韩老师多目标优化：NSGA-II算法
一. 内容简介
韩老师多目标优化：NSGA-II算法
视频: 【2022.2.5韩老师十七课时（上）多目标优化：NSGA-II算法】 https://www.bilibili.com/video/BV1v34y1y728/?share_source=copy_web&vd_source=7b377d4a833a67013df5f95f32b390f8
二. 软件环境
2.1 matlab
三.主要流程
3.1 代码
function Rfit = NSGAII(params,MultiObj)
Np = params.Np;
maxgen = params.maxgen;
pc = params.pc;
pm = params.pm;
ms = params.ms;
fun = fun(x);
nVar = MultiObj.nVar;
var_min = MultiObj.var_min(:);
var_max = MultiObj.var_max(:);
gen = 1;
P = repmat((var_max - var_min)', Np, 1) .* rand(Np, nVar) + repmat(var_min', Np, 1);
Pfit = fun(P);
Prank = FastNonDominatedSorting_Vectorized(Pfit);
[P, ~] = selectParentByRank(P, Prank);
Q = applyCrossoverAndMutation(P, pc, pm, ms, var_max, var_min);
h_fig = figure(1);
scatter(Pfit(:, 1), Pfit(:, 2), 20, 'filled', 'markerFaceAlpha', 0.3, 'MarkerFaceColor', [128, 193, 219] ./ 255);
hold on
h_rep = plot(Pfit(:,1), Pfit(:,2), 'ok');
hold on
grid on
xlabel('f1')
ylabel('f2')
drawnow
axis square;
display(['Generation #' num2str(gen) ' - First front size: ' num2str(sum(Prank==1))]);
stopCondition = false;
while ~stopCondition
R = [P; Q];
Rfit = fun(R);
Rrank = FastNonDominatedSorting_Vectorized(Rfit);
figure(h_fig)
delete(h_rep)
scatter(Rfit(1 : Np, 1), Rfit(1 : Np, 2), 20, 'filled', 'markerFaceAlpha', 0.3, 'MarkerFaceColor', [128, 193 219] ./ 255);
hold on
h_rep = plot(Rfit(1 : Np, 1), Rfit(1 : Np, 2),'ok');
hold on;
grid on
xlabel('f1')
ylabel('f2')
drawnow;
axis square;
display(['Generation #' num2str(gen) ' - First front size: ' num2str(sum(Rrank==1))]);
[Rrank,idx] = sort(Rrank, 'ascend');
Rfit = Rfit(idx, :);
R = R(idx, :);
[Rcrowd, Rrank, ~, R] = crowdingDistances(Rrank, Rfit, R);
P = selectParentByRankAndDistance(Rcrowd, Rrank, R);
Q = applyCrossoverAndMutation(P, pc, pm, ms, var_max, var_min);
gen = gen + 1;
if(gen > maxgen)
stopCondition = true;
end
end
end
function newParent = selectParentByRankAndDistance(Rcrowd, Rrank, R)
N = length(Rcrowd) / 2;
Npf = length(unique(Rrank));
newParent = zeros(N, size(R, 2));
pf = 1;
numberOfSolutions = 0;
while pf <= Npf
if numberOfSolutions + sum(Rrank == pf) <= N
newParent(numberOfSolutions + 1 : numberOfSolutions + sum(Rrank == pf), :) = R(Rrank == pf, :);
numberOfSolutions = numberOfSolutions + sum(Rrank == pf);
else
rest = N - numberOfSolutions;
lastPF = R(Rrank == pf,:);
lastPFdist = Rcrowd(Rrank == pf);
[~,idx] = sort(lastPFdist, 'descend');
lastPF = lastPF(idx, :);
newParent(numberOfSolutions + 1 : numberOfSolutions+rest, :) = lastPF(1 : rest, :);
numberOfSolutions = numberOfSolutions + rest;
end
pf = pf + 1;
end
end
function [sortCrowd, sortRank, sortFit, sortPop] = crowdingDistances(rank, fitness, pop)
sortPop = [];
sortFit = [];
sortRank = [];
sortCrowd = [];
Npf = length(unique(rank));
for pf = 1 : 1 : Npf
index = find(rank == pf);
temp_fit = fitness(index, :);
temp_rank = rank(index, :);
temp_pop = pop(index, :);
[temp_fit, sort_idx] = sortrows(temp_fit, 1);
temp_rank = temp_rank(sort_idx);
sortFit = [sortFit; temp_fit];
sortRank = [sortRank; temp_rank];
sortPop = [sortPop; temp_pop(sort_idx, :)];
temp_crowd = zeros(size(temp_rank));
for m = 1 : 1 : size(fitness, 2)
temp_max = max(temp_fit(:, m));
temp_min = min(temp_fit(:, m));
for l = 2 : 1 : length(temp_crowd) - 1
temp_crowd(l) = temp_crowd(l) + (abs(temp_fit(l - 1, m) - temp_fit(l + 1, m))) ./ (temp_max - temp_min);
end
end
temp_crowd(1) = Inf;
temp_crowd(length(temp_crowd)) = Inf;
sortCrowd = [sortCrowd; temp_crowd];
end
end
function Q = applyCrossoverAndMutation(parent, pc, pm, ms, var_max, var_min)
N = size(parent, 1);
nVar = size(parent, 2);
Q = parent;
cross_idx = rand(N, 1) < pc;
cross_idx = find(cross_idx);
for c = 1 : 1 : length(cross_idx)
selected = randi(N, 1, 1);
while selected == c
selected = randi(N, 1, 1);
end
cut = randi(nVar, 1, 1);
Q(c, :) = [parent(c, 1 : cut), parent(selected, cut + 1 : nVar)];
end
mutatedPop = Q + ms .* repmat((var_max - var_min)', N, 1) .* randn(N, nVar);
minVal = repmat(var_min', N, 1);
maxVal = repmat(var_max', N, 1);
mutatedPop(mutatedPop < minVal) = minVal(mutatedPop < minVal);
mutatedPop(mutatedPop > maxVal) = maxVal(mutatedPop > maxVal);
mut_idx = rand(N, nVar) < pm;
Q(mut_idx) = mutatedPop(mut_idx);
end
function [P1, P1rank] = selectParentByRank(P, Prank)
N = length(Prank);
left_idx = randi(N, N, 1);
right_idx = randi(N, N, 1);
while sum(left_idx == right_idx) > 0
right_idx(left_idx == right_idx) = randi(N, sum(left_idx == right_idx), 1);
end
winners = zeros(N, 1);
winners(Prank(left_idx) <= Prank(right_idx)) = left_idx(Prank(left_idx) <= Prank(right_idx));
winners(Prank(right_idx) < Prank(left_idx)) = right_idx(Prank(right_idx) < Prank(left_idx));
P1 = P(winners, :);
P1rank = Prank(winners, :);
end
function RANK = FastNonDominatedSorting_Vectorized(fitness)
Np = size(fitness, 1);
RANK = zeros(Np, 1);
current_vector = (1 : 1 : Np)';
current_pf = 1;
all_perm = [repmat((1 : 1 : Np)', Np', 1), reshape(repmat((1: 1: Np), Np, 1), Np ^ 2, 1)];
all_perm(all_perm(:, 1) == all_perm(:, 2), :) = [];
while ~isempty(current_vector)
if length(current_vector) == 1
RANK(current_vector) = current_pf;
break;
end
d = dominates(fitness(all_perm(:, 1), :), fitness(all_perm(:, 2), :));
dominated_particles = unique(all_perm(d == 1, 2));
if sum(~ismember(current_vector,dominated_particles)) == 0
break;
end
non_dom_idx = ~ismember(current_vector, dominated_particles);
RANK(current_vector(non_dom_idx)) = current_pf;
all_perm(ismember(all_perm(:, 1), current_vector(non_dom_idx)), :) = [];
all_perm(ismember(all_perm(:, 2), current_vector(non_dom_idx)), :) = [];
current_vector(non_dom_idx) = [];
current_pf = current_pf + 1;
end
end
function d = dominates(x,y)
d = (all(x <= y, 2) & any(x < y, 2));
end
function y = fun(x)
y = xxxx;
if x(1)
end
clear
clc
MultiObj.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.pc = 0.9;
params.pm = 0.5;
params.maxgen = 100;
params.ms = 0.05;
REP = NSGAII(params, MultiObj);