基于PESA-II实现多目标优化求解附Matlab代码

% % clc; clear; close all; %% Problem Definition CostFunction = @(x) ZDT(x); nVar = 3; % Number of Decision Variables VarSize = [nVar 1]; % Decision Variables Matrix Size VarMin = 0; % Decision Varibales Lower Bound VarMax = 1; % Decision Varibales Upper Bound nObj = numel(CostFunction(unifrnd(VarMin, VarMax, VarSize))); % Number of Objectives %% PESA-II Settings MaxIt = 100; % Maximum Number of Iterations nPop = 50; % Population Size nArchive = 50; % Archive Size nGrid = 7; % Number of Grids per Dimension InflationFactor = 0.1; % Grid Inflation beta_deletion = 1; beta_selection = 2; pCrossover = 0.5; nCrossover = round(pCrossover*nPop/2)*2; pMutation = 1-pCrossover; nMutation = nPop-nCrossover; crossover_params.gamma = 0.15; crossover_params.VarMin = VarMin; crossover_params.VarMax = VarMax; mutation_params.h = 0.3; mutation_params.VarMin = VarMin; mutation_params.VarMax = VarMax; %% Initialization empty_individual.Position = []; empty_individual.Cost = []; empty_individual.IsDominated = []; empty_individual.GridIndex = []; pop = repmat(empty_individual, nPop, 1); for i = 1:nPop pop(i).Position = unifrnd(VarMin, VarMax, VarSize); pop(i).Cost = CostFunction(pop(i).Position); end archive = []; %% Main Loop for it = 1:MaxIt pop = DetermineDomination(pop); ndpop = pop(~[pop.IsDominated]); archive = [archive ndpop]; %#ok archive = DetermineDomination(archive); archive = archive(~[archive.IsDominated]); [archive, grid] = CreateGrid(archive, nGrid, InflationFactor); if numel(archive)>nArchive E = numel(archive)-nArchive; archive = TruncatePopulation(archive, grid, E, beta_deletion); [archive, grid] = CreateGrid(archive, nGrid, InflationFactor); end PF = archive; figure(1); PlotCosts(PF); pause(0.01); disp(['Iteration ' num2str(it) ': Number of PF Members = ' num2str(numel(PF))]); if it >= MaxIt break; end % Crossover popc = repmat(empty_individual, nCrossover/2, 2); for c = 1:nCrossover/2 p1 = SelectFromPopulation(archive, grid, beta_selection); p2 = SelectFromPopulation(archive, grid, beta_selection); [popc(c, 1).Position, popc(c, 2).Position] = Crossover(p1.Position, ... p2.Position, ... crossover_params); popc(c, 1).Cost = CostFunction(popc(c, 1).Position); popc(c, 2).Cost = CostFunction(popc(c, 2).Position); end popc = popc(:); % Mutation popm = repmat(empty_individual, nMutation, 1); for m = 1:nMutation p = SelectFromPopulation(archive, grid, beta_selection); popm(m).Position = Mutate(p.Position, mutation_params); popm(m).Cost = CostFunction(popm(m).Position); end pop = [popc popm]; end %% Results disp(' '); PFC = [PF.Cost]; for j = 1:size(PFC, 1) disp(['Objective #' num2str(j) ':']); disp([' Min = ' num2str(min(PFC(j, :)))]); disp([' Max = ' num2str(max(PFC(j, :)))]); disp([' Range = ' num2str(max(PFC(j, :))-min(PFC(j, :)))]); disp([' St.D. = ' num2str(std(PFC(j, :)))]); disp([' Mean = ' num2str(mean(PFC(j, :)))]); disp(' '); end