一. 内容简介

韩老师多目标优化：多目标粒子群算法

视频: 【.2.5韩老师十七课时（中）多目标优化：多目标粒子群算法】

/video/BV1eS4y157Xg/?share_source=copy_web&vd_source=7b377d4a833a67013df5f95f32b390f8

二. 软件环境

2.1 matlab

三.主要流程

3.1 代码

clearclcMultiObj.fun = @(x) [-10.*(exp(-0.2.*sqrt(x(:,1).^2+x(:,2).^2)) + exp(-0.2.*sqrt(x(:,2).^2+x(:,3).^2))), ...sum(abs(x).^0.8 + 5.*sin(x.^3),2)];MultiObj.nVar = 3;MultiObj.var_min = -5 .* ones(1, MultiObj.nVar);MultiObj.var_max = 5 .* ones(1, MultiObj.nVar);params.Np = 200;params.Nr = 150;params.maxgen = 100;params.W = 0.4;params.C1 = 2;params.C2 = 2;params.ngrid = 20;params.maxvel = 5;params.u_mut = 0.5;REP = MOPSO(params, MultiObj);

function REP = MOPSO(params, MultiObj)Np = params.Np;Nr = params.Nr;maxgen = params.maxgen;W = params.W;C1 = params.C1;C2 = params.C2;ngrid = params.ngrid;maxvel = params.maxvel;u_mut = params.u_mut;fun = MultiObj.fun;nVar = MultiObj.nVar;var_min = MultiObj.var_min(:);var_max = MultiObj.var_max(:);POS = repmat((var_max-var_min)', Np, 1) .* rand(Np, nVar) + repmat(var_min', Np, 1);VEL = zeros(Np, nVar);POS_fit = fun(POS);PBEST = POS;PBEST_fit = POS_fit;DOMINATED = checkDomination(POS_fit);REP.pos = POS(~DOMINATED, :);REP.pos_fit = POS_fit(~DOMINATED, :);REP = updateGrid(REP, ngrid);maxvel = (var_max - var_min) .* maxvel ./ 100;gen = 1;display(['Generation #0 - Repository size: ' num2str(size(REP.pos,1))]);stopCondition = false;while ~stopConditionh = selectLeader(REP);VEL = W .* VEL + C1 * rand(Np, nVar) .* (PBEST - POS) ...+ C2 * rand(Np, nVar) .* (repmat(REP.pos(h, :), Np, 1) - POS);POS = POS + VEL;POS = mutation(POS, gen, maxgen, Np, var_max, var_min, nVar, u_mut);[POS, VEL] = checkBoundaries(POS, VEL, maxvel, var_max, var_min); POS_fit = fun(POS);REP = updateRepository(REP, POS, POS_fit, ngrid);if(size(REP.pos, 1) > Nr)REP = deleteFromRepository(REP, size(REP.pos, 1) - Nr, ngrid);endpos_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, :);endif(sum(best_pos) > 1)PBEST_fit(best_pos, :) = POS_fit(best_pos, :);PBEST(best_pos, :) = POS(best_pos, :);enddisplay(['Generation #' num2str(gen) ' - Repository size: ' num2str(size(REP.pos,1))]);gen = gen + 1;if(gen > maxgen)stopCondition = true;endendh_rep = plot(REP.pos_fit(:,1),REP.pos_fit(:,2),'ok');endfunction REP = updateRepository(REP, POS, POS_fit, ngrid)DOMINATED = checkDomination(POS_fit);REP.pos = [REP.pos; POS(~DOMINATED, :)];REP.pos_fit = [REP.pos_fit; POS_fit(~DOMINATED, :)];DOMINATED = checkDomination(REP.pos_fit);REP.pos_fit = REP.pos_fit(~DOMINATED, :);REP.pos = REP.pos(~DOMINATED, :);REP = updateGrid(REP, ngrid);endfunction [POS, VEL] = checkBoundaries(POS, VEL, maxvel, var_max, var_min)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);VEL(VEL > MAXVEL) = MAXVEL(VEL > MAXVEL);VEL(VEL < MINVEL) = MINVEL(VEL < MINVEL);VEL(POS > MAXLIM) = (-1) .* VEL(POS > MAXLIM);POS(POS > MAXLIM) = MAXLIM(POS > MAXLIM);VEL(POS < MINLIM) = (-1) .* VEL(POS < MINLIM);POS(POS < MINLIM) = MINLIM(POS < MINLIM);endfunction dom_vector = checkDomination(fitness)Np = size(fitness, 1);dom_vector = zeros(Np, 1);all_perm = nchoosek(1 : Np, 2);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;endfunction d = dominates(x, y)d = all(x <= y, 2) & any(x < y, 2);endfunction REP = updateGrid(REP, ngrid)ndim = size(REP.pos_fit, 2);REP.hypercube_limits = zeros(ngrid + 1, ndim);for dim = 1 : ndimREP.hypercube_limits(:, dim) = linspace(min(REP.pos_fit(:, dim)), max(REP.pos_fit(:, dim)), ngrid + 1)';endnpar = size(REP.pos_fit, 1);REP.grid_idx = zeros(npar, 1);REP.grid_subidx = zeros(npar, ndim);for n = 1 : 1 : nparidnames = [];for d = 1 : 1 : ndimREP.grid_subidx(n, d) = find(REP.pos_fit(n, d) <= REP.hypercube_limits(:, d)', 1, 'first') - 1;if(REP.grid_subidx(n,d) == 0)REP.grid_subidx(n,d) = 1;endidnames = [idnames ',' num2str(REP.grid_subidx(n, d))];endREP.grid_idx(n) = eval(['sub2ind(ngrid.*ones(1,ndim)' idnames ');']);endREP.quality = zeros(ngrid, 2);ids = unique(REP.grid_idx);for i = 1 : length(ids)REP.quality(i, 1) = ids(i);REP.quality(i, 2) = 10 / sum(REP.grid_idx == ids(i));endendfunction selected = selectLeader(REP)prob = cumsum(REP.quality(:,2));sel_hyp = REP.quality(find(rand(1, 1) * max(prob) <= prob, 1, 'first'), 1);idx = 1 : 1 : length(REP.grid_idx);selected = idx(REP.grid_idx == sel_hyp);selected = selected(randi(length(selected)));endfunction REP = deleteFromRepository(REP, n_extra, ngrid)crowding = zeros(size(REP.pos, 1), 1);for m = 1 : 1 : size(REP.pos_fit, 2)[m_fit, idx] = sort(REP.pos_fit(:, m), 'ascend');m_up = [m_fit(2 : end); Inf];m_down = [Inf; m_fit(1 : end - 1)];distance = (m_up - m_down) ./ (max(m_fit) - min(m_fit));[~, idx] = sort(idx, 'ascend');crowding = crowding + distance(idx);endcrowding(isnan(crowding)) = Inf;[~, del_idx] = sort(crowding, 'ascend');del_idx = del_idx(1 : n_extra);REP.pos(del_idx, :) = [];REP.pos_fit(del_idx, :) = [];REP = updateGrid(REP, ngrid); endfunction POS = mutation(POS, gen, maxgen, Np, var_max, var_min, nVar, u_mut)fract = Np / 3 - floor(Np / 3);if fract < 0.5sub_sizes =[ceil(Np / 3), round(Np / 3), round(Np / 3)];elsesub_sizes =[round(Np / 3), round(Np / 3), floor(Np / 3)];endcum_sizes = cumsum(sub_sizes);nmut = round(u_mut * sub_sizes(2));if(nmut > 0)idx = cum_sizes(1) + randperm(sub_sizes(2), nmut);POS(idx, :) = repmat((var_max - var_min)', nmut, 1) .* rand(nmut, nVar) + repmat(var_min', nmut, 1);endper_mut = (1 - gen / maxgen) ^ (5 * nVar);nmut = round(per_mut * sub_sizes(3));if nmut > 0idx = cum_sizes(2) + randperm(sub_sizes(3), nmut);POS(idx, :) = repmat((var_max - var_min)', nmut, 1) .* rand(nmut, nVar) + repmat(var_min', nmut, 1);endend

上边就是全部代码了，

下面说里面有些不太理解的问题

这个函数里面实现的的和视频里面讲的还不太一样，这个还是有可能选到拥挤的点的，（视频里面也是这个）

function selected = selectLeader(REP)prob = cumsum(REP.quality(:,2));% 这块随机取得，有点按概率的意思sel_hyp = REP.quality(find(rand(1, 1) * max(prob) <= prob, 1, 'first'), 1);idx = 1 : 1 : length(REP.grid_idx);selected = idx(REP.grid_idx == sel_hyp);selected = selected(randi(length(selected)));end

REP.quality = zeros(ngrid, 2);

这网格质量，他实际是把网格分成了400个的，两个方向各20网格，但是这个还是写的20，好像是有点不够的

function REP = updateGrid(REP, ngrid)ndim = size(REP.pos_fit, 2);REP.hypercube_limits = zeros(ngrid + 1, ndim);for dim = 1 : ndimREP.hypercube_limits(:, dim) = linspace(min(REP.pos_fit(:, dim)), max(REP.pos_fit(:, dim)), ngrid + 1)';endnpar = size(REP.pos_fit, 1);REP.grid_idx = zeros(npar, 1);REP.grid_subidx = zeros(npar, ndim);for n = 1 : 1 : nparidnames = [];for d = 1 : 1 : ndimREP.grid_subidx(n, d) = find(REP.pos_fit(n, d) <= REP.hypercube_limits(:, d)', 1, 'first') - 1;if(REP.grid_subidx(n,d) == 0)REP.grid_subidx(n,d) = 1;endidnames = [idnames ',' num2str(REP.grid_subidx(n, d))];endREP.grid_idx(n) = eval(['sub2ind(ngrid.*ones(1,ndim)' idnames ');']);endREP.quality = zeros(ngrid, 2);ids = unique(REP.grid_idx);for i = 1 : length(ids)REP.quality(i, 1) = ids(i);REP.quality(i, 2) = 10 / sum(REP.grid_idx == ids(i));endend