使用NSGA-II的投资组合优化

% % Copyright (c) 2015, Yarpiz (www.yarpiz.com) % All rights reserved. Please read the "license.txt" for license terms. % % Project Code: YPAP112 % Project Title: % Portfolio Optimization using Classic and Intelligent Methods in MATLAB % % Publisher: Yarpiz (www.yarpiz.com) % % Developer: S. Mostapha Kalami Heris (Member of Yarpiz Team) % % Contact Info: sm.kalami@gmail.com, info@yarpiz.com % 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