xlemoo.fitness_indicators

XLEMOO.fitness_indicators.asf_wrapper(asf: ASFBase, asf_kwargs: dict) → Callable[[ndarray, [Optional[numpy.ndarray]]], ndarray][source]

Wraps a scalarization function into a callable function that accepts a 2D array of objective function values and a 2D array of decision variable values. This callable can then be used as an indicator. The lower the scalarized value is, the better.

Parameters:

  • asf (ASFBase) – A scalarization function.

  • asf_kwargs (dict) – The keyword arguments passed to the scalarization function when it is evaluated.

Returns:

A function that accepts a 2D array of objective vectors, and optionally a 2D array of the corresponding decision variable vectors, and computes the scalarized values of the objective vectors returning them in a 2D array of singleton values where each value is the result of the scalarization.

Return type:

Callable[[np.ndarray, [Optional[np.ndarray]]], np.ndarray]

XLEMOO.fitness_indicators.hypervolume_contribution(ref_point: ndarray) → Callable[[ndarray, ndarray], ndarray][source]

Creates a function based on the hypervolume. This function accepts a 2D array of objective vectors, and optionally a 2D array of decision variable vectors as well. This function when computes the individual contribution of each objective vector to the cumulative hypervolume of all the vectors. This function may then be used as an indicator. The decision variable values are not currently used.

Parameters:

ref_point (np.ndarray) – The reference point used to compute the hypervolume.

Returns:

A hypervolume indicator function that computes the contribution of each provided objective vector to the cumulative hypervolume of all the vectors. The lower the value, the better.

Return type:

Callable[[np.ndarray, np.ndarray], np.ndarray]

XLEMOO.fitness_indicators.inside_ranges(lower_limits: ndarray, upper_limits: ndarray, sim_cost: float, asf_fun: Optional[Callable[[ndarray], ndarray]] = None) → Callable[[ndarray, ndarray, ndarray], ndarray][source]

Creates a function that computes a fitness value for objective vectors based on whether the values conform to given bounds. As an optional second argument, this function accepts a 2D array of decision variable vectors. Additionally, a similarity penalty can also be included where an objective vector is penalized if it is similar to another, and a scalarization contribution may also be added. The decision variable vectors are not used currently.

Parameters:

  • lower_limits (np.ndarray) – An array with the lower bounds of the objective function values.

  • upper_limits (np.ndarray) – An array with the upper bounds of the objective function values.

  • sim_cost (float) – The similarity penalty.

  • asf_fun (Callable[[np.ndarray], np.ndarray], optional) – A wrapped scalarization function that is used to compute the scalarization contribution for each objective vector. See asf_wrapper(). Defaults to None.

Raises:

ValueError – The shape of the lower_limits and upper_limits mismatch.

Returns:

A function that computes the fitness values of objective vectors based on whether the values are withing defined lower and upper bounds penalized by a similarity cost. Additional contributions may be calculated with a scalarization function.

Return type:

Callable[[np.ndarray, np.ndarray, np.ndarray], np.ndarray]

XLEMOO.fitness_indicators.naive_sum(objectives_fitnesses: ndarray, variables: Optional[ndarray] = None) → ndarray[source]

An indicator that computes the sum of the objective function values in each objective vector provided.

Parameters:

  • objectives_fitnesses (np.ndarray) – A 2D vector with each row, and objective vector, representing the objective values of an objective function. Minimization assumed for each objective.

  • variables (Optional[np.ndarray], optional) – A 2D array of the decision variable value corresponding to the objective vectors in objective_fitness. Not used. Defaults to None.

Returns:

A 2D array with singleton entries, where each entry is the sum of the objective function value in each objective vector. The lower the value of the sum, the better the fitness.

Return type:

np.ndarray