nsga-ⅱ算法matlab
时间: 2023-11-07 16:57:49 浏览: 53
NSGA-II算法是一种多目标优化算法,主要用于解决多目标优化问题。在MATLAB中,可以使用以下步骤实现NSGA-II算法:
1. 定义问题的目标函数和约束条件;
2. 初始化种群,可以使用随机数生成初始种群;
3. 计算每个个体的适应度,可以使用目标函数值和约束条件值计算适应度;
4. 对种群进行排序和拥挤度计算,以确定每个个体的等级和种群的多样性;
5. 选择父代个体,可以使用锦标赛选择或轮盘赌选择等方法;
6. 交叉和变异,生成子代个体;
7. 计算子代个体的适应度,并将它们合并到种群中;
8. 对种群进行排序和拥挤度计算,以确定每个个体的等级和种群的多样性;
9. 选择下一代个体,重复步骤5到8,直到达到指定的停止条件。
需要注意的是,NSGA-II算法是一种较为复杂的优化算法,需要深入了解其原理和实现细节,才能正确地编写MATLAB程序。
相关问题
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。
NSGA-Ⅱ算法 matlab代码
NSGA-II(Non-dominated Sorting Genetic Algorithm II)是一种常用的多目标优化算法,它是基于遗传算法的一种改进算法。NSGA-II算法通过非支配排序和拥挤度距离来维护种群的多样性,从而有效地解决了多目标优化问题。下面是NSGA-II算法的Matlab代码实现:
```
function [pop,fit] = nsga2(pop,fit,n,m,popsize,pcross,pmut)
% NSGA-II算法
% 输入:
% pop - 种群
% fit - 种群适应度
% n - 变量个数
% m - 目标个数
% popsize - 种群大小
% pcross - 交叉概率
% pmut - 变异概率
% 输出:
% pop - 新种群
% fit - 新种群适应度
% 计算拥挤度距离
function d = crowding_distance(f)
[m,n] = size(f);
d = zeros(m,1);
for i = 1:n
[~,idx] = sort(f(:,i));
d(idx(1)) = inf;
d(idx(end)) = inf;
for j = 2:m-1
d(idx(j)) = d(idx(j)) + (f(idx(j+1),i)-f(idx(j-1),i))/(f(idx(end),i)-f(idx(1),i));
end
end
end
% 非支配排序
function [F,S] = non_domination_sort(f)
[m,n] = size(f);
F{1} = [];
S{1} = zeros(m,1);
n(1) = 0;
for p = 1:m
S{1}(p) = 0;
for q = 1:m
if all(f(q,:)<=f(p,:)) && any(f(q,:)<f(p,:))
S{1}(p) = S{1}(p) + 1;
end
end
if S{1}(p) == 0
F{1} = [F{1} p];
n(1) = n(1) + 1;
end
end
i = 1;
while ~isempty(F{i})
Q = [];
for p = F{i}
for q = 1:m
if all(f(q,:)<=f(p,:)) && any(f(q,:)<f(p,:))
S{1}(q) = S{1}(q) - 1;
if S{1}(q) == 0
Q = [Q q];
n(i+1) = n(i+1) + 1;
end
end
end
end
i = i + 1;
F{i} = Q;
end
end
% 选择操作
function [pop,fit] = selection(pop,fit,n,m,popsize)
[m,n] = size(fit);
F = non_domination_sort(fit);
newpop = [];
newfit = [];
i = 1;
while length(newpop) + length(F{i}) <= popsize
% 按拥挤度距离排序
cd = crowding_distance(fit(F{i},:));
[~,idx] = sort(cd,'descend');
newpop = [newpop; pop(F{i}(idx),:)];
newfit = [newfit; fit(F{i}(idx),:)];
i = i + 1;
end
if length(newpop) < popsize
cd = crowding_distance(fit(F{i},:));
[~,idx] = sort(cd,'descend');
newpop = [newpop; pop(F{i}(idx(1:popsize-length(newpop))),:)];
newfit = [newfit; fit(F{i}(idx(1:popsize-length(newpop))),:)];
end
pop = newpop;
fit = newfit;
end
% 交叉操作
function pop = crossover(pop,pcross)
[m,n] = size(pop);
for i = 1:2:m
if rand < pcross
j = randi(n-1);
pop(i:i+1,j+1:end) = pop(i+1:-1:i,j+1:end);
end
end
end
% 变异操作
function pop = mutation(pop,pmut)
[m,n] = size(pop);
for i = 1:m
if rand < pmut
j = randi(n);
pop(i,j) = rand;
end
end
end
% 主程序
pop = rand(popsize,n);
fit = zeros(popsize,m);
for i = 1:popsize
fit(i,:) = objfun(pop(i,:));
end
for i = 1:100
pop = [pop; crossover(pop,pcross)];
pop = mutation(pop,pmut);
for j = popsize+1:size(pop,1)
fit(j,:) = objfun(pop(j,:));
end
[pop,fit] = selection(pop,fit,n,m,popsize);
end
end
```
其中,objfun是目标函数,需要根据具体问题进行定义。在使用该代码时,需要将objfun替换为自己定义的目标函数,并设置好其他参数。此外,该代码实现了非支配排序、拥挤度距离和选择操作,可以有效地维护种群的多样性。