Problems

Package related to problem description and design of experiment.

Classes summary

`Problems.Problem.Problem`(n_dvar, n_obj)	Abstract class for real-valued optimization problems.
`Problems.Box_Constrained.Box_Constrained`(...)	Abstract class for real-valued box-constrained optimization problems.
`Problems.Single_Objective.Single_Objective`(n_dvar)	Abstract class for artificial single-objective real-valued box-constrained optimization problems.
`Problems.Multi_Objective.Multi_Objective`(...)	Abstract class for artificial multi-objective real-valued box-constrained optimization problems.
`Problems.Ackley.Ackley`(n_dvar)	Class for the single-objective Ackley problem.
`Problems.Xiong.Xiong`()	Class for 1D single-objective Xiong problem.
`Problems.Schwefel.Schwefel`(n_dvar)	Class for the single-objective Schwefel problem.
`Problems.Rastrigin.Rastrigin`(n_dvar)	Class for the single-objective Rastrigin problem.
`Problems.Rosenbrock.Rosenbrock`(n_dvar)	Class for the single-objective Rosenbrock problem.
`Problems.CEC2013.CEC2013`(f_id, n_dvar)	Class for single-objective problems from the CEC2013.
`Problems.CEC2014.CEC2014`(f_id, n_dvar)	Class for single-objective problems from the CEC2014.
`Problems.DTLZ.DTLZ`(f_id, n_dvar, n_obj)	Class for multi-objective problems from the DTLZ test suite.
`Problems.ZDT.ZDT`(f_id, n_dvar)	Class for bi-objective problems from the ZDT test suite.
`Problems.DoE.DoE`(pb)	Class for Design of Experiments.

Abstract classes

Problem

class Problems.Problem.Problem(n_dvar, n_obj)

Bases: ABC

Abstract class for real-valued optimization problems.

Parameters:

n_dvar (positive int, not zero) – number of decision variables
n_obj (positive int, not zero) – number of objectives

Box-constrained

class Problems.Box_Constrained.Box_Constrained(n_dvar, n_obj)

Bases: Problem

Abstract class for real-valued box-constrained optimization problems.

Single_Objective

class Problems.Single_Objective.Single_Objective(n_dvar)

Bases: Box_Constrained

Abstract class for artificial single-objective real-valued box-constrained optimization problems.

Parameters:: n_dvar (positive int, not zero) – number of decision variables

Multi_Objective

class Problems.Multi_Objective.Multi_Objective(n_dvar, n_obj)

Bases: Box_Constrained

Abstract class for artificial multi-objective real-valued box-constrained optimization problems.

Parameters:: n_dvar (positive int, not zero) – number of decision variables

Single-Objective Problems

Ackley

class Problems.Ackley.Ackley(n_dvar)

Bases: Single_Objective

Class for the single-objective Ackley problem.

Parameters:: n_dvar (positive int, not zero) – number of decision variable

perform_real_evaluation(candidates)

Objective function.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: objective values
Return type:: np.ndarray

get_bounds()

Returns search space bounds.

Returns:: search space bounds
Return type:: np.ndarray

is_feasible(candidates)

Check feasibility of candidates.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: boolean indicating whether candidates are feasible
Return type:: bool

plot(): Plot the 1D or 2-D Ackley objective function.

Xiong

class Problems.Xiong.Xiong

Bases: Single_Objective

Class for 1D single-objective Xiong problem.

perform_real_evaluation(candidates)

Objective function.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: objective values
Return type:: np.ndarray

get_bounds()

Returns search space bounds.

Returns:: search space bounds
Return type:: np.ndarray

is_feasible(candidates)

Check feasibility of candidates.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: boolean indicating whether candidates are feasible
Return type:: bool

plot(): Plot the 1D Xiong objective function.

Schwefel

class Problems.Schwefel.Schwefel(n_dvar)

Bases: Single_Objective

Class for the single-objective Schwefel problem.

Parameters:: n_dvar (positive int, not zero) – number of decision variables

perform_real_evaluation(candidates)

Objective function.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: objective values
Return type:: np.ndarray

get_bounds()

Returns search space bounds.

Returns:: search space bounds
Return type:: np.ndarray

is_feasible(candidates)

Check feasibility of candidates.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: boolean indicating whether candidates are feasible
Return type:: bool

plot(): Plot the 1D or 2D Schwefel objective function.

Rastrigin

class Problems.Rastrigin.Rastrigin(n_dvar)

Bases: Single_Objective

Class for the single-objective Rastrigin problem.

Parameters:: n_dvar (positive int, not zero) – number of decision variable

perform_real_evaluation(candidates)

Objective function.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: objective values
Return type:: np.ndarray

get_bounds()

Returns search space bounds.

Returns:: search space bounds
Return type:: np.ndarray

is_feasible(candidates)

Check feasibility of candidates.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: boolean indicating whether candidates are feasible
Return type:: bool

plot(): Plot the 1D or 2D Rastrigin objective function.

Rosenbrock

class Problems.Rosenbrock.Rosenbrock(n_dvar)

Bases: Single_Objective

Class for the single-objective Rosenbrock problem.

Parameters:: n_dvar (positive int, >1) – number of decision variable

perform_real_evaluation(candidates)

Objective function.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: objective values
Return type:: np.ndarray

get_bounds()

Returns search space bounds.

Returns:: search space bounds
Return type:: np.ndarray

is_feasible(candidates)

Check feasibility of candidates.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: boolean indicating whether candidates are feasible
Return type:: bool

plot(): Plot the 2D Rosenbrock objective function.

CEC2013

class Problems.CEC2013.CEC2013(f_id, n_dvar)

Bases: Single_Objective

Class for single-objective problems from the CEC2013.

Parameters:

f_id (int in {1,...,28}) – problem’s identifier into the pygmo library
n_dvar (int in {2,5,20,30,40,50,60,70,80,90,100}) – number of decision variables

perform_real_evaluation(candidates)

Objective function.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: objective values
Return type:: np.ndarray

get_bounds()

Returns search space bounds.

Returns:: search space bounds
Return type:: np.ndarray

is_feasible(candidates)

Check feasibility of candidates.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: boolean indicating whether candidates are feasible
Return type:: bool

plot(): Plot the 2D CEC2013 considered problem’s objective function.

CEC2014

class Problems.CEC2014.CEC2014(f_id, n_dvar)

Bases: Single_Objective

Class for single-objective problems from the CEC2014.

Parameters:

f_id (int in {1,...,30}) – problem’s identifier into the pygmo library
n_dvar (int in {2,10,20,30,50,100}) – number of decision variable

perform_real_evaluation(candidates)

Objective function.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: objective values
Return type:: np.ndarray

get_bounds()

Returns search space bounds.

Returns:: search space bounds
Return type:: np.ndarray

is_feasible(candidates)

Check feasibility of candidates.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: boolean indicating whether candidates are feasible
Return type:: bool

plot(): Plot the 2D CEC2014 considered problem’s objective function.

Multi-Objective Problems

DTLZ

class Problems.DTLZ.DTLZ(f_id, n_dvar, n_obj)

Bases: Multi_Objective

Class for multi-objective problems from the DTLZ test suite.

Parameters:

f_id (int in {1,...,7}) – problem’s identifier into the pygmo library
n_dvar (positive int, not zero, strictly greater than n_obj) – number of decision variables
n_obj (positive int, strictly greater than 1) – number of objectives

perform_real_evaluation(candidates)

Objective function.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: objective values
Return type:: np.ndarray

get_bounds()

Returns search space bounds.

Returns:: search space bounds
Return type:: np.ndarray

is_feasible(candidates)

Check feasibility of candidates.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: boolean indicating whether candidates are feasible
Return type:: bool

ZDT

class Problems.ZDT.ZDT(f_id, n_dvar)

Bases: Multi_Objective

Class for bi-objective problems from the ZDT test suite.

Parameters:

f_id (int in {1,2,3,4,6}) – problem’s identifier into the pygmo library
n_dvar (positive int, strictly greater than 1) – number of decision variables

perform_real_evaluation(candidates)

Objective function.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: objective values
Return type:: np.ndarray

get_bounds()

Returns search space bounds.

Returns:: search space bounds
Return type:: np.ndarray

is_feasible(candidates)

Check feasibility of candidates.

Parameters:: candidates (np.ndarray) – candidate decision vectors
Returns:: boolean indicating whether candidates are feasible
Return type:: bool

Design of Experiments

class Problems.DoE.DoE(pb)

Bases: object

Class for Design of Experiments.

Parameters:: pb (Box_Constrained) – related optimization problem

random_uniform_sampling(nb_samples)

Returns samples generated by random uniform sampling over the search space.

Parameters:: nb_samples (positive int, not zero) – number of samples to generate
Returns:: samples
Return type:: np.ndarray

latin_hypercube_sampling(nb_samples)

Returns samples generated by latin hypercube sampling over the search space.

Parameters:: nb_samples (positive int, not zero) – number of samples to generate
Returns:: samples
Return type:: np.ndarray