多目标粒子群优化算法 （MOPSO）（Matlab代码实现）

欢迎来到本博客❤️❤️❤️

博主优势：博客内容尽量做到思维缜密，逻辑清晰，为了方便读者。

⛳️座右铭：行百里者，半于九十。

目录

1 概述

2 运行结果

3 参考文献

4 Matlab代码实现

1 概述

   多目标粒子群优化( Multi-objective Parti-cle Swarm Optimization，MOPSO)算法是由Carlos A、Coello C等在2004年提出来的,用于将单目标粒子群算法扩展应用于多目标优化问题中。MOPSO算法使用帕累托支配的概念来确定粒子的飞行方向，通过粒子间的支配关系比较得到非支配个体并存入全局精英库REP中,依据密度自适应网格估计法从全局精英库中选出全局最优解个体Gsest,同时依据新旧代的种群个体间的支配关系比较,来选出个体历史最优解Pest ,进而通过公式(6)来不断更新粒子群的速度和位置,最终用尽可能少的计算资源得到覆盖整个搜索空间、分布均匀、靠近真帕累托前沿的非劣解集。

2 运行结果

部分代码：

% Plotting and verbose
    if(size(POS_fit,2)==2)
        h_fig = figure(1);
        h_par = plot(POS_fit(:,1),POS_fit(:,2),'or'); hold on;
        h_rep = plot(REP.pos_fit(:,1),REP.pos_fit(:,2),'ok'); hold on;
        try
            set(gca,'xtick',REP.hypercube_limits(:,1)','ytick',REP.hypercube_limits(:,2)');
            axis([min(REP.hypercube_limits(:,1)) max(REP.hypercube_limits(:,1)) ...
                  min(REP.hypercube_limits(:,2)) max(REP.hypercube_limits(:,2))]);
            grid on; xlabel('f1'); ylabel('f2');
        end
        drawnow;
    end
    if(size(POS_fit,2)==3)
        h_fig = figure(1);
        h_par = plot3(POS_fit(:,1),POS_fit(:,2),POS_fit(:,3),'or'); hold on;
        h_rep = plot3(REP.pos_fit(:,1),REP.pos_fit(:,2),REP.pos_fit(:,3),'ok'); hold on;
        try
                set(gca,'xtick',REP.hypercube_limits(:,1)','ytick',REP.hypercube_limits(:,2)','ztick',REP.hypercube_limits(:,3)');
                axis([min(REP.hypercube_limits(:,1)) max(REP.hypercube_limits(:,1)) ...
                      min(REP.hypercube_limits(:,2)) max(REP.hypercube_limits(:,2))]);
        end
        grid on; xlabel('f1'); ylabel('f2'); zlabel('f3');
        drawnow;
        axis square;
    end
    display(['Generation #0 - Repository size: ' num2str(size(REP.pos,1))]);
    
    % Main MPSO loop
    stopCondition = false;
    while ~stopCondition
        
        % Select leader
        h = selectLeader(REP);
        
        % Update speeds and positions
        VEL = W.*VEL + C1*rand(Np,nVar).*(PBEST-POS) ...
                     + C2*rand(Np,nVar).*(repmat(REP.pos(h,:),Np,1)-POS);
        POS = POS + VEL;
        
        % Perform mutation
        POS = mutation(POS,gen,maxgen,Np,var_max,var_min,nVar,u_mut);
        
        % Check boundaries
        [POS,VEL] = checkBoundaries(POS,VEL,maxvel,var_max,var_min);       
        
        % Evaluate the population
        POS_fit = fun(POS);
        
        % Update the repository
        REP = updateRepository(REP,POS,POS_fit,ngrid);
        if(size(REP.pos,1)>Nr)
             REP = deleteFromRepository(REP,size(REP.pos,1)-Nr,ngrid);
        end
        
        % Update the best positions found so far for each particle
        pos_best = dominates(POS_fit, PBEST_fit);
        best_pos = ~dominates(PBEST_fit, POS_fit);
        best_pos(rand(Np,1)>=0.5) = 0;
        if(sum(pos_best)>1)
            PBEST_fit(pos_best,:) = POS_fit(pos_best,:);
            PBEST(pos_best,:) = POS(pos_best,:);
        end
        if(sum(best_pos)>1)
            PBEST_fit(best_pos,:) = POS_fit(best_pos,:);
            PBEST(best_pos,:) = POS(best_pos,:);
        end
        
        % Plotting and verbose
        if(size(POS_fit,2)==2)
            figure(h_fig); delete(h_par); delete(h_rep);
            h_par = plot(POS_fit(:,1),POS_fit(:,2),'or'); hold on;
            h_rep = plot(REP.pos_fit(:,1),REP.pos_fit(:,2),'ok'); hold on;
            try
                set(gca,'xtick',REP.hypercube_limits(:,1)','ytick',REP.hypercube_limits(:,2)');
                axis([min(REP.hypercube_limits(:,1)) max(REP.hypercube_limits(:,1)) ...
                      min(REP.hypercube_limits(:,2)) max(REP.hypercube_limits(:,2))]);
            end
            if(isfield(MultiObj,'truePF'))
                try delete(h_pf); end
                h_pf = plot(MultiObj.truePF(:,1),MultiObj.truePF(:,2),'.','color',0.8.*ones(1,3)); hold on;
            end
            grid on; xlabel('f1'); ylabel('f2');
            drawnow;
            axis square;
        end
        if(size(POS_fit,2)==3)
            figure(h_fig); delete(h_par); delete(h_rep); 
            h_par = plot3(POS_fit(:,1),POS_fit(:,2),POS_fit(:,3),'or'); hold on;
            h_rep = plot3(REP.pos_fit(:,1),REP.pos_fit(:,2),REP.pos_fit(:,3),'ok'); hold on;
            try
                set(gca,'xtick',REP.hypercube_limits(:,1)','ytick',REP.hypercube_limits(:,2)','ztick',REP.hypercube_limits(:,3)');
                axis([min(REP.hypercube_limits(:,1)) max(REP.hypercube_limits(:,1)) ...
                      min(REP.hypercube_limits(:,2)) max(REP.hypercube_limits(:,2)) ...
                      min(REP.hypercube_limits(:,3)) max(REP.hypercube_limits(:,3))]);
            end
            if(isfield(MultiObj,'truePF'))
                try delete(h_pf); end
                h_pf = plot3(MultiObj.truePF(:,1),MultiObj.truePF(:,2),MultiObj.truePF(:,3),'.','color',0.8.*ones(1,3)); hold on;
            end
            grid on; xlabel('f1'); ylabel('f2'); zlabel('f3');
            drawnow;
            axis square;
        end
        display(['Generation #' num2str(gen) ' - Repository size: ' num2str(size(REP.pos,1))]);
        
        % Update generation and check for termination
        gen = gen + 1;
        if(gen>maxgen), stopCondition = true; end
    end
    hold off;
end

% Function that updates the repository given a new population and its
% fitness
function REP = updateRepository(REP,POS,POS_fit,ngrid)
    % Domination between particles
    DOMINATED  = checkDomination(POS_fit);
    REP.pos    = [REP.pos; POS(~DOMINATED,:)];
    REP.pos_fit= [REP.pos_fit; POS_fit(~DOMINATED,:)];
    % Domination between nondominated particles and the last repository
    DOMINATED  = checkDomination(REP.pos_fit);
    REP.pos_fit= REP.pos_fit(~DOMINATED,:);
    REP.pos    = REP.pos(~DOMINATED,:);
    % Updating the grid
    REP        = updateGrid(REP,ngrid);
end

% Function that corrects the positions and velocities of the particles that
% exceed the boundaries
function [POS,VEL] = checkBoundaries(POS,VEL,maxvel,var_max,var_min)
    % Useful matrices
    Np = size(POS,1);
    MAXLIM   = repmat(var_max(:)',Np,1);
    MINLIM   = repmat(var_min(:)',Np,1);
    MAXVEL   = repmat(maxvel(:)',Np,1);
    MINVEL   = repmat(-maxvel(:)',Np,1);
    
    % Correct positions and velocities
    VEL(VEL>MAXVEL) = MAXVEL(VEL>MAXVEL);
    VEL(VEL     VEL(POS>MAXLIM) = (-1).*VEL(POS>MAXLIM);
    POS(POS>MAXLIM) = MAXLIM(POS>MAXLIM);
    VEL(POS     POS(POS end

% Function for checking the domination between the population. It
% returns a vector that indicates if each particle is dominated (1) or not
function dom_vector = checkDomination(fitness)
    Np = size(fitness,1);
    dom_vector = zeros(Np,1);
    all_perm = nchoosek(1:Np,2);    % Possible permutations
    all_perm = [all_perm; [all_perm(:,2) all_perm(:,1)]];
    
    d = dominates(fitness(all_perm(:,1),:),fitness(all_perm(:,2),:));
    dominated_particles = unique(all_perm(d==1,2));
    dom_vector(dominated_particles) = 1;
end

% Function that returns 1 if x dominates y and 0 otherwise
function d = dominates(x,y)
    d = all(x<=y,2) & any(x end
 

3 参考文献

​

  References:                                                           

   [1]Coello, C. A. C., Pulido, G. T., & Lechuga, M. S. (2004). Handling multiple objectives with particle swarm optimization. IEEE Tran-  sactions on evolutionary computation, 8(3), 256-279.                                

   [2]Sierra, M. R., & Coello, C. A. C. (2005, March). Improving PSO-  based multi-objective optimization using crowding, mutation and -dominance. In International Conference on Evolutionary Multi-Criterion Optimization (pp. 505-519). Springer Berlin Heidelberg.      

[3]刘俊贤,王宏强,陶新龙.基于改进多目标粒子群优化算法的雷达资源分配方法[J].中国电子科学研究院学报,2022,17(6):549-556565

[4]王万良,金雅文,陈嘉诚,李国庆,胡明志,董建杭.多角色多策略多目标粒子群优化算法[J].浙江大学学报:工学版,2022,56(3):531-541

4 Matlab代码实现