多目标水循环算法（MOWCA）【含Matlab源码 1433期】.zip

function [Non_Dominated_Solutions,Pareto_Front,NFEs,Elapsed_Time]=MOWCA_Unconstrained(objective_function,LB,UB,nvars,Npop,Nsr,dmax,max_it) %% Information % Last Revised: 10th April 2016 % Multi-objective Water Cycle Algorithm (MOWCA) (Standard Version) % This code is prepared for multiple objective functions, unconstrained, and continuous problems. % Note that in order to obey the copy-right rules, please kindly cite our published paper properly. Thank you. % A. Sadollah, H. Eskandar, J.H. Kim, A. Bahreininejad, �Water cycle algorithm for solving multi-objective optimization problems�, Soft Computing, 19(9) (2015) 2587-2603. % A. Sadollah, H. Eskandar, J.H. Kim, �Water cycle algorithm for solving constrained multi-objective problems�, Applied Soft Computing, 27 (2015) 279-298. % INPUTS: % objective_function: Objective functions which you wish to minimize or maximize % LB: Lower bound of a problem % UB: Upper bound of a problem % nvars: Number of design variables % Npop Population size % Nsr Number of rivers + sea % dmax Evporation condition constant % max_it: Maximum number of iterations % OUTPUTS: % Non_Dominated_Solutions: Optimum non-dominated solutions % Pareto_Front: Obtained optimum objective function values % NFEs: Number of function evaluations % Elapsed_Time Elasped time for solving an optimization problem %% Default Values for MOWCA format long g if (nargin <5 || isempty(Npop)), Npop=50; end if (nargin <6 || isempty(Nsr)), Nsr=4; end if (nargin <7 || isempty(dmax)), dmax=1e-16; end if (nargin <8 || isempty(max_it)), max_it=100; end %% -------------------------------------------------------------------------- % Create initial population tic N_stream=Npop-Nsr; NPF=Npop; % Pareto Front Archive Size ind.Position=[]; ind.Cost=[]; ind.Rank=[]; ind.DominationSet=[]; ind.DominatedCount=[]; ind.CrowdingDistance=[]; pop=repmat(ind,Npop,1); for i=1:Npop pop(i).Position=LB+(UB-LB).*rand; pop(i).Cost=objective_function(pop(i).Position); end [pop, F]=NonDominatedSorting(pop); % Non-dominated sorting pop=CalcCrowdingDistance(pop,F); % Calculate crowding distance pop=SortPopulation(pop); % Sort population %------------- Forming Sea, Rivers, and Streams -------------------------- sea=pop(1); river=pop(2:Nsr); stream=pop(Nsr+1:end); cs=[sea.CrowdingDistance';[river.CrowdingDistance]';stream(1).CrowdingDistance]; f=0; if length(unique(cs))~=1 CN=cs-max(cs); else CN=cs; f=1; end NS=round(abs(CN/(sum(CN)+eps))*N_stream); if f~=1 NS(end)=[]; end NS=sort(NS,'descend'); % ------------------------- Modification on NS ----------------------- i=Nsr; while sum(NS)>N_stream if NS(i)>1 NS(i)=NS(i)-1; else i=i-1; end end i=1; while sum(NS)<N_stream NS(i)=NS(i)+1; end if find(NS==0) index=find(NS==0); for i=1:size(index,1) while NS(index(i))==0 NS(index(i))=NS(index(i))+round(NS(i)/6); NS(i)=NS(i)-round(NS(i)/6); end end end NS=sort(NS,'descend'); NB=NS(2:end); %% %----------- Main Loop for MOWCA -------------------------------------------- disp('********** Multi-objective Water Cycle Algorithm (MOWCA)************'); disp('*Iterations Number of Pareto Front Members *'); disp('********************************************************************'); FF=zeros(max_it,numel(sea.Cost)); for i=1:max_it %---------- Moving stream to sea--------------------------------------- for j=1:NS(1) stream(j).Position=stream(j).Position+2.*rand(1).*(sea.Position-stream(j).Position); stream(j).Position=min(stream(j).Position,UB); stream(j).Position=max(stream(j).Position,LB); stream(j).Cost=objective_function(stream(j).Position); end %---------- Moving Streams to rivers----------------------------------- for k=1:Nsr-1 for j=1:NB(k) stream(j+sum(NS(1:k))).Position=stream(j+sum(NS(1:k))).Position+2.*rand(1,nvars).*(river(k).Position-stream(j+sum(NS(1:k))).Position); stream(j+sum(NS(1:k))).Position=min(stream(j+sum(NS(1:k))).Position,UB); stream(j+sum(NS(1:k))).Position=max(stream(j+sum(NS(1:k))).Position,LB); stream(j+sum(NS(1:k))).Cost=objective_function(stream(j+sum(NS(1:k))).Position); end end %---------- Moving rivers to Sea -------------------------------------- for j=1:Nsr-1 river(j).Position=river(j).Position+2.*rand(1,nvars).*(sea.Position-river(j).Position); river(j).Position=min(river(j).Position,UB); river(j).Position=max(river(j).Position,LB); river(j).Cost=objective_function(river(j).Position); end %-------------- Evaporation condition and raining process-------------- % Check the evaporation condition for rivers and sea for k=1:Nsr-1 if ((norm(river(k).Position-sea.Position)<dmax) || rand<0.1) for j=1:NB(k) stream(j+sum(NS(1:k))).Position=LB+rand(1,nvars).*(UB-LB); end end end % Check the evaporation condition for streams and sea for j=1:NS(1) if ((norm(stream(j).Position-sea.Position)<dmax)) stream(j).Position=LB+rand(1,nvars).*(UB-LB); end end %---------------------------------------------------------------------- pop=[pop;sea;river;stream]; [pop, F]=NonDominatedSorting(pop); % Non-dominated sorting pop=CalcCrowdingDistance(pop,F); % Calculate crowding distance pop=SortPopulation(pop); % Sort population pop=pop(1:NPF); [pop, F]=NonDominatedSorting(pop); % Non-dominated sorting pop=CalcCrowdingDistance(pop,F); % Calculate crowding distance [pop, F]=SortPopulation(pop); % Sort population sea=pop(1);river=pop(2:Nsr);stream=pop(Nsr+1:end); F1=pop(F{1}); dmax=dmax-(dmax/max_it); disp(['Iteration: ',num2str(i),' ((Number of Members in the Pareto Front)): ',num2str(numel(F{1}))]); FF(i,:)=sea.Cost; % Plot F1 costs figure(1); PlotCosts(F1); pause(0.01) end %% Optimization Results toc; Elapsed_Time=toc; NFEs=Npop*max_it; k=1; a=[river.Position stream.Position]; A=zeros(N_stream+Nsr-1,nvars); for i=1:N_stream+Nsr-1 A(i,:)=a(1,k:i*nvars); k=k+nvars; end Non_Dominated_Solutions=[sea.Position;A]; b=[[river.Cost]';[stream.Cost]']; Pareto_Front=[sea.Cost';b]; end