evomo.operators.selection.non_dominate#

Functions#

dominate_relation(→ torch.Tensor)

Return the domination relation matrix A, where A_{ij} is True if x_i dominates y_j.

update_dc_and_rank(dominate_relation_matrix, ...)

Update the dominate count and ranks for the current Pareto front.

non_dominate_rank(→ torch.Tensor)

Compute the non-domination rank for a set of solutions in multi-objective optimization.

crowding_distance(costs, mask)

Compute the crowding distance for a set of solutions in multi-objective optimization.

nd_environmental_selection(x, f, topk[, cv])

Perform environmental selection based on non-domination rank and crowding distance.

Module Contents#

evomo.operators.selection.non_dominate.dominate_relation(x: torch.Tensor, y: torch.Tensor, cv_x: torch.Tensor = None, cv_y: torch.Tensor = None) → torch.Tensor#

Return the domination relation matrix A, where A_{ij} is True if x_i dominates y_j.

Parameters:

  • x – An array with shape (n1, m) where n1 is the population size and m is the number of objectives.

  • y – An array with shape (n2, m) where n2 is the population size and m is the number of objectives.

Returns:

The domination relation matrix of x and y.

evomo.operators.selection.non_dominate.update_dc_and_rank(dominate_relation_matrix: torch.Tensor, dominate_count: torch.Tensor, pareto_front: torch.BoolTensor, rank: torch.Tensor, current_rank: int)#

Update the dominate count and ranks for the current Pareto front.

Parameters:

  • dominate_relation_matrix – The domination relation matrix between individuals.

  • dominate_count – The count of how many individuals dominate each individual.

  • pareto_front – A tensor indicating which individuals are in the current Pareto front.

  • rank – A tensor storing the rank of each individual.

  • current_rank – The current Pareto front rank.

Returns:

  • rank: Updated rank tensor.

  • dominate_count: Updated dominate count tensor.

evomo.operators.selection.non_dominate.non_dominate_rank(x: torch.Tensor, cv: torch.Tensor = None) → torch.Tensor#

Compute the non-domination rank for a set of solutions in multi-objective optimization.

The non-domination rank is a measure of the Pareto optimality of each solution.

Parameters:

  • x – A 2D tensor where each row represents a solution, and each column represents an objective.

  • cv – An optional tensor containing the constraint violations of the solutions.

Returns:

A 1D tensor containing the zero-based non-domination rank for each solution. Solutions in the first Pareto front have rank 0.

evomo.operators.selection.non_dominate.crowding_distance(costs: torch.Tensor, mask: torch.Tensor)#

Compute the crowding distance for a set of solutions in multi-objective optimization.

The crowding distance is a measure of the diversity of solutions within a Pareto front.

Parameters:

  • costs – A 2D tensor where each row represents a solution, and each column represents an objective.

  • mask – A 1D boolean tensor indicating which solutions should be considered.

Returns:

A 1D tensor containing the crowding distance for each solution.

evomo.operators.selection.non_dominate.nd_environmental_selection(x: torch.Tensor, f: torch.Tensor, topk: int, cv: torch.Tensor = None)#

Perform environmental selection based on non-domination rank and crowding distance.

Ranking stops after the complete front containing the topk-th solution. Negative or nonfinite total constraint violations require full ranking to preserve the CV-first selection order. Returned ranks are always complete for the selected individuals; use non_dominate_rank for all input ranks.

Parameters:

  • x – A 2D tensor where each row represents a solution, and each column represents a decision variable.

  • f – A 2D tensor where each row represents a solution, and each column represents an objective.

  • topk – The number of solutions to select.

  • cv – An optional tensor containing the constraint violations of the solutions.

Returns:

A tuple of five values: - x: The selected solutions. - f: The corresponding objective values. - rank: The non-domination rank of the selected solutions. - crowding_dis: The crowding distance of the selected solutions. - cv: The selected constraint violations, or None for an unconstrained problem.