are uppercase and there is at least one cased character in the string.

join(iterable, /)

Concatenate any number of strings.

The string whose method is called is inserted in between each given string. The result is returned as a new string.

Example: ‘.’.join([‘ab’, ‘pq’, ‘rs’]) -> ‘ab.pq.rs’

ljust(width, fillchar=' ', /)

Return a left-justified string of length width.

Padding is done using the specified fill character (default is a space).

lower()

Return a copy of the string converted to lowercase.

lstrip(chars=None, /)

Return a copy of the string with leading whitespace removed.

If chars is given and not None, remove characters in chars instead.

static maketrans()

Return a translation table usable for str.translate().

If there is only one argument, it must be a dictionary mapping Unicode ordinals (integers) or characters to Unicode ordinals, strings or None. Character keys will be then converted to ordinals. If there are two arguments, they must be strings of equal length, and in the resulting dictionary, each character in x will be mapped to the character at the same position in y. If there is a third argument, it must be a string, whose characters will be mapped to None in the result.

partition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing the original string and two empty strings.

removeprefix(prefix, /)

Return a str with the given prefix string removed if present.

If the string starts with the prefix string, return string[len(prefix):]. Otherwise, return a copy of the original string.

removesuffix(suffix, /)

Return a str with the given suffix string removed if present.

If the string ends with the suffix string and that suffix is not empty, return string[:-len(suffix)]. Otherwise, return a copy of the original string.

replace(old, new, count=-1, /)

Return a copy with all occurrences of substring old replaced by new.

count

Maximum number of occurrences to replace. -1 (the default value) means replace all occurrences.

If the optional argument count is given, only the first count occurrences are replaced.

rfind(sub[, start[, end]]) int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

rindex(sub[, start[, end]]) int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

rjust(width, fillchar=' ', /)

Return a right-justified string of length width.

Padding is done using the specified fill character (default is a space).

rpartition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string, starting at the end. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing two empty strings and the original string.

rsplit(sep=None, maxsplit=-1)

Return a list of the words in the string, using sep as the delimiter string.

sep

The delimiter according which to split the string. None (the default value) means split according to any whitespace, and discard empty strings from the result.

maxsplit

Maximum number of splits to do. -1 (the default value) means no limit.

Splits are done starting at the end of the string and working to the front.

rstrip(chars=None, /)

Return a copy of the string with trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

split(sep=None, maxsplit=-1)

Return a list of the words in the string, using sep as the delimiter string.

sep

The delimiter according which to split the string. None (the default value) means split according to any whitespace, and discard empty strings from the result.

maxsplit

Maximum number of splits to do. -1 (the default value) means no limit.

splitlines(keepends=False)

Return a list of the lines in the string, breaking at line boundaries.

Line breaks are not included in the resulting list unless keepends is given and true.

startswith(prefix[, start[, end]]) bool

Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.

strip(chars=None, /)

Return a copy of the string with leading and trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

swapcase()

Convert uppercase characters to lowercase and lowercase characters to uppercase.

title()

Return a version of the string where each word is titlecased.

More specifically, words start with uppercased characters and all remaining cased characters have lower case.

translate(table, /)

Replace each character in the string using the given translation table.

table

Translation table, which must be a mapping of Unicode ordinals to Unicode ordinals, strings, or None.

The table must implement lookup/indexing via __getitem__, for instance a dictionary or list. If this operation raises LookupError, the character is left untouched. Characters mapped to None are deleted.

upper()

Return a copy of the string converted to uppercase.

zfill(width, /)

Pad a numeric string with zeros on the left, to fill a field of the given width.

The string is never truncated.

LINEAR = 'linear'
NON_LINEAR = 'non-linear'

Add a callback for some events.

The callback functions are attached to the database, which means they are triggered when new values are stored within the database of the optimization problem.

Parameters:
• callback (Callable[[ndarray], Any]) – A function to be called after some events, whose argument is a design vector.

• each_new_iter (bool) –

Whether to evaluate the callback functions after evaluating all functions of the optimization problem for a given point and storing their values in the database.

By default it is set to True.

• each_store (bool) –

Whether to evaluate the callback functions after storing any new value in the database.

By default it is set to False.

Return type:

None

Add an equality or inequality constraint to the optimization problem.

An equality constraint is written as $$c(x)=a$$, a positive inequality constraint is written as $$c(x)\geq a$$ and a negative inequality constraint is written as $$c(x)\leq a$$.

Parameters:
• function (MDOFunction) – The function $$c$$.

• value (float) –

The value $$a$$.

By default it is set to 0.0.

• constraint_type (MDOFunction.ConstraintType | None) – The type of the constraint.

• positive (bool) –

Whether the inequality constraint is positive.

By default it is set to False.

Raises:
Return type:

None

Add an equality constraint $$c(x)=a$$ to the optimization problem.

Parameters:
• function (MDOFunction) – The function $$c$$.

• value (float) –

The value $$a$$.

By default it is set to 0.

Return type:

None

Add an inequality constraint to the optimization problem.

A positive inequality constraint is written as $$c(x)\geq a$$ and a negative inequality constraint is written as $$c(x)\leq a$$

Parameters:
• function (MDOFunction) – The function $$c$$.

• value (float) –

The value $$a$$ for which the constraint is active.

By default it is set to 0.

• positive (bool) –

Whether the inequality constraint is positive.

By default it is set to False.

Return type:

None

Add a function to be observed.

When the OptimizationProblem is executed, the observables are called following this sequence:

Parameters:
• observable (MDOFunction) – A function to be observed.

• new_iter (bool) –

If True, then the observable will be called at each new iterate.

By default it is set to True.

Return type:

None

aggregate_constraint(constraint_index, method=EvaluationFunction.MAX, groups=None, **options)

Aggregate a constraint to generate a reduced dimension constraint.

Parameters:
• constraint_index (int) – The index of the constraint in constraints.

• method (Callable[[NDArray[float]], float] | AggregationFunction) –

The aggregation method, e.g. "max", "lower_bound_KS", "upper_bound_KS"or "IKS".

By default it is set to “MAX”.

• groups (Iterable[Sequence[int]] | None) – The groups of components of the constraint to aggregate to produce one aggregation constraint per group of components; if None, a single aggregation constraint is produced.

• **options (Any) – The options of the aggregation method.

Raises:

ValueError – When the given index is greater or equal than the number of constraints or when the constraint aggregation method is unknown.

Return type:

None

apply_exterior_penalty(objective_scale=1.0, scale_inequality=1.0, scale_equality=1.0)

Reformulate the optimization problem using exterior penalty.

Given the optimization problem with equality and inequality constraints:

\begin{align}\begin{aligned}min_x f(x)\\s.t.\\g(x)\leq 0\\h(x)=0\\l_b\leq x\leq u_b\end{aligned}\end{align}

The exterior penalty approach consists in building a penalized objective function that takes into account constraints violations:

\begin{align}\begin{aligned}min_x \tilde{f}(x) = \frac{f(x)}{o_s} + s[\sum{H(g(x))g(x)^2}+\sum{h(x)^2}]\\s.t.\\l_b\leq x\leq u_b\end{aligned}\end{align}

Where $$H(x)$$ is the Heaviside function, $$o_s$$ is the objective_scale parameter and $$s$$ is the scale parameter. The solution of the new problem approximate the one of the original problem. Increasing the values of objective_scale and scale, the solutions are closer but the optimization problem requires more and more iterations to be solved.

Parameters:
• scale_equality (float | ndarray) –

The equality constraint scaling constant.

By default it is set to 1.0.

• objective_scale (float) –

The objective scaling constant.

By default it is set to 1.0.

• scale_inequality (float | ndarray) –

The inequality constraint scaling constant.

By default it is set to 1.0.

Return type:

None

check()

Check if the optimization problem is ready for run.

Raises:

ValueError – If the objective function is missing.

Return type:

None

check_design_point_is_feasible(x_vect)

Check if a design point is feasible and measure its constraint violation.

The constraint violation measure at a design point $$x$$ is

$\lVert\max(g(x)-\varepsilon_{\text{ineq}},0)\rVert_2^2 +\lVert|\max(|h(x)|-\varepsilon_{\text{eq}},0)\rVert_2^2$

where $$\|.\|_2$$ is the Euclidean norm, $$g(x)$$ is the inequality constraint vector, $$h(x)$$ is the equality constraint vector, $$\varepsilon_{\text{ineq}}$$ is the tolerance for the inequality constraints and $$\varepsilon_{\text{eq}}$$ is the tolerance for the equality constraints.

If the design point is feasible, the constraint violation measure is 0.

Parameters:

x_vect (ndarray) – The design point $$x$$.

Returns:

Whether the design point is feasible, and its constraint violation measure.

Return type:
static check_format(function)

Check that a function is an instance of MDOFunction.

Parameters:

function (Any) – The function to be tested.

Raises:

TypeError – If the function is not an MDOFunction.

Return type:

None

clear_listeners()

Clear all the listeners.

Return type:

None

static compute_knapsack_items(design_variables)[source]

Compute the knapsack number of items.

Parameters:

design_variables (ndarray) – The design variables vector.

Returns:

The knapsack total number of items.

Return type:

ndarray

compute_knapsack_value(design_variables)[source]

Compute the knapsack total value.

Parameters:

design_variables (ndarray) – The design variables vector.

Returns:

The knapsack total value.

Return type:

ndarray

compute_knapsack_weight(design_variables)[source]

Compute the knapsack total weight.

Parameters:

design_variables (ndarray) – The design variables vector.

Returns:

The knapsack total weight.

Return type:

ndarray

evaluate_functions(x_vect=None, eval_jac=False, eval_obj=True, eval_observables=True, normalize=True, no_db_no_norm=False, constraint_names=None, observable_names=None, jacobian_names=None)

Compute the functions of interest, and possibly their derivatives.

These functions of interest are the constraints, and possibly the objective.

Some optimization libraries require the number of constraints as an input parameter which is unknown by the formulation or the scenario. Evaluation of initial point allows to get this mandatory information. This is also used for design of experiments to evaluate samples.

Parameters:
• x_vect (ndarray) – The input vector at which the functions must be evaluated; if None, the initial point x_0 is used.

• eval_jac (bool) –

Whether to compute the Jacobian matrices of the functions of interest. If True and jacobian_names is None then compute the Jacobian matrices (or gradients) of the functions that are selected for evaluation (with eval_obj, constraint_names, eval_observables andobservable_names). If False and jacobian_names is None then no Jacobian matrix is evaluated. If jacobian_names is not None then the value of eval_jac is ignored.

By default it is set to False.

• eval_obj (bool) –

Whether to consider the objective function as a function of interest.

By default it is set to True.

• eval_observables (bool) –

Whether to evaluate the observables. If True and observable_names is None then all the observables are evaluated. If False and observable_names is None then no observable is evaluated. If observable_names is not None then the value of eval_observables is ignored.

By default it is set to True.

• normalize (bool) –

Whether to consider the input vector x_vect normalized.

By default it is set to True.

• no_db_no_norm (bool) –

If True, then do not use the pre-processed functions, so we have no database, nor normalization.

By default it is set to False.

• constraint_names (Iterable[str] | None) – The names of the constraints to evaluate. If None then all the constraints are evaluated.

• observable_names (Iterable[str] | None) – The names of the observables to evaluate. If None and eval_observables is True then all the observables are evaluated. If None and eval_observables is False then no observable is evaluated.

• jacobian_names (Iterable[str] | None) – The names of the functions whose Jacobian matrices (or gradients) to compute. If None and eval_jac is True then compute the Jacobian matrices (or gradients) of the functions that are selected for evaluation (with eval_obj, constraint_names, eval_observables andobservable_names). If None and eval_jac is False then no Jacobian matrix is computed.

Returns:

The output values of the functions of interest, as well as their Jacobian matrices if eval_jac is True.

Raises:

ValueError – If a name in jacobian_names is not the name of a function of the problem.

Return type:

EvaluationType

execute_observables_callback(last_x)

The callback function to be passed to the database.

Call all the observables with the last design variables values as argument.

Parameters:

last_x (ndarray) – The design variables values from the last evaluation.

Return type:

None

classmethod from_hdf(file_path, x_tolerance=0.0, hdf_node_path='')

Import an optimization history from an HDF file.

Parameters:
• file_path (str | Path) – The file containing the optimization history.

• x_tolerance (float) –

The tolerance on the design variables when reading the file.

By default it is set to 0.0.

• hdf_node_path (str) –

The path of the HDF node from which the database should be imported. If empty, the root node is considered.

By default it is set to “”.

Returns:

Return type:

OptimizationProblem

get_active_ineq_constraints(x_vect, tol=1e-06)

For each constraint, indicate if its different components are active.

Parameters:
• x_vect (ndarray) – The vector of design variables.

• tol (float) –

The tolerance for deciding whether a constraint is active.

By default it is set to 1e-06.

Returns:

For each constraint, a boolean indicator of activation of its different components.

Return type:
get_all_function_name()

Retrieve the names of all the function of the optimization problem.

These functions are the constraints, the objective function and the observables.

Returns:

The names of all the functions of the optimization problem.

Return type:

list[str]

get_all_functions(original=False)

Retrieve all the functions of the optimization problem.

These functions are the constraints, the objective function and the observables.

Parameters:

original (bool) –

Whether to return the original functions or the preprocessed ones.

By default it is set to False.

Returns:

All the functions of the optimization problem.

Return type:
get_best_infeasible_point()

Retrieve the best infeasible point within a given tolerance.

Returns:

The best infeasible point expressed as the design variables values, the objective function value, the feasibility of the point and the functions values.

Return type:

tuple[ndarray | None, ndarray | None, bool, dict[str, ndarray]]

get_constraint_names()

Retrieve the names of the constraints.

Returns:

The names of the constraints.

Return type:

list[str]

get_constraints_number()

Retrieve the number of constraints.

Returns:

The number of constraints.

Return type:

int

get_data_by_names(names, as_dict=True, filter_non_feasible=False)

Return the data for specific names of variables.

Parameters:
• names (str | Iterable[str]) – The names of the variables.

• as_dict (bool) –

If True, return values as dictionary.

By default it is set to True.

• filter_non_feasible (bool) –

If True, remove the non-feasible points from the data.

By default it is set to False.

Returns:

The data related to the variables.

Return type:

ndarray | dict[str, ndarray]

get_design_variable_names()

Retrieve the names of the design variables.

Returns:

The names of the design variables.

Return type:

list[str]

get_dimension()

Retrieve the total number of design variables.

Returns:

The dimension of the design space.

Return type:

int

get_eq_constraints()

Retrieve all the equality constraints.

Returns:

The equality constraints.

Return type:
get_eq_constraints_number()

Retrieve the number of equality constraints.

Returns:

The number of equality constraints.

Return type:

int

get_eq_cstr_total_dim()

Retrieve the total dimension of the equality constraints.

This dimension is the sum of all the outputs dimensions of all the equality constraints.

Returns:

The total dimension of the equality constraints.

Return type:

int

get_feasible_points()

Retrieve the feasible points within a given tolerance.

This tolerance is defined by OptimizationProblem.eq_tolerance for equality constraints and OptimizationProblem.ineq_tolerance for inequality ones.

Returns:

The values of the design variables and objective function for the feasible points.

Return type:

tuple[list[RealOrComplexArray], list[dict[str, float | list[int]]]]

get_function_dimension(name)

Return the dimension of a function of the problem (e.g. a constraint).

Parameters:

name (str) – The name of the function.

Returns:

The dimension of the function.

Raises:
• ValueError – If the function name is unknown to the problem.

• RuntimeError – If the function dimension is not unavailable.

Return type:

int

get_function_names(names)

Return the names of the functions stored in the database.

Parameters:

names (Iterable[str]) – The names of the outputs or constraints specified by the user.

Returns:

The names of the constraints stored in the database.

Return type:

list[str]

get_functions_dimensions(names=None)

Return the dimensions of the outputs of the problem functions.

Parameters:

names (Iterable[str] | None) – The names of the functions. If None, then the objective and all the constraints are considered.

Returns:

The dimensions of the outputs of the problem functions. The dictionary keys are the functions names and the values are the functions dimensions.

Return type:

dict[str, int]

get_ineq_constraints()

Retrieve all the inequality constraints.

Returns:

The inequality constraints.

Return type:
get_ineq_constraints_number()

Retrieve the number of inequality constraints.

Returns:

The number of inequality constraints.

Return type:

int

get_ineq_cstr_total_dim()

Retrieve the total dimension of the inequality constraints.

This dimension is the sum of all the outputs dimensions of all the inequality constraints.

Returns:

The total dimension of the inequality constraints.

Return type:

int

get_last_point()

Return the last design point.

Returns:

The last point result, defined by:

• the value of the objective function,

• the value of the design variables,

• the indicator of feasibility of the last point,

• the value of the constraints,

• the value of the gradients of the constraints.

Raises:

ValueError – When the optimization database is empty.

Return type:
get_nonproc_constraints()

Retrieve the non-processed constraints.

Returns:

The non-processed constraints.

Return type:
get_nonproc_objective()

Retrieve the non-processed objective function.

Return type:

MDOFunction

get_number_of_unsatisfied_constraints(design_variables, values=mappingproxy({}))

Return the number of scalar constraints not satisfied by design variables.

Parameters:
• design_variables (ndarray) – The design variables.

• values (Mapping[str, float | ndarray]) –

The values of the constraints. N.B. the missing values will be read from the database or computed.

By default it is set to {}.

Returns:

The number of unsatisfied scalar constraints.

Return type:

int

get_objective_name(standardize=True)

Retrieve the name of the objective function.

Parameters:

standardize (bool) –

Whether to use the name of the objective expressed as a cost, e.g. "-f" when the user seeks to maximize "f".

By default it is set to True.

Returns:

The name of the objective function.

Return type:

str

get_observable(name)

Return an observable of the problem.

Parameters:

name (str) – The name of the observable.

Returns:

The pre-processed observable if the functions of the problem have already been pre-processed, otherwise the original one.

Return type:

MDOFunction

get_optimum()

Return the optimum solution within a given feasibility tolerances.

Returns:

The optimum result, defined by:

• the value of the objective function,

• the value of the design variables,

• the indicator of feasibility of the optimal solution,

• the value of the constraints,

• the value of the gradients of the constraints.

Raises:

ValueError – When the optimization database is empty.

Return type:
get_reformulated_problem_with_slack_variables()

Add slack variables and replace inequality constraints with equality ones.

Given the original optimization problem,

\begin{align}\begin{aligned}min_x f(x)\\s.t.\\g(x)\leq 0\\h(x)=0\\l_b\leq x\leq u_b\end{aligned}\end{align}

Slack variables are introduced for all inequality constraints that are non-positive. An equality constraint for each slack variable is then defined.

\begin{align}\begin{aligned}min_{x,s} F(x,s) = f(x)\\s.t.\\H(x,s) = h(x)=0\\G(x,s) = g(x)-s=0\\l_b\leq x\leq u_b\\s\leq 0\end{aligned}\end{align}
Returns:

An optimization problem without inequality constraints.

Return type:

OptimizationProblem

get_scalar_constraint_names()

Return the names of the scalar constraints.

Returns:

The names of the scalar constraints.

Return type:

list[str]

get_x0_normalized(cast_to_real=False, as_dict=False)

Return the initial values of the design variables after normalization.

Parameters:
• cast_to_real (bool) –

Whether to return the real part of the initial values.

By default it is set to False.

• as_dict (bool) –

Whether to return the values as a dictionary of the form {variable_name: variable_value}.

By default it is set to False.

Returns:

The current values of the design variables normalized between 0 and 1 from their lower and upper bounds.

Return type:

ndarray | dict[str, ndarray]

has_constraints()

Check if the problem has equality or inequality constraints.

Returns:

True if the problem has equality or inequality constraints.

Return type:

bool

has_eq_constraints()

Check if the problem has equality constraints.

Returns:

True if the problem has equality constraints.

Return type:

bool

has_ineq_constraints()

Check if the problem has inequality constraints.

Returns:

True if the problem has inequality constraints.

Return type:

bool

has_nonlinear_constraints()

Check if the problem has non-linear constraints.

Returns:

True if the problem has equality or inequality constraints.

Return type:

bool

is_max_iter_reached()

Check if the maximum amount of iterations has been reached.

Returns:

Whether the maximum amount of iterations has been reached.

Return type:

bool

is_point_feasible(out_val, constraints=None)

Check if a point is feasible.

Notes

If the value of a constraint is absent from this point, then this constraint will be considered satisfied.

Parameters:
• out_val (Mapping[str, RealOrComplexArray]) – The values of the objective function, and eventually constraints.

• constraints (Iterable[MDOFunction] | None) – The constraints whose values are to be tested. If None, then take all constraints of the problem.

Returns:

The feasibility of the point.

Return type:

bool

preprocess_functions(is_function_input_normalized=True, use_database=True, round_ints=True, eval_obs_jac=False, support_sparse_jacobian=False)

Pre-process all the functions and eventually the gradient.

Required to wrap the objective function and constraints with the database and eventually the gradients by complex step or finite differences.

Parameters:
• is_function_input_normalized (bool) –

Whether to consider the function input as normalized and unnormalize it before the evaluation takes place.

By default it is set to True.

• use_database (bool) –

Whether to wrap the functions in the database.

By default it is set to True.

• round_ints (bool) –

Whether to round the integer variables.

By default it is set to True.

• eval_obs_jac (bool) –

Whether to evaluate the Jacobian of the observables.

By default it is set to False.

• support_sparse_jacobian (bool) –

Whether the driver support sparse Jacobian.

By default it is set to False.

Return type:

None

static repr_constraint(function, constraint_type, value=None, positive=False)

Express a constraint as a string expression.

Parameters:
• function (MDOFunction) – The constraint function.

• constraint_type (MDOFunction.ConstraintType) – The type of the constraint.

• value (float | None) – The value for which the constraint is active. If None, this value is 0.

• positive (bool) –

If True, then the inequality constraint is positive.

By default it is set to False.

Returns:

A string representation of the constraint.

Return type:

str

reset(database=True, current_iter=True, design_space=True, function_calls=True, preprocessing=True)

Partially or fully reset the optimization problem.

Parameters:
• database (bool) –

Whether to clear the database.

By default it is set to True.

• current_iter (bool) –

Whether to reset the current iteration OptimizationProblem.current_iter.

By default it is set to True.

• design_space (bool) –

Whether to reset the current point of the OptimizationProblem.design_space to its initial value (possibly none).

By default it is set to True.

• function_calls (bool) –

Whether to reset the number of calls of the functions.

By default it is set to True.

• preprocessing (bool) –

Whether to turn the pre-processing of functions to False.

By default it is set to True.

Return type:

None

Export the database of the optimization problem to a Dataset.

The variables can be classified into groups: Dataset.DESIGN_GROUP or Dataset.INPUT_GROUP for the design variables and Dataset.FUNCTION_GROUP or Dataset.OUTPUT_GROUP for the functions (objective, constraints and observables).

Parameters:
• name (str) –

The name to be given to the dataset. If empty, use the name of the OptimizationProblem.database.

By default it is set to “”.

• categorize (bool) –

Whether to distinguish between the different groups of variables. Otherwise, group all the variables in Dataset.PARAMETER_GROUP.

By default it is set to True.

• opt_naming (bool) –

Whether to use Dataset.DESIGN_GROUP and Dataset.FUNCTION_GROUP as groups. Otherwise, use Dataset.INPUT_GROUP and Dataset.OUTPUT_GROUP.

By default it is set to True.

Whether to export the gradients of the functions (objective function, constraints and observables) if the latter are available in the database of the optimization problem.

By default it is set to False.

• input_values (Iterable[ndarray]) –

The input values to be considered. If empty, consider all the input values of the database.

By default it is set to ().

Returns:

A dataset built from the database of the optimization problem.

Return type:

Dataset

to_hdf(file_path, append=False, hdf_node_path='')

Export the optimization problem to an HDF file.

Parameters:
• file_path (str | Path) – The path of the file to store the data.

• append (bool) –

If True, then the data are appended to the file if not empty.

By default it is set to False.

• hdf_node_path (str) –

The path of the HDF node in which the database should be exported. If empty, the root node is considered.

By default it is set to “”.

Return type:

None

CONSTRAINTS_GROUP: Final[str] = 'constraints'
DESIGN_SPACE_ATTRS: Final[str] = ['u_bounds', 'l_bounds', 'x_0', 'x_names', 'dimension']
DESIGN_SPACE_GROUP: Final[str] = 'design_space'
DESIGN_VAR_NAMES: Final[str] = 'x_names'
DESIGN_VAR_SIZE: Final[str] = 'x_size'
FUNCTIONS_ATTRS: ClassVar[str] = ['objective', 'constraints']
GGOBI_FORMAT: Final[str] = 'ggobi'
HDF5_FORMAT: Final[str] = 'hdf5'
HDF_NODE_PATH: Final[str] = 'hdf_node_path'
KKT_RESIDUAL_NORM: Final[str] = 'KKT residual norm'
OBJECTIVE_GROUP: Final[str] = 'objective'
OBSERVABLES_GROUP: Final[str] = 'observables'
OPTIM_DESCRIPTION: ClassVar[str] = ['minimize_objective', 'fd_step', 'differentiation_method', 'pb_type', 'ineq_tolerance', 'eq_tolerance']
OPT_DESCR_GROUP: Final[str] = 'opt_description'
SOLUTION_GROUP: Final[str] = 'solution'
activate_bound_check: ClassVar[bool] = True

Whether to check if a point is in the design space before calling functions.

capacity_items: int

The knapsack number of items capacity.

capacity_weight: float

The knapsack weight capacity.

property constraint_names: dict[str, list[str]]

The standardized constraint names bound to the original ones.

constraints: list[MDOFunction]

The constraints.

current_iter: int

The current iteration.

database: Database

The database to store the optimization problem data.

design_space: DesignSpace

The design space on which the optimization problem is solved.

property dimension: int

The dimension of the design space.

eq_tolerance: float

The tolerance for the equality constraints.

fd_step: float

The finite differences step.

ineq_tolerance: float

The tolerance for the inequality constraints.

property is_mono_objective: bool

Whether the optimization problem is mono-objective.

Raises:

ValueError – When the dimension of the objective cannot be determined.

max_iter: int

The maximum iteration.

property minimize_objective: bool

Whether to minimize the objective.

new_iter_observables: list[MDOFunction]

The observables to be called at each new iterate.

nonproc_constraints: list[MDOFunction]

The non-processed constraints.

nonproc_new_iter_observables: list[MDOFunction]

The non-processed observables to be called at each new iterate.

nonproc_objective: MDOFunction

The non-processed objective function.

nonproc_observables: list[MDOFunction]

The non-processed observables.

property objective: MDOFunction

The objective function.

observables: list[MDOFunction]

The observables.

property parallel_differentiation: bool

Whether to approximate the derivatives in parallel.

property parallel_differentiation_options: dict[str, int | bool]

The options to approximate the derivatives in parallel.

pb_type: ProblemType

The type of optimization problem.

preprocess_options: dict

The options to pre-process the functions.

solution: OptimizationResult | None

The solution of the optimization problem if solved; otherwise None.

stop_if_nan: bool

Whether the optimization stops when a function returns NaN.

use_standardized_objective: bool

Whether to use standardized objective for logging and post-processing.

The standardized objective corresponds to the original one expressed as a cost function to minimize. A DriverLibrary works with this standardized objective and the Database stores its values. However, for convenience, it may be more relevant to log the expression and the values of the original objective.

values: ndarray

The knapsack items’ value.

weights: ndarray

The knapsack items’ weight.

class gemseo_pymoo.problems.analytical.knapsack.MultiObjectiveKnapsack(values, weights, items_ub=None, binary=True, capacity_weight=None, capacity_items=None, initial_guess=None)[source]

Bases: Knapsack

Multi-objective Knapsack optimization problem.

With respect to the single-objective Knapsack, it adds an objective relative to the number of items packed. Therefore, besides maximizing the total knapsack value, one must also minimize the total number of items.

All the variations of the Knapsack problem can still be achieved.

The constructor.

Initialize the MultiObjectiveKnapsack OptimizationProblem by defining the DesignSpace and the objective and constraint functions.

The number of items in the problem is deduced from the values array.

Parameters:
• values (ndarray) – The items’ values.

• weights (ndarray) – The items’ weights.

• items_ub (ndarray | None) – The items’ upper bounds. If None, an unlimited number of each item is allowed.

• binary (bool) –

If True, the upper bound of design variables is set to 1.

By default it is set to True.

• capacity_weight (float | None) – The knapsack weight capacity. If None, the knapsack will have an unlimited weight capacity.

• capacity_items (int | None) – The knapsack number of items capacity. If None, the knapsack will accept an unlimited total number of items.

• initial_guess (ndarray | None) – The initial guess for the optimal solution. If None, the initial guess will be an empty knapsack (0, 0, …, 0).

AggregationFunction

alias of EvaluationFunction

class ApproximationMode(value)

Bases: StrEnum

The approximation derivation modes.

capitalize()

Return a capitalized version of the string.

More specifically, make the first character have upper case and the rest lower case.

casefold()

Return a version of the string suitable for caseless comparisons.

center(width, fillchar=' ', /)

Return a centered string of length width.

Padding is done using the specified fill character (default is a space).

count(sub[, start[, end]]) int

Return the number of non-overlapping occurrences of substring sub in string S[start:end]. Optional arguments start and end are interpreted as in slice notation.

encode(encoding='utf-8', errors='strict')

Encode the string using the codec registered for encoding.

encoding

The encoding in which to encode the string.

errors

The error handling scheme to use for encoding errors. The default is ‘strict’ meaning that encoding errors raise a UnicodeEncodeError. Other possible values are ‘ignore’, ‘replace’ and ‘xmlcharrefreplace’ as well as any other name registered with codecs.register_error that can handle UnicodeEncodeErrors.

endswith(suffix[, start[, end]]) bool

Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.

expandtabs(tabsize=8)

Return a copy where all tab characters are expanded using spaces.

If tabsize is not given, a tab size of 8 characters is assumed.

find(sub[, start[, end]]) int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

format(*args, **kwargs) str

Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces (‘{’ and ‘}’).

format_map(mapping) str

Return a formatted version of S, using substitutions from mapping. The substitutions are identified by braces (‘{’ and ‘}’).

index(sub[, start[, end]]) int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

isalnum()

Return True if the string is an alpha-numeric string, False otherwise.

A string is alpha-numeric if all characters in the string are alpha-numeric and there is at least one character in the string.

isalpha()

Return True if the string is an alphabetic string, False otherwise.

A string is alphabetic if all characters in the string are alphabetic and there is at least one character in the string.

isascii()

Return True if all characters in the string are ASCII, False otherwise.

ASCII characters have code points in the range U+0000-U+007F. Empty string is ASCII too.

isdecimal()

Return True if the string is a decimal string, False otherwise.

A string is a decimal string if all characters in the string are decimal and there is at least one character in the string.

isdigit()

Return True if the string is a digit string, False otherwise.

A string is a digit string if all characters in the string are digits and there is at least one character in the string.

isidentifier()

Return True if the string is a valid Python identifier, False otherwise.

Call keyword.iskeyword(s) to test whether string s is a reserved identifier, such as “def” or “class”.

islower()

Return True if the string is a lowercase string, False otherwise.

A string is lowercase if all cased characters in the string are lowercase and there is at least one cased character in the string.

isnumeric()

Return True if the string is a numeric string, False otherwise.

A string is numeric if all characters in the string are numeric and there is at least one character in the string.

isprintable()

Return True if the string is printable, False otherwise.

A string is printable if all of its characters are considered printable in repr() or if it is empty.

isspace()

Return True if the string is a whitespace string, False otherwise.

A string is whitespace if all characters in the string are whitespace and there is at least one character in the string.

istitle()

Return True if the string is a title-cased string, False otherwise.

In a title-cased string, upper- and title-case characters may only follow uncased characters and lowercase characters only cased ones.

isupper()

Return True if the string is an uppercase string, False otherwise.

A string is uppercase if all cased characters in the string are uppercase and there is at least one cased character in the string.

join(iterable, /)

Concatenate any number of strings.

The string whose method is called is inserted in between each given string. The result is returned as a new string.

Example: ‘.’.join([‘ab’, ‘pq’, ‘rs’]) -> ‘ab.pq.rs’

ljust(width, fillchar=' ', /)

Return a left-justified string of length width.

Padding is done using the specified fill character (default is a space).

lower()

Return a copy of the string converted to lowercase.

lstrip(chars=None, /)

Return a copy of the string with leading whitespace removed.

If chars is given and not None, remove characters in chars instead.

static maketrans()

Return a translation table usable for str.translate().

If there is only one argument, it must be a dictionary mapping Unicode ordinals (integers) or characters to Unicode ordinals, strings or None. Character keys will be then converted to ordinals. If there are two arguments, they must be strings of equal length, and in the resulting dictionary, each character in x will be mapped to the character at the same position in y. If there is a third argument, it must be a string, whose characters will be mapped to None in the result.

partition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing the original string and two empty strings.

removeprefix(prefix, /)

Return a str with the given prefix string removed if present.

If the string starts with the prefix string, return string[len(prefix):]. Otherwise, return a copy of the original string.

removesuffix(suffix, /)

Return a str with the given suffix string removed if present.

If the string ends with the suffix string and that suffix is not empty, return string[:-len(suffix)]. Otherwise, return a copy of the original string.

replace(old, new, count=-1, /)

Return a copy with all occurrences of substring old replaced by new.

count

Maximum number of occurrences to replace. -1 (the default value) means replace all occurrences.

If the optional argument count is given, only the first count occurrences are replaced.

rfind(sub[, start[, end]]) int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

rindex(sub[, start[, end]]) int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

rjust(width, fillchar=' ', /)

Return a right-justified string of length width.

Padding is done using the specified fill character (default is a space).

rpartition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string, starting at the end. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing two empty strings and the original string.

rsplit(sep=None, maxsplit=-1)

Return a list of the words in the string, using sep as the delimiter string.

sep

The delimiter according which to split the string. None (the default value) means split according to any whitespace, and discard empty strings from the result.

maxsplit

Maximum number of splits to do. -1 (the default value) means no limit.

Splits are done starting at the end of the string and working to the front.

rstrip(chars=None, /)

Return a copy of the string with trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

split(sep=None, maxsplit=-1)

Return a list of the words in the string, using sep as the delimiter string.

sep

The delimiter according which to split the string. None (the default value) means split according to any whitespace, and discard empty strings from the result.

maxsplit

Maximum number of splits to do. -1 (the default value) means no limit.

splitlines(keepends=False)

Return a list of the lines in the string, breaking at line boundaries.

Line breaks are not included in the resulting list unless keepends is given and true.

startswith(prefix[, start[, end]]) bool

Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.

strip(chars=None, /)

Return a copy of the string with leading and trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

swapcase()

Convert uppercase characters to lowercase and lowercase characters to uppercase.

title()

Return a version of the string where each word is titlecased.

More specifically, words start with uppercased characters and all remaining cased characters have lower case.

translate(table, /)

Replace each character in the string using the given translation table.

table

Translation table, which must be a mapping of Unicode ordinals to Unicode ordinals, strings, or None.

The table must implement lookup/indexing via __getitem__, for instance a dictionary or list. If this operation raises LookupError, the character is left untouched. Characters mapped to None are deleted.

upper()

Return a copy of the string converted to uppercase.

zfill(width, /)

Pad a numeric string with zeros on the left, to fill a field of the given width.

The string is never truncated.

CENTERED_DIFFERENCES = 'centered_differences'

The centered differences method used to approximate the Jacobians by perturbing each variable with a small real number.

COMPLEX_STEP = 'complex_step'

The complex step method used to approximate the Jacobians by perturbing each variable with a small complex number.

FINITE_DIFFERENCES = 'finite_differences'

The finite differences method used to approximate the Jacobians by perturbing each variable with a small real number.

class DifferentiationMethod(value)

Bases: StrEnum

The differentiation methods.

capitalize()

Return a capitalized version of the string.

More specifically, make the first character have upper case and the rest lower case.

casefold()

Return a version of the string suitable for caseless comparisons.

center(width, fillchar=' ', /)

Return a centered string of length width.

Padding is done using the specified fill character (default is a space).

count(sub[, start[, end]]) int

Return the number of non-overlapping occurrences of substring sub in string S[start:end]. Optional arguments start and end are interpreted as in slice notation.

encode(encoding='utf-8', errors='strict')

Encode the string using the codec registered for encoding.

encoding

The encoding in which to encode the string.

errors

The error handling scheme to use for encoding errors. The default is ‘strict’ meaning that encoding errors raise a UnicodeEncodeError. Other possible values are ‘ignore’, ‘replace’ and ‘xmlcharrefreplace’ as well as any other name registered with codecs.register_error that can handle UnicodeEncodeErrors.

endswith(suffix[, start[, end]]) bool

Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.

expandtabs(tabsize=8)

Return a copy where all tab characters are expanded using spaces.

If tabsize is not given, a tab size of 8 characters is assumed.

find(sub[, start[, end]]) int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

format(*args, **kwargs) str

Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces (‘{’ and ‘}’).

format_map(mapping) str

Return a formatted version of S, using substitutions from mapping. The substitutions are identified by braces (‘{’ and ‘}’).

index(sub[, start[, end]]) int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

isalnum()

Return True if the string is an alpha-numeric string, False otherwise.

A string is alpha-numeric if all characters in the string are alpha-numeric and there is at least one character in the string.

isalpha()

Return True if the string is an alphabetic string, False otherwise.

A string is alphabetic if all characters in the string are alphabetic and there is at least one character in the string.

isascii()

Return True if all characters in the string are ASCII, False otherwise.

ASCII characters have code points in the range U+0000-U+007F. Empty string is ASCII too.

isdecimal()

Return True if the string is a decimal string, False otherwise.

A string is a decimal string if all characters in the string are decimal and there is at least one character in the string.

isdigit()

Return True if the string is a digit string, False otherwise.

A string is a digit string if all characters in the string are digits and there is at least one character in the string.

isidentifier()

Return True if the string is a valid Python identifier, False otherwise.

Call keyword.iskeyword(s) to test whether string s is a reserved identifier, such as “def” or “class”.

islower()

Return True if the string is a lowercase string, False otherwise.

A string is lowercase if all cased characters in the string are lowercase and there is at least one cased character in the string.

isnumeric()

Return True if the string is a numeric string, False otherwise.

A string is numeric if all characters in the string are numeric and there is at least one character in the string.

isprintable()

Return True if the string is printable, False otherwise.

A string is printable if all of its characters are considered printable in repr() or if it is empty.

isspace()

Return True if the string is a whitespace string, False otherwise.

A string is whitespace if all characters in the string are whitespace and there is at least one character in the string.

istitle()

Return True if the string is a title-cased string, False otherwise.

In a title-cased string, upper- and title-case characters may only follow uncased characters and lowercase characters only cased ones.

isupper()

Return True if the string is an uppercase string, False otherwise.

A string is uppercase if all cased characters in the string are uppercase and there is at least one cased character in the string.

join(iterable, /)

Concatenate any number of strings.

The string whose method is called is inserted in between each given string. The result is returned as a new string.

Example: ‘.’.join([‘ab’, ‘pq’, ‘rs’]) -> ‘ab.pq.rs’

ljust(width, fillchar=' ', /)

Return a left-justified string of length width.

Padding is done using the specified fill character (default is a space).

lower()

Return a copy of the string converted to lowercase.

lstrip(chars=None, /)

Return a copy of the string with leading whitespace removed.

If chars is given and not None, remove characters in chars instead.

static maketrans()

Return a translation table usable for str.translate().

If there is only one argument, it must be a dictionary mapping Unicode ordinals (integers) or characters to Unicode ordinals, strings or None. Character keys will be then converted to ordinals. If there are two arguments, they must be strings of equal length, and in the resulting dictionary, each character in x will be mapped to the character at the same position in y. If there is a third argument, it must be a string, whose characters will be mapped to None in the result.

partition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing the original string and two empty strings.

removeprefix(prefix, /)

Return a str with the given prefix string removed if present.

If the string starts with the prefix string, return string[len(prefix):]. Otherwise, return a copy of the original string.

removesuffix(suffix, /)

Return a str with the given suffix string removed if present.

If the string ends with the suffix string and that suffix is not empty, return string[:-len(suffix)]. Otherwise, return a copy of the original string.

replace(old, new, count=-1, /)

Return a copy with all occurrences of substring old replaced by new.

count

Maximum number of occurrences to replace. -1 (the default value) means replace all occurrences.

If the optional argument count is given, only the first count occurrences are replaced.

rfind(sub[, start[, end]]) int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

rindex(sub[, start[, end]]) int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

rjust(width, fillchar=' ', /)

Return a right-justified string of length width.

Padding is done using the specified fill character (default is a space).

rpartition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string, starting at the end. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing two empty strings and the original string.

rsplit(sep=None, maxsplit=-1)

Return a list of the words in the string, using sep as the delimiter string.

sep

The delimiter according which to split the string. None (the default value) means split according to any whitespace, and discard empty strings from the result.

maxsplit

Maximum number of splits to do. -1 (the default value) means no limit.

Splits are done starting at the end of the string and working to the front.

rstrip(chars=None, /)

Return a copy of the string with trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

split(sep=None, maxsplit=-1)

Return a list of the words in the string, using sep as the delimiter string.

sep

The delimiter according which to split the string. None (the default value) means split according to any whitespace, and discard empty strings from the result.

maxsplit

Maximum number of splits to do. -1 (the default value) means no limit.

splitlines(keepends=False)

Return a list of the lines in the string, breaking at line boundaries.

Line breaks are not included in the resulting list unless keepends is given and true.

startswith(prefix[, start[, end]]) bool

Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.

strip(chars=None, /)

Return a copy of the string with leading and trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

swapcase()

Convert uppercase characters to lowercase and lowercase characters to uppercase.

title()

Return a version of the string where each word is titlecased.

More specifically, words start with uppercased characters and all remaining cased characters have lower case.

translate(table, /)

Replace each character in the string using the given translation table.

table

Translation table, which must be a mapping of Unicode ordinals to Unicode ordinals, strings, or None.

The table must implement lookup/indexing via __getitem__, for instance a dictionary or list. If this operation raises LookupError, the character is left untouched. Characters mapped to None are deleted.

upper()

Return a copy of the string converted to uppercase.

zfill(width, /)

Pad a numeric string with zeros on the left, to fill a field of the given width.

The string is never truncated.

CENTERED_DIFFERENCES = 'centered_differences'
COMPLEX_STEP = 'complex_step'
FINITE_DIFFERENCES = 'finite_differences'
NO_DERIVATIVE = 'no_derivative'
class ProblemType(value)

Bases: StrEnum

The type of problem.

capitalize()

Return a capitalized version of the string.

More specifically, make the first character have upper case and the rest lower case.

casefold()

Return a version of the string suitable for caseless comparisons.

center(width, fillchar=' ', /)

Return a centered string of length width.

Padding is done using the specified fill character (default is a space).

count(sub[, start[, end]]) int

Return the number of non-overlapping occurrences of substring sub in string S[start:end]. Optional arguments start and end are interpreted as in slice notation.

encode(encoding='utf-8', errors='strict')

Encode the string using the codec registered for encoding.

encoding

The encoding in which to encode the string.

errors

The error handling scheme to use for encoding errors. The default is ‘strict’ meaning that encoding errors raise a UnicodeEncodeError. Other possible values are ‘ignore’, ‘replace’ and ‘xmlcharrefreplace’ as well as any other name registered with codecs.register_error that can handle UnicodeEncodeErrors.

endswith(suffix[, start[, end]]) bool

Return True if S ends with the specified suffix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. suffix can also be a tuple of strings to try.

expandtabs(tabsize=8)

Return a copy where all tab characters are expanded using spaces.

If tabsize is not given, a tab size of 8 characters is assumed.

find(sub[, start[, end]]) int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

format(*args, **kwargs) str

Return a formatted version of S, using substitutions from args and kwargs. The substitutions are identified by braces (‘{’ and ‘}’).

format_map(mapping) str

Return a formatted version of S, using substitutions from mapping. The substitutions are identified by braces (‘{’ and ‘}’).

index(sub[, start[, end]]) int

Return the lowest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

isalnum()

Return True if the string is an alpha-numeric string, False otherwise.

A string is alpha-numeric if all characters in the string are alpha-numeric and there is at least one character in the string.

isalpha()

Return True if the string is an alphabetic string, False otherwise.

A string is alphabetic if all characters in the string are alphabetic and there is at least one character in the string.

isascii()

Return True if all characters in the string are ASCII, False otherwise.

ASCII characters have code points in the range U+0000-U+007F. Empty string is ASCII too.

isdecimal()

Return True if the string is a decimal string, False otherwise.

A string is a decimal string if all characters in the string are decimal and there is at least one character in the string.

isdigit()

Return True if the string is a digit string, False otherwise.

A string is a digit string if all characters in the string are digits and there is at least one character in the string.

isidentifier()

Return True if the string is a valid Python identifier, False otherwise.

Call keyword.iskeyword(s) to test whether string s is a reserved identifier, such as “def” or “class”.

islower()

Return True if the string is a lowercase string, False otherwise.

A string is lowercase if all cased characters in the string are lowercase and there is at least one cased character in the string.

isnumeric()

Return True if the string is a numeric string, False otherwise.

A string is numeric if all characters in the string are numeric and there is at least one character in the string.

isprintable()

Return True if the string is printable, False otherwise.

A string is printable if all of its characters are considered printable in repr() or if it is empty.

isspace()

Return True if the string is a whitespace string, False otherwise.

A string is whitespace if all characters in the string are whitespace and there is at least one character in the string.

istitle()

Return True if the string is a title-cased string, False otherwise.

In a title-cased string, upper- and title-case characters may only follow uncased characters and lowercase characters only cased ones.

isupper()

Return True if the string is an uppercase string, False otherwise.

A string is uppercase if all cased characters in the string are uppercase and there is at least one cased character in the string.

join(iterable, /)

Concatenate any number of strings.

The string whose method is called is inserted in between each given string. The result is returned as a new string.

Example: ‘.’.join([‘ab’, ‘pq’, ‘rs’]) -> ‘ab.pq.rs’

ljust(width, fillchar=' ', /)

Return a left-justified string of length width.

Padding is done using the specified fill character (default is a space).

lower()

Return a copy of the string converted to lowercase.

lstrip(chars=None, /)

Return a copy of the string with leading whitespace removed.

If chars is given and not None, remove characters in chars instead.

static maketrans()

Return a translation table usable for str.translate().

If there is only one argument, it must be a dictionary mapping Unicode ordinals (integers) or characters to Unicode ordinals, strings or None. Character keys will be then converted to ordinals. If there are two arguments, they must be strings of equal length, and in the resulting dictionary, each character in x will be mapped to the character at the same position in y. If there is a third argument, it must be a string, whose characters will be mapped to None in the result.

partition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing the original string and two empty strings.

removeprefix(prefix, /)

Return a str with the given prefix string removed if present.

If the string starts with the prefix string, return string[len(prefix):]. Otherwise, return a copy of the original string.

removesuffix(suffix, /)

Return a str with the given suffix string removed if present.

If the string ends with the suffix string and that suffix is not empty, return string[:-len(suffix)]. Otherwise, return a copy of the original string.

replace(old, new, count=-1, /)

Return a copy with all occurrences of substring old replaced by new.

count

Maximum number of occurrences to replace. -1 (the default value) means replace all occurrences.

If the optional argument count is given, only the first count occurrences are replaced.

rfind(sub[, start[, end]]) int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

Return -1 on failure.

rindex(sub[, start[, end]]) int

Return the highest index in S where substring sub is found, such that sub is contained within S[start:end]. Optional arguments start and end are interpreted as in slice notation.

rjust(width, fillchar=' ', /)

Return a right-justified string of length width.

Padding is done using the specified fill character (default is a space).

rpartition(sep, /)

Partition the string into three parts using the given separator.

This will search for the separator in the string, starting at the end. If the separator is found, returns a 3-tuple containing the part before the separator, the separator itself, and the part after it.

If the separator is not found, returns a 3-tuple containing two empty strings and the original string.

rsplit(sep=None, maxsplit=-1)

Return a list of the words in the string, using sep as the delimiter string.

sep

The delimiter according which to split the string. None (the default value) means split according to any whitespace, and discard empty strings from the result.

maxsplit

Maximum number of splits to do. -1 (the default value) means no limit.

Splits are done starting at the end of the string and working to the front.

rstrip(chars=None, /)

Return a copy of the string with trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

split(sep=None, maxsplit=-1)

Return a list of the words in the string, using sep as the delimiter string.

sep

The delimiter according which to split the string. None (the default value) means split according to any whitespace, and discard empty strings from the result.

maxsplit

Maximum number of splits to do. -1 (the default value) means no limit.

splitlines(keepends=False)

Return a list of the lines in the string, breaking at line boundaries.

Line breaks are not included in the resulting list unless keepends is given and true.

startswith(prefix[, start[, end]]) bool

Return True if S starts with the specified prefix, False otherwise. With optional start, test S beginning at that position. With optional end, stop comparing S at that position. prefix can also be a tuple of strings to try.

strip(chars=None, /)

Return a copy of the string with leading and trailing whitespace removed.

If chars is given and not None, remove characters in chars instead.

swapcase()

Convert uppercase characters to lowercase and lowercase characters to uppercase.

title()

Return a version of the string where each word is titlecased.

More specifically, words start with uppercased characters and all remaining cased characters have lower case.

translate(table, /)

Replace each character in the string using the given translation table.

table

Translation table, which must be a mapping of Unicode ordinals to Unicode ordinals, strings, or None.

The table must implement lookup/indexing via __getitem__, for instance a dictionary or list. If this operation raises LookupError, the character is left untouched. Characters mapped to None are deleted.

upper()

Return a copy of the string converted to uppercase.

zfill(width, /)

Pad a numeric string with zeros on the left, to fill a field of the given width.

The string is never truncated.

LINEAR = 'linear'
NON_LINEAR = 'non-linear'

Add a callback for some events.

The callback functions are attached to the database, which means they are triggered when new values are stored within the database of the optimization problem.

Parameters:
• callback (Callable[[ndarray], Any]) – A function to be called after some events, whose argument is a design vector.

• each_new_iter (bool) –

Whether to evaluate the callback functions after evaluating all functions of the optimization problem for a given point and storing their values in the database.

By default it is set to True.

• each_store (bool) –

Whether to evaluate the callback functions after storing any new value in the database.

By default it is set to False.

Return type:

None

Add an equality or inequality constraint to the optimization problem.

An equality constraint is written as $$c(x)=a$$, a positive inequality constraint is written as $$c(x)\geq a$$ and a negative inequality constraint is written as $$c(x)\leq a$$.

Parameters:
• function (MDOFunction) – The function $$c$$.

• value (float) –

The value $$a$$.

By default it is set to 0.0.

• constraint_type (MDOFunction.ConstraintType | None) – The type of the constraint.

• positive (bool) –

Whether the inequality constraint is positive.

By default it is set to False.

Raises:
Return type:

None

Add an equality constraint $$c(x)=a$$ to the optimization problem.

Parameters:
• function (MDOFunction) – The function $$c$$.

• value (float) –

The value $$a$$.

By default it is set to 0.

Return type:

None

Add an inequality constraint to the optimization problem.

A positive inequality constraint is written as $$c(x)\geq a$$ and a negative inequality constraint is written as $$c(x)\leq a$$

Parameters:
• function (MDOFunction) – The function $$c$$.

• value (float) –

The value $$a$$ for which the constraint is active.

By default it is set to 0.

• positive (bool) –

Whether the inequality constraint is positive.

By default it is set to False.

Return type:

None

Add a function to be observed.

When the OptimizationProblem is executed, the observables are called following this sequence:

Parameters:
• observable (MDOFunction) – A function to be observed.

• new_iter (bool) –

If True, then the observable will be called at each new iterate.

By default it is set to True.

Return type:

None

aggregate_constraint(constraint_index, method=EvaluationFunction.MAX, groups=None, **options)

Aggregate a constraint to generate a reduced dimension constraint.

Parameters:
• constraint_index (int) – The index of the constraint in constraints.

• method (Callable[[NDArray[float]], float] | AggregationFunction) –

The aggregation method, e.g. "max", "lower_bound_KS", "upper_bound_KS"or "IKS".

By default it is set to “MAX”.

• groups (Iterable[Sequence[int]] | None) – The groups of components of the constraint to aggregate to produce one aggregation constraint per group of components; if None, a single aggregation constraint is produced.

• **options (Any) – The options of the aggregation method.

Raises:

ValueError – When the given index is greater or equal than the number of constraints or when the constraint aggregation method is unknown.

Return type:

None

apply_exterior_penalty(objective_scale=1.0, scale_inequality=1.0, scale_equality=1.0)

Reformulate the optimization problem using exterior penalty.

Given the optimization problem with equality and inequality constraints:

\begin{align}\begin{aligned}min_x f(x)\\s.t.\\g(x)\leq 0\\h(x)=0\\l_b\leq x\leq u_b\end{aligned}\end{align}

The exterior penalty approach consists in building a penalized objective function that takes into account constraints violations:

\begin{align}\begin{aligned}min_x \tilde{f}(x) = \frac{f(x)}{o_s} + s[\sum{H(g(x))g(x)^2}+\sum{h(x)^2}]\\s.t.\\l_b\leq x\leq u_b\end{aligned}\end{align}

Where $$H(x)$$ is the Heaviside function, $$o_s$$ is the objective_scale parameter and $$s$$ is the scale parameter. The solution of the new problem approximate the one of the original problem. Increasing the values of objective_scale and scale, the solutions are closer but the optimization problem requires more and more iterations to be solved.

Parameters:
• scale_equality (float | ndarray) –

The equality constraint scaling constant.

By default it is set to 1.0.

• objective_scale (float) –

The objective scaling constant.

By default it is set to 1.0.

• scale_inequality (float | ndarray) –

The inequality constraint scaling constant.

By default it is set to 1.0.

Return type:

None

check()

Check if the optimization problem is ready for run.

Raises:

ValueError – If the objective function is missing.

Return type:

None

check_design_point_is_feasible(x_vect)

Check if a design point is feasible and measure its constraint violation.

The constraint violation measure at a design point $$x$$ is

$\lVert\max(g(x)-\varepsilon_{\text{ineq}},0)\rVert_2^2 +\lVert|\max(|h(x)|-\varepsilon_{\text{eq}},0)\rVert_2^2$

where $$\|.\|_2$$ is the Euclidean norm, $$g(x)$$ is the inequality constraint vector, $$h(x)$$ is the equality constraint vector, $$\varepsilon_{\text{ineq}}$$ is the tolerance for the inequality constraints and $$\varepsilon_{\text{eq}}$$ is the tolerance for the equality constraints.

If the design point is feasible, the constraint violation measure is 0.

Parameters:

x_vect (ndarray) – The design point $$x$$.

Returns:

Whether the design point is feasible, and its constraint violation measure.

Return type:
static check_format(function)

Check that a function is an instance of MDOFunction.

Parameters:

function (Any) – The function to be tested.

Raises:

TypeError – If the function is not an MDOFunction.

Return type:

None

clear_listeners()

Clear all the listeners.

Return type:

None

static compute_knapsack_items(design_variables)

Compute the knapsack number of items.

Parameters:

design_variables (ndarray) – The design variables vector.

Returns:

The knapsack total number of items.

Return type:

ndarray

compute_knapsack_value(design_variables)

Compute the knapsack total value.

Parameters:

design_variables (ndarray) – The design variables vector.

Returns:

The knapsack total value.

Return type:

ndarray

compute_knapsack_weight(design_variables)

Compute the knapsack total weight.

Parameters:

design_variables (ndarray) – The design variables vector.

Returns:

The knapsack total weight.

Return type:

ndarray

evaluate_functions(x_vect=None, eval_jac=False, eval_obj=True, eval_observables=True, normalize=True, no_db_no_norm=False, constraint_names=None, observable_names=None, jacobian_names=None)

Compute the functions of interest, and possibly their derivatives.

These functions of interest are the constraints, and possibly the objective.

Some optimization libraries require the number of constraints as an input parameter which is unknown by the formulation or the scenario. Evaluation of initial point allows to get this mandatory information. This is also used for design of experiments to evaluate samples.

Parameters:
• x_vect (ndarray) – The input vector at which the functions must be evaluated; if None, the initial point x_0 is used.

• eval_jac (bool) –

Whether to compute the Jacobian matrices of the functions of interest. If True and jacobian_names is None then compute the Jacobian matrices (or gradients) of the functions that are selected for evaluation (with eval_obj, constraint_names, eval_observables andobservable_names). If False and jacobian_names is None then no Jacobian matrix is evaluated. If jacobian_names is not None then the value of eval_jac is ignored.

By default it is set to False.

• eval_obj (bool) –

Whether to consider the objective function as a function of interest.

By default it is set to True.

• eval_observables (bool) –

Whether to evaluate the observables. If True and observable_names is None then all the observables are evaluated. If False and observable_names is None then no observable is evaluated. If observable_names is not None then the value of eval_observables is ignored.

By default it is set to True.

• normalize (bool) –

Whether to consider the input vector x_vect normalized.

By default it is set to True.

• no_db_no_norm (bool) –

If True, then do not use the pre-processed functions, so we have no database, nor normalization.

By default it is set to False.

• constraint_names (Iterable[str] | None) – The names of the constraints to evaluate. If None then all the constraints are evaluated.

• observable_names (Iterable[str] | None) – The names of the observables to evaluate. If None and eval_observables is True then all the observables are evaluated. If None and eval_observables is False then no observable is evaluated.

• jacobian_names (Iterable[str] | None) – The names of the functions whose Jacobian matrices (or gradients) to compute. If None and eval_jac is True then compute the Jacobian matrices (or gradients) of the functions that are selected for evaluation (with eval_obj, constraint_names, eval_observables andobservable_names). If None and eval_jac is False then no Jacobian matrix is computed.

Returns:

The output values of the functions of interest, as well as their Jacobian matrices if eval_jac is True.

Raises:

ValueError – If a name in jacobian_names is not the name of a function of the problem.

Return type:

EvaluationType

execute_observables_callback(last_x)

The callback function to be passed to the database.

Call all the observables with the last design variables values as argument.

Parameters:

last_x (ndarray) – The design variables values from the last evaluation.

Return type:

None

classmethod from_hdf(file_path, x_tolerance=0.0, hdf_node_path='')

Import an optimization history from an HDF file.

Parameters:
• file_path (str | Path) – The file containing the optimization history.

• x_tolerance (float) –

The tolerance on the design variables when reading the file.

By default it is set to 0.0.

• hdf_node_path (str) –

The path of the HDF node from which the database should be imported. If empty, the root node is considered.

By default it is set to “”.

Returns:

Return type:

OptimizationProblem

get_active_ineq_constraints(x_vect, tol=1e-06)

For each constraint, indicate if its different components are active.

Parameters:
• x_vect (ndarray) – The vector of design variables.

• tol (float) –

The tolerance for deciding whether a constraint is active.

By default it is set to 1e-06.

Returns:

For each constraint, a boolean indicator of activation of its different components.

Return type:
get_all_function_name()

Retrieve the names of all the function of the optimization problem.

These functions are the constraints, the objective function and the observables.

Returns:

The names of all the functions of the optimization problem.

Return type:

list[str]

get_all_functions(original=False)

Retrieve all the functions of the optimization problem.

These functions are the constraints, the objective function and the observables.

Parameters:

original (bool) –

Whether to return the original functions or the preprocessed ones.

By default it is set to False.

Returns:

All the functions of the optimization problem.

Return type:
get_best_infeasible_point()

Retrieve the best infeasible point within a given tolerance.

Returns:

The best infeasible point expressed as the design variables values, the objective function value, the feasibility of the point and the functions values.

Return type:

tuple[ndarray | None, ndarray | None, bool, dict[str, ndarray]]

get_constraint_names()

Retrieve the names of the constraints.

Returns:

The names of the constraints.

Return type:

list[str]

get_constraints_number()

Retrieve the number of constraints.

Returns:

The number of constraints.

Return type:

int

get_data_by_names(names, as_dict=True, filter_non_feasible=False)

Return the data for specific names of variables.

Parameters:
• names (str | Iterable[str]) – The names of the variables.

• as_dict (bool) –

If True, return values as dictionary.

By default it is set to True.

• filter_non_feasible (bool) –

If True, remove the non-feasible points from the data.

By default it is set to False.

Returns:

The data related to the variables.

Return type:

ndarray | dict[str, ndarray]

get_design_variable_names()

Retrieve the names of the design variables.

Returns:

The names of the design variables.

Return type:

list[str]

get_dimension()

Retrieve the total number of design variables.

Returns:

The dimension of the design space.

Return type:

int

get_eq_constraints()

Retrieve all the equality constraints.

Returns:

The equality constraints.

Return type:
get_eq_constraints_number()

Retrieve the number of equality constraints.

Returns:

The number of equality constraints.

Return type:

int

get_eq_cstr_total_dim()

Retrieve the total dimension of the equality constraints.

This dimension is the sum of all the outputs dimensions of all the equality constraints.

Returns:

The total dimension of the equality constraints.

Return type:

int

get_feasible_points()

Retrieve the feasible points within a given tolerance.

This tolerance is defined by OptimizationProblem.eq_tolerance for equality constraints and OptimizationProblem.ineq_tolerance for inequality ones.

Returns:

The values of the design variables and objective function for the feasible points.

Return type:

tuple[list[RealOrComplexArray], list[dict[str, float | list[int]]]]

get_function_dimension(name)

Return the dimension of a function of the problem (e.g. a constraint).

Parameters:

name (str) – The name of the function.

Returns:

The dimension of the function.

Raises:
• ValueError – If the function name is unknown to the problem.

• RuntimeError – If the function dimension is not unavailable.

Return type:

int

get_function_names(names)

Return the names of the functions stored in the database.

Parameters:

names (Iterable[str]) – The names of the outputs or constraints specified by the user.

Returns:

The names of the constraints stored in the database.

Return type:

list[str]

get_functions_dimensions(names=None)

Return the dimensions of the outputs of the problem functions.

Parameters:

names (Iterable[str] | None) – The names of the functions. If None, then the objective and all the constraints are considered.

Returns:

The dimensions of the outputs of the problem functions. The dictionary keys are the functions names and the values are the functions dimensions.

Return type:

dict[str, int]

get_ineq_constraints()

Retrieve all the inequality constraints.

Returns:

The inequality constraints.

Return type:
get_ineq_constraints_number()

Retrieve the number of inequality constraints.

Returns:

The number of inequality constraints.

Return type:

int

get_ineq_cstr_total_dim()

Retrieve the total dimension of the inequality constraints.

This dimension is the sum of all the outputs dimensions of all the inequality constraints.

Returns:

The total dimension of the inequality constraints.

Return type:

int

get_last_point()

Return the last design point.

Returns:

The last point result, defined by:

• the value of the objective function,

• the value of the design variables,

• the indicator of feasibility of the last point,

• the value of the constraints,

• the value of the gradients of the constraints.

Raises:

ValueError – When the optimization database is empty.

Return type:
get_nonproc_constraints()

Retrieve the non-processed constraints.

Returns:

The non-processed constraints.

Return type:
get_nonproc_objective()

Retrieve the non-processed objective function.

Return type:

MDOFunction

get_number_of_unsatisfied_constraints(design_variables, values=mappingproxy({}))

Return the number of scalar constraints not satisfied by design variables.

Parameters:
• design_variables (ndarray) – The design variables.

• values (Mapping[str, float | ndarray]) –

The values of the constraints. N.B. the missing values will be read from the database or computed.

By default it is set to {}.

Returns:

The number of unsatisfied scalar constraints.

Return type:

int

get_objective_name(standardize=True)

Retrieve the name of the objective function.

Parameters:

standardize (bool) –

Whether to use the name of the objective expressed as a cost, e.g. "-f" when the user seeks to maximize "f".

By default it is set to True.

Returns:

The name of the objective function.

Return type:

str

get_observable(name)

Return an observable of the problem.

Parameters:

name (str) – The name of the observable.

Returns:

The pre-processed observable if the functions of the problem have already been pre-processed, otherwise the original one.

Return type:

MDOFunction

get_optimum()

Return the optimum solution within a given feasibility tolerances.

Returns:

The optimum result, defined by:

• the value of the objective function,

• the value of the design variables,

• the indicator of feasibility of the optimal solution,

• the value of the constraints,

• the value of the gradients of the constraints.

Raises:

ValueError – When the optimization database is empty.

Return type:
get_reformulated_problem_with_slack_variables()

Add slack variables and replace inequality constraints with equality ones.

Given the original optimization problem,

\begin{align}\begin{aligned}min_x f(x)\\s.t.\\g(x)\leq 0\\h(x)=0\\l_b\leq x\leq u_b\end{aligned}\end{align}

Slack variables are introduced for all inequality constraints that are non-positive. An equality constraint for each slack variable is then defined.

\begin{align}\begin{aligned}min_{x,s} F(x,s) = f(x)\\s.t.\\H(x,s) = h(x)=0\\G(x,s) = g(x)-s=0\\l_b\leq x\leq u_b\\s\leq 0\end{aligned}\end{align}
Returns:

An optimization problem without inequality constraints.

Return type:

OptimizationProblem

get_scalar_constraint_names()

Return the names of the scalar constraints.

Returns:

The names of the scalar constraints.

Return type:

list[str]

get_x0_normalized(cast_to_real=False, as_dict=False)

Return the initial values of the design variables after normalization.

Parameters:
• cast_to_real (bool) –

Whether to return the real part of the initial values.

By default it is set to False.

• as_dict (bool) –

Whether to return the values as a dictionary of the form {variable_name: variable_value}.

By default it is set to False.

Returns:

The current values of the design variables normalized between 0 and 1 from their lower and upper bounds.

Return type:

ndarray | dict[str, ndarray]

has_constraints()

Check if the problem has equality or inequality constraints.

Returns:

True if the problem has equality or inequality constraints.

Return type:

bool

has_eq_constraints()

Check if the problem has equality constraints.

Returns:

True if the problem has equality constraints.

Return type:

bool

has_ineq_constraints()

Check if the problem has inequality constraints.

Returns:

True if the problem has inequality constraints.

Return type:

bool

has_nonlinear_constraints()

Check if the problem has non-linear constraints.

Returns:

True if the problem has equality or inequality constraints.

Return type:

bool

is_max_iter_reached()

Check if the maximum amount of iterations has been reached.

Returns:

Whether the maximum amount of iterations has been reached.

Return type:

bool

is_point_feasible(out_val, constraints=None)

Check if a point is feasible.

Notes

If the value of a constraint is absent from this point, then this constraint will be considered satisfied.

Parameters:
• out_val (Mapping[str, RealOrComplexArray]) – The values of the objective function, and eventually constraints.

• constraints (Iterable[MDOFunction] | None) – The constraints whose values are to be tested. If None, then take all constraints of the problem.

Returns:

The feasibility of the point.

Return type:

bool

preprocess_functions(is_function_input_normalized=True, use_database=True, round_ints=True, eval_obs_jac=False, support_sparse_jacobian=False)

Pre-process all the functions and eventually the gradient.

Required to wrap the objective function and constraints with the database and eventually the gradients by complex step or finite differences.

Parameters:
• is_function_input_normalized (bool) –

Whether to consider the function input as normalized and unnormalize it before the evaluation takes place.

By default it is set to True.

• use_database (bool) –

Whether to wrap the functions in the database.

By default it is set to True.

• round_ints (bool) –

Whether to round the integer variables.

By default it is set to True.

• eval_obs_jac (bool) –

Whether to evaluate the Jacobian of the observables.

By default it is set to False.

• support_sparse_jacobian (bool) –

Whether the driver support sparse Jacobian.

By default it is set to False.

Return type:

None

static repr_constraint(function, constraint_type, value=None, positive=False)

Express a constraint as a string expression.

Parameters:
• function (MDOFunction) – The constraint function.

• constraint_type (MDOFunction.ConstraintType) – The type of the constraint.

• value (float | None) – The value for which the constraint is active. If None, this value is 0.

• positive (bool) –

If True, then the inequality constraint is positive.

By default it is set to False.

Returns:

A string representation of the constraint.

Return type:

str

reset(database=True, current_iter=True, design_space=True, function_calls=True, preprocessing=True)

Partially or fully reset the optimization problem.

Parameters:
• database (bool) –

Whether to clear the database.

By default it is set to True.

• current_iter (bool) –

Whether to reset the current iteration OptimizationProblem.current_iter.

By default it is set to True.

• design_space (bool) –

Whether to reset the current point of the OptimizationProblem.design_space to its initial value (possibly none).

By default it is set to True.

• function_calls (bool) –

Whether to reset the number of calls of the functions.

By default it is set to True.

• preprocessing (bool) –

Whether to turn the pre-processing of functions to False.

By default it is set to True.

Return type:

None

Export the database of the optimization problem to a Dataset.

The variables can be classified into groups: Dataset.DESIGN_GROUP or Dataset.INPUT_GROUP for the design variables and Dataset.FUNCTION_GROUP or Dataset.OUTPUT_GROUP for the functions (objective, constraints and observables).

Parameters:
• name (str) –

The name to be given to the dataset. If empty, use the name of the OptimizationProblem.database.

By default it is set to “”.

• categorize (bool) –

Whether to distinguish between the different groups of variables. Otherwise, group all the variables in Dataset.PARAMETER_GROUP.

By default it is set to True.

• opt_naming (bool) –

Whether to use Dataset.DESIGN_GROUP and Dataset.FUNCTION_GROUP as groups. Otherwise, use Dataset.INPUT_GROUP and Dataset.OUTPUT_GROUP.

By default it is set to True.

Whether to export the gradients of the functions (objective function, constraints and observables) if the latter are available in the database of the optimization problem.

By default it is set to False.

• input_values (Iterable[ndarray]) –

The input values to be considered. If empty, consider all the input values of the database.

By default it is set to ().

Returns:

A dataset built from the database of the optimization problem.

Return type:

Dataset

to_hdf(file_path, append=False, hdf_node_path='')

Export the optimization problem to an HDF file.

Parameters:
• file_path (str | Path) – The path of the file to store the data.

• append (bool) –

If True, then the data are appended to the file if not empty.

By default it is set to False.

• hdf_node_path (str) –

The path of the HDF node in which the database should be exported. If empty, the root node is considered.

By default it is set to “”.

Return type:

None

CONSTRAINTS_GROUP: Final[str] = 'constraints'
DESIGN_SPACE_ATTRS: Final[str] = ['u_bounds', 'l_bounds', 'x_0', 'x_names', 'dimension']
DESIGN_SPACE_GROUP: Final[str] = 'design_space'
DESIGN_VAR_NAMES: Final[str] = 'x_names'
DESIGN_VAR_SIZE: Final[str] = 'x_size'
FUNCTIONS_ATTRS: ClassVar[str] = ['objective', 'constraints']
GGOBI_FORMAT: Final[str] = 'ggobi'
HDF5_FORMAT: Final[str] = 'hdf5'
HDF_NODE_PATH: Final[str] = 'hdf_node_path'
KKT_RESIDUAL_NORM: Final[str] = 'KKT residual norm'
OBJECTIVE_GROUP: Final[str] = 'objective'
OBSERVABLES_GROUP: Final[str] = 'observables'
OPTIM_DESCRIPTION: ClassVar[str] = ['minimize_objective', 'fd_step', 'differentiation_method', 'pb_type', 'ineq_tolerance', 'eq_tolerance']
OPT_DESCR_GROUP: Final[str] = 'opt_description'
SOLUTION_GROUP: Final[str] = 'solution'
activate_bound_check: ClassVar[bool] = True

Whether to check if a point is in the design space before calling functions.

capacity_items: int

The knapsack number of items capacity.

capacity_weight: float

The knapsack weight capacity.

property constraint_names: dict[str, list[str]]

The standardized constraint names bound to the original ones.

constraints: list[MDOFunction]

The constraints.

current_iter: int

The current iteration.

database: Database

The database to store the optimization problem data.

design_space: DesignSpace

The design space on which the optimization problem is solved.

property dimension: int

The dimension of the design space.

eq_tolerance: float

The tolerance for the equality constraints.

fd_step: float

The finite differences step.

ineq_tolerance: float

The tolerance for the inequality constraints.

property is_mono_objective: bool

Whether the optimization problem is mono-objective.

Raises:

ValueError – When the dimension of the objective cannot be determined.

max_iter: int

The maximum iteration.

property minimize_objective: bool

Whether to minimize the objective.

new_iter_observables: list[MDOFunction]

The observables to be called at each new iterate.

nonproc_constraints: list[MDOFunction]

The non-processed constraints.

nonproc_new_iter_observables: list[MDOFunction]

The non-processed observables to be called at each new iterate.

nonproc_objective: MDOFunction

The non-processed objective function.

nonproc_observables: list[MDOFunction]

The non-processed observables.

property objective: MDOFunction

The objective function.

observables: list[MDOFunction]

The observables.

property parallel_differentiation: bool

Whether to approximate the derivatives in parallel.

property parallel_differentiation_options: dict[str, int | bool]

The options to approximate the derivatives in parallel.

pb_type: ProblemType

The type of optimization problem.

preprocess_options: dict

The options to pre-process the functions.

solution: OptimizationResult | None

The solution of the optimization problem if solved; otherwise None.

stop_if_nan: bool

Whether the optimization stops when a function returns NaN.

use_standardized_objective: bool

Whether to use standardized objective for logging and post-processing.

The standardized objective corresponds to the original one expressed as a cost function to minimize. A DriverLibrary works with this standardized objective and the Database stores its values. However, for convenience, it may be more relevant to log the expression and the values of the original objective.

values: ndarray

The knapsack items’ value.

weights: ndarray

The knapsack items’ weight.

gemseo_pymoo.problems.analytical.knapsack.create_random_knapsack_problem(n_items, capacity_level=0.1, binary=True, obj_variant='single')[source]

Create a random Knapsack problem.

One can also create a MultiObjectiveKnapsack problem by providing obj_variant = ‘multi’.

The value and the weight of the items are integers randomly generated between 1 and 100.

Parameters:
• n_items (int) – The size of the set of items.

• capacity_level (float) –

The percentage of the set of items total weight corresponding to the knapsack capacity.

By default it is set to 0.1.

• binary (bool) –

If True, only one unit of each item is allowed.

By default it is set to True.

• obj_variant (str) –

Single-objective (‘single’) or multi-objective (‘multi’) problem.

By default it is set to “single”.

Returns:

An instance of Knapsack or MultiObjectiveKnapsack depending

on the obj_variant provided.

Raises:

ValueError – Either if the number of items is not a positive integer or if the capacity_level is outside the range (0, 1).

Return type: