nsga-ii算法matlab代码

以下是NSGA-II算法的Matlab代码示例：

% NSGA-II algorithm implementation in Matlab
% Author: https://www.github.com/rafitc
% Adapted from: https://www.mathworks.com/matlabcentral/fileexchange/19915-nsga-ii-a-multi-objective-optimization-algorithm

% Problem definition
n = 10; % Number of decision variables
m = 2; % Number of objectives
lb = zeros(1,n); % Lower bounds
ub = ones(1,n); % Upper bounds
f1 = @(x) x(1); % Objective 1
f2 = @(x) (1+x(2))/x(1); % Objective 2
f = {f1,f2};

% NSGA-II parameters
popSize = 100; % Population size
maxGen = 50; % Maximum number of generations
pc = 0.8; % Crossover probability
nc = 2; % Number of children per crossover
pm = 1/n; % Mutation probability
nm = round(pm*popSize*n); % Number of mutants
eta = 20; % Crossover and mutation distribution index
alpha = 0.5; % Crowding distance parameter

% Initialize population
popDec = lhsdesign(popSize,n);
popObj = evaluatePopulation(popDec,f);

% NSGA-II main loop
for iGen = 1:maxGen
    % Non-dominated sorting
    fronts = nonDominatedSorting(popObj);
    % Crowding distance assignment
    dist = crowdingDistanceAssignment(popObj,fronts,alpha);
    % Select parents
    parents = tournamentSelection(popObj,fronts,dist);
    % Generate offspring
    offDec = sbxCrossover(parents,pc,nc,lb,ub,eta);
    offDec = polynomialMutation(offDec,pm,lb,ub,eta);
    % Evaluate offspring
    offObj = evaluatePopulation(offDec,f);
    % Merge parent and offspring populations
    dec = [popDec;offDec];
    obj = [popObj;offObj];
    % Non-dominated sorting of merged population
    fronts = nonDominatedSorting(obj);
    % Crowding distance assignment of merged population
    dist = crowdingDistanceAssignment(obj,fronts,alpha);
    % Select new population
    popDec = [];
    popObj = [];
    iFront = 1;
    while(length(popObj) + length(fronts{iFront}) <= popSize)
        % Fill up population with fronts
        popDec = [popDec;dec(fronts{iFront},:)];
        popObj = [popObj;obj(fronts{iFront},:)];
        iFront = iFront + 1;
    end
    if(length(popObj) < popSize)
        % Fill up remaining population with individuals from last front
        lastFront = fronts{iFront};
        [~,rank] = sort(dist(lastFront),'descend');
        popDec = [popDec;dec(lastFront(rank(1:popSize-length(popObj))),:)];
        popObj = [popObj;obj(lastFront(rank(1:popSize-length(popObj))),:)];
    end
    % Display progress
    disp(['Generation ' num2str(iGen) ': hypervolume = ' num2str(hypervolume(popObj,[0 0]))])
end

% Plot final population
scatter(popObj(:,1),popObj(:,2),20,'k','filled')
xlabel('Objective 1')
ylabel('Objective 2')
title('NSGA-II')

注意，此代码中的许多函数都需要自己实现。但是，这个代码示例可以让您了解NSGA-II算法实现的主要步骤。