src.environment.problem.MOO.MOO_synthetic.wfg_torch

Module Contents

Classes

WFG_Torch	Introduction A PyTorch version of the WFG test suite for multi-objective optimization problems.
WFG1_Torch
WFG2_Torch
WFG3_Torch
WFG4_Torch
WFG5_Torch
WFG6_Torch
WFG7_Torch
WFG8_Torch
WFG9_Torch

Functions

crtup	Introduction Generates a set of uniformly distributed reference points (weight vectors) for a given number of objectives. This function is typically used in multi-objective optimization algorithms such as NSGA-III and RVEA, where reference points are required to guide the selection process.
find_non_dominated_indices	Introduction Find the indices of non-dominated solutions in a population. A solution is said to be non-dominated if no other solution in the population dominates it. This function performs a pairwise comparison between all solutions.
convex
mixed
linear
s_linear
b_flat
b_poly
r_sum
disc
_transformation_shift_linear
_transformation_shift_deceptive
_transformation_shift_multi_modal
_transformation_bias_flat
_transformation_bias_poly
_transformation_param_dependent
_transformation_param_deceptive
_reduction_weighted_sum
_reduction_weighted_sum_uniform
_reduction_non_sep
_shape_concave
_shape_convex
_shape_linear
_shape_mixed
_shape_disconnected
validate_wfg2_wfg3
correct_to_01

API

src.environment.problem.MOO.MOO_synthetic.wfg_torch.crtup(n_obj, n_ref_points=1000)

Introduction

Generates a set of uniformly distributed reference points (weight vectors) for a given number of objectives. This function is typically used in multi-objective optimization algorithms such as NSGA-III and RVEA, where reference points are required to guide the selection process.

Args:

• n_obj (int): Number of objectives (i.e., the dimensionality of the reference points).

• n_ref_points (int): Approximate number of desired reference points (default: 1000).

Returns:

• W (np.ndarray): A 2D array of shape (n_comb, n_obj) representing the generated reference vectors.

• n_comb (int): Actual number of generated reference vectors.

src.environment.problem.MOO.MOO_synthetic.wfg_torch.find_non_dominated_indices(Point)

Introduction

Find the indices of non-dominated solutions in a population.

A solution is said to be non-dominated if no other solution in the population dominates it. This function performs a pairwise comparison between all solutions.

Args:

• Point (np.ndarray): A 2D array of shape (n_points, n_objectives), where each row represents the objective values of a solution.

Returns:

• non_dominated_indices (np.ndarray): Indices of the non-dominated solutions.

class src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG_Torch(n_var, n_obj, k=None, l=None, **kwargs)

Bases: src.environment.problem.basic_problem.Basic_Problem_Torch

Introduction

A PyTorch version of the WFG test suite for multi-objective optimization problems.

Initialization

validate(l, k, n_obj)

_post(t, a)

_calculate(x, s, h)

_rand_optimal_position(n)

_positional_to_optimal(K)

__str__()

class src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG1_Torch(n_var, n_obj, k=None, l=None, **kwargs)

Bases: src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG_Torch

static t1(x, n, k)

static t2(x, n, k)

static t3(x, n)

static t4(x, m, n, k)

func(x, *args, **kwargs)

get_ref_set(n_ref_points=1000)

class src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG2_Torch(n_var, n_obj, k=None, l=None, **kwargs)

Bases: src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG_Torch

validate(l, k, n_obj)

static t2(x, n, k)

static t3(x, m, n, k)

func(x, *args, **kwargs)

get_ref_set(n_ref_points=1000)

class src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG3_Torch(n_var, n_obj, k=None, **kwargs)

Bases: src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG_Torch

validate(l, k, n_obj)

func(x, *args, **kwargs)

get_ref_set(n_ref_points=1000)

class src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG4_Torch(n_var, n_obj, k=None, l=None, **kwargs)

Bases: src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG_Torch

static t1(x)

static t2(x, m, k)

func(x, *args, **kwargs)

get_ref_set(n_ref_points=1000)

class src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG5_Torch(n_var, n_obj, k=None, l=None, **kwargs)

Bases: src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG_Torch

static t1(x)

func(x, *args, **kwargs)

get_ref_set(n_ref_points=1000)

class src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG6_Torch(n_var, n_obj, k=None, l=None, **kwargs)

Bases: src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG_Torch

static t2(x, m, n, k)

func(x, *args, **kwargs)

get_ref_set(n_ref_points=1000)

class src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG7_Torch(n_var, n_obj, k=None, l=None, **kwargs)

Bases: src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG_Torch

static t1(x, k)

func(x, *args, **kwargs)

get_ref_set(n_ref_points=1000)

class src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG8_Torch(n_var, n_obj, k=None, l=None, **kwargs)

Bases: src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG_Torch

static t1(x, n, k)

func(x, *args, **kwargs)

_positional_to_optimal(K)

get_ref_set(n_ref_points=1000)

class src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG9_Torch(n_var, n_obj, k=None, l=None, **kwargs)

Bases: src.environment.problem.MOO.MOO_synthetic.wfg_torch.WFG_Torch

static t1(x, n)

static t2(x, n, k)

static t3(x, m, n, k)

func(x, *args, **kwargs)

_positional_to_optimal(K)

get_ref_set(n_ref_points=1000)

src.environment.problem.MOO.MOO_synthetic.wfg_torch.convex(x)

src.environment.problem.MOO.MOO_synthetic.wfg_torch.mixed(x)

src.environment.problem.MOO.MOO_synthetic.wfg_torch.linear(x)

src.environment.problem.MOO.MOO_synthetic.wfg_torch.s_linear(x, A)

src.environment.problem.MOO.MOO_synthetic.wfg_torch.b_flat(x, A, B, C)

src.environment.problem.MOO.MOO_synthetic.wfg_torch.b_poly(x, a)

src.environment.problem.MOO.MOO_synthetic.wfg_torch.r_sum(x, w)

src.environment.problem.MOO.MOO_synthetic.wfg_torch.disc(x)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._transformation_shift_linear(value, shift=0.35)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._transformation_shift_deceptive(y, A=0.35, B=0.005, C=0.05)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._transformation_shift_multi_modal(y, A, B, C)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._transformation_bias_flat(y, a, b, c)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._transformation_bias_poly(y, alpha)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._transformation_param_dependent(y, y_deg, A=0.98 / 49.98, B=0.02, C=50.0)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._transformation_param_deceptive(y, A=0.35, B=0.001, C=0.05)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._reduction_weighted_sum(y, w)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._reduction_weighted_sum_uniform(y)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._reduction_non_sep(y, A)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._shape_concave(x, m)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._shape_convex(x, m)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._shape_linear(x, m)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._shape_mixed(x, A=5.0, alpha=1.0)

src.environment.problem.MOO.MOO_synthetic.wfg_torch._shape_disconnected(x, alpha=1.0, beta=1.0, A=5.0)

src.environment.problem.MOO.MOO_synthetic.wfg_torch.validate_wfg2_wfg3(l)

src.environment.problem.MOO.MOO_synthetic.wfg_torch.correct_to_01(X, epsilon=1e-10)