matlab【多目标优化算法】MOMPA附代码

% Please refer to the main paper: % MOMPA: a high performance multi-objective optimizer based on marine predator algorithm % Long Chen, Fangyi Xu, Kezhong Jin and Zhenzhou Tang % GECCO '21: Proceedings of the Genetic and Evolutionary Computation Conference Companion % DOI: https://doi.org/10.1145/3449726.3459581 % AND % Marine Predators Algorithm: A nature-inspired metaheuristic % Afshin Faramarzi, Mohammad Heidarinejad, Seyedali Mirjalili, Amir H. Gandomi % Expert Systems with Applications % DOI: https://doi.org/10.1016/j.eswa.2020.113377 % _____________________________________________________ function [fobj, fcon,P] = mompa_getMOFcn(F, decisionVar, numObj) [N,D] = size(decisionVar); switch F case 'ZDT1' fobj(:, 1) = decisionVar(:, 1); g = 1 + 9*mean(decisionVar(:,2:end),2); h = 1 - (fobj(:,1)./g).^0.5; fobj(:,2) = g.*h; fcon(:, 1:D) = -decisionVar; fcon(:, D+1: 2*D) = decisionVar - 1; P(:,1) = (0:1/(N-1):1)'; P(:,2) = 1 - P(:,1).^0.5; case 'ZDT2' fobj(:,1) = decisionVar(:,1); g = 1 + 9*mean(decisionVar(:,2:end),2); h = 1 - (fobj(:,1)./g).^2; fobj(:,2) = g.*h; fcon(:, 1:D) = -decisionVar; fcon(:, D+1: 2*D) = decisionVar - 1; P(:,1) = (0:1/(N-1):1)'; P(:,2) = 1 - P(:,1).^2; case 'ZDT3' fobj(:,1) = decisionVar(:,1); g = 1 + 9*mean(decisionVar(:,2:end),2); h = 1 - (fobj(:,1)./g).^0.5 - fobj(:,1)./g.*sin(10*pi*fobj(:,1)); fobj(:,2) = g.*h; fcon(:, 1:D) = -decisionVar; fcon(:, D+1: 2*D) = decisionVar - 1; P(:,1) = (0:1/(N-1):1)'; P(:,2) = 1 - P(:,1).^0.5 - P(:,1).*sin(10*pi*P(:,1)); P = P(NDSort(P,fcon,1)==1,:); case 'ZDT4' fobj(:,1) = decisionVar(:,1); g = 1 + 10*(size(decisionVar,2)-1) + sum(decisionVar(:,2:end).^2-10*cos(4*pi*decisionVar(:,2:end)),2); h = 1 - (fobj(:,1)./g).^0.5; fobj(:,2) = g.*h; fcon(:, 1:D) = -decisionVar; fcon(:, D+1: 2*D) = decisionVar - 1; P(:,1) = (0:1/(N-1):1)'; P(:,2) = 1 - P(:,1).^0.5; case 'ZDT6' fobj(:,1) = 1 - exp(-4*decisionVar(:,1)).*sin(6*pi*decisionVar(:,1)).^6; g = 1 + 9*mean(decisionVar(:,2:end),2).^0.25; h = 1 - (fobj(:,1)./g).^2; fobj(:,2) = g.*h; fcon(:, 1:D) = -decisionVar; fcon(:, D+1: 2*D) = decisionVar - 1; minf1 = 0.280775; P(:,1) = (minf1:(1-minf1)/(N-1):1)'; P(:,2) = 1 - P(:,1).^2; case 'DTLZ1' M = numObj; g = 100*(D-M+1+sum((decisionVar(:,M:end)-0.5).^2-cos(20.*pi.*(decisionVar(:,M:end)-0.5)),2)); fobj = 0.5*repmat(1+g,1,M).*fliplr(cumprod([ones(N,1),decisionVar(:,1:M-1)],2)).*[ones(N,1),1-decisionVar(:,M-1:-1:1)]; %...................... fcon(:, 1:D) = -decisionVar; fcon(:, D+1: 2*D) = decisionVar - 1; P = UniformPoint(N,numObj)/2; case 'DTLZ2' M = numObj; g = sum((decisionVar(:,M:end)-0.5).^2,2); fobj = repmat(1+g,1,M).*fliplr(cumprod([ones(size(g,1),1),cos(decisionVar(:,1:M-1)*pi/2)],2)).*[ones(size(g,1),1),sin(decisionVar(:,M-1:-1:1)*pi/2)]; %...................... fcon(:, 1:D) = -decisionVar; fcon(:, D+1: 2*D) = decisionVar - 1; P = UniformPoint(N,numObj); P = P./repmat(sqrt(sum(P.^2,2)),1,numObj); case 'DTLZ3' M = numObj; g = 100*(D-M+1+sum((decisionVar(:,M:end)-0.5).^2-cos(20.*pi.*(decisionVar(:,M:end)-0.5)),2)); fobj = repmat(1+g,1,M).*fliplr(cumprod([ones(N,1),cos(decisionVar(:,1:M-1)*pi/2)],2)).*[ones(N,1),sin(decisionVar(:,M-1:-1:1)*pi/2)]; %...................... fcon(:, 1:D) = -decisionVar; fcon(:, D+1: 2*D) = decisionVar - 1; P = UniformPoint(N,M); P = P./repmat(sqrt(sum(P.^2,2)),1,M); case 'DTLZ4' M = numObj; decisionVar(:,1:M-1) = decisionVar(:,1:M-1).^100; g = sum((decisionVar(:,M:end)-0.5).^2,2); fobj = repmat(1+g,1,M).*fliplr(cumprod([ones(size(g,1),1),cos(decisionVar(:,1:M-1)*pi/2)],2)).*[ones(size(g,1),1),sin(decisionVar(:,M-1:-1:1)*pi/2)]; %...................... fcon(:, 1:D) = -decisionVar; fcon(:, D+1: 2*D) = decisionVar - 1; P = UniformPoint(N,M); P = P./repmat(sqrt(sum(P.^2,2)),1,M); case 'DTLZ5' M = numObj; g = sum((decisionVar(:,M:end)-0.5).^2,2); Temp = repmat(g,1,M-2); decisionVar(:,2:M-1) = (1+2*Temp.*decisionVar(:,2:M-1))./(2+2*Temp); fobj = repmat(1+g,1,M).*fliplr(cumprod([ones(size(g,1),1),cos(decisionVar(:,1:M-1)*pi/2)],2)).*[ones(size(g,1),1),sin(decisionVar(:,M-1:-1:1)*pi/2)]; %...................... fcon(:, 1:D) = -decisionVar; fcon(:, D+1: 2*D) = decisionVar - 1; P = [0:1/(N-1):1;1:-1/(N-1):0]'; P = P./repmat(sqrt(sum(P.^2,2)),1,size(P,2)); P = [P(:,ones(1,M-2)),P]; P = P./sqrt(2).^repmat([M-2,M-2:-1:0],size(P,1),1); case 'DTLZ6' M = numObj; g = sum(decisionVar(:,M:end).^0.1,2); Temp = repmat(g,1,M-2); decisionVar(:,2:M-1) = (1+2*Temp.*decisionVar(:,2:M-1))./(2+2*Temp); fobj = repmat(1+g,1,M).*fliplr(cumprod([ones(size(g,1),1),cos(decisionVar(:,1:M-1)*pi/2)],2)).*[ones(size(g,1),1),sin(decisionVar(:,M-1:-1:1)*pi/2)]; %...................... fcon(:, 1:D) = -decisionVar; fcon(:, D+1: 2*D) = decisionVar - 1; P = [0:1/(N-1):1;1:-1/(N-1):0]'; P = P./repmat(sqrt(sum(P.^2,2)),1,size(P,2)); P = [P(:,ones(1,M-2)),P]; P = P./sqrt(2).^repmat([M-2,M-2:-1:0],size(P,1),1); case 'DTLZ7' M = numObj; fobj = zeros(size(decisionVar,1),M); g = 1+9*mean(decisionVar(:,M:end),2); fobj(:,1:M-1) = decisionVar(:,1:M-1); fobj(:,M) = (1+g).*(M-sum(fobj(:,1:M-1)./(1+repmat(g,1,M-1)).*(1+sin(3*pi.*fobj(:,1:M-1))),2)); %...................... fcon(:, 1:D) = -decisionVar; fcon(:, D+1: 2*D) = decisionVar - 1; interval = [0,0.251412,0.631627,0.859401]; median = (interval(2)-interval(1))/(interval(4)-interval(3)+interval(2)-interval(1)); X = ReplicatePoint(N,M-1); X(X<=median) = X(X<=median)*(interval(2)-interval(1))/median+interval(1); X(X>median) = (X(X>median)-median)*(interval(4)-interval(3))/(1-median)+interval(3); P = [X,2*(M-sum(X/2.*(1+sin(3*pi.*X)),2))]; case 'WFG1' M = numObj; K = M-1; L = D - K; D = 1; S = 2 : 2 : 2*M; A = ones(1,M-1); z01 = decisionVar./repmat(2:2:size(decisionVar,2)*2,N,1); t1 = zeros(N,K+L); t1(:,1:K) = z01(:,1:K); t1(:,K+1:end) = WFG_s_linear(z01(:,K+1:end),0.35); t2 = zeros(N,K+L); t2(:,1:K) = t1(:,1:K); t2(:,K+1:end) = WFG1_b_flat(t1(:,K+1:end),0.8,0.75,0.85); t3 = zeros(N,K+L); t3 = WFG1_b_poly(t2,0.02); t4 = zeros(N,M); for i = 1 : M-1 t4(:,i) = WFG_r_sum(t3(:,(i-1)*K/(M-1)+1:i*K/(M-1)),2*((i-1)*K/(M-1)+1):2:2*i*K/(M-1)); end t4(:,M) = WFG_r_sum(t3(:,K+1:K+L),2*(K+1):2:2*(K+L)); x = zeros(N,M); for i = 1 : M-1 x(:,i) = max(t4(:,M),A(i)).*(t4(:,i)-0.5)+0.5; end x(:,M) = t4(:,M); h = WFG_convex(x); h(:,M) = WFG1_mixed(x); fobj = repmat(D*x(:,M),1,M) + repmat(S,N,1).*h; %...................... fcon = -decisionVar; P = UniformPoint(N,M); c = ones(size(P,1),M); for i = 1 : size(P,1)