【优化求解】基于NSGA2算法求解多目标优化问题matlab代码

​1 模型简介

2 部分代码

clc;

clear;

close all;

%% Problem Definition

data=load('mydata');

R=data.R;

model.R=R;

model.method='cvar';

model.alpha=0.95;

CostFunction=@(x) PortMOC(x,model);      % Cost Function

nVar=size(R,2);             % Number of Decision Variables

VarSize=[1 nVar];   % Size of Decision Variables Matrix

VarMin=0;          % Lower Bound of Variables

VarMax=1;          % Upper Bound of Variables

% Number of Objective Functions

nObj=numel(CostFunction(unifrnd(VarMin,VarMax,VarSize)));

%% NSGA-II Parameters

MaxIt=100;      % Maximum Number of Iterations

nPop=50;        % Population Size

pCrossover=0.7;                         % Crossover Percentage

nCrossover=2*round(pCrossover*nPop/2);  % Number of Parnets (Offsprings)

pMutation=0.4;                          % Mutation Percentage

nMutation=round(pMutation*nPop);        % Number of Mutants

mu=0.02;                    % Mutation Rate

sigma=0.1*(VarMax-VarMin);  % Mutation Step Size

%% Initialization

empty_individual.Position=[];

empty_individual.Cost=[];

empty_individual.Out=[];

empty_individual.Rank=[];

empty_individual.DominationSet=[];

empty_individual.DominatedCount=[];

empty_individual.CrowdingDistance=[];

pop=repmat(empty_individual,nPop,1);

for i=1:nPop

    

    pop(i).Position=unifrnd(VarMin,VarMax,VarSize);

    

    [pop(i).Cost, pop(i).Out]=CostFunction(pop(i).Position);

    

end

% Non-Dominated Sorting

[pop, F]=NonDominatedSorting(pop);

% Calculate Crowding Distance

pop=CalcCrowdingDistance(pop,F);

% Sort Population

[pop, F]=SortPopulation(pop);

%% NSGA-II Main Loop

for it=1:MaxIt

    

    % Crossover

    popc=repmat(empty_individual,nCrossover/2,2);

    for k=1:nCrossover/2

        

        i1=randi([1 nPop]);

        p1=pop(i1);

        

        i2=randi([1 nPop]);

        p2=pop(i2);

        

        [popc(k,1).Position, popc(k,2).Position]=Crossover(p1.Position,p2.Position,VarMin,VarMax);

        

        [popc(k,1).Cost, popc(k,1).Out]=CostFunction(popc(k,1).Position);

        [popc(k,2).Cost, popc(k,2).Out]=CostFunction(popc(k,2).Position);

        

    end

    popc=popc(:);

    

    % Mutation

    popm=repmat(empty_individual,nMutation,1);

    for k=1:nMutation

        

        i=randi([1 nPop]);

        p=pop(i);

        

        popm(k).Position=Mutate(p.Position,mu,sigma,VarMin,VarMax);

        

        [popm(k).Cost, popm(k).Out]=CostFunction(popm(k).Position);

        

    end

    

    % Merge

    pop=[pop

         popc

         popm]; %#ok

     

    % Non-Dominated Sorting

    [pop, F]=NonDominatedSorting(pop);

    % Calculate Crowding Distance

    pop=CalcCrowdingDistance(pop,F);

    % Sort Population

    pop=SortPopulation(pop);

    

    % Truncate

    pop=pop(1:nPop);

    

    % Non-Dominated Sorting

    [pop, F]=NonDominatedSorting(pop);

    % Calculate Crowding Distance

    pop=CalcCrowdingDistance(pop,F);

    % Sort Population

    [pop, F]=SortPopulation(pop);

    

    % Store F1

    F1=pop(F{1});

    

    % Show Iteration Information

    disp(['Iteration ' num2str(it) ': Number of F1 Members = ' num2str(numel(F1))]);

    

    % Plot F1 Costs

    figure(1);

    PlotCosts(F1);

    pause(0.01);

    

end

%% Results

3 仿真结果

4 参考文献

[1]张利. NSGA2算法及其在电力系统稳定器参数优化中的应用[D]. 西南交通大学, 2013.

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