In this post, I’m going to show you a simple but very effective method to find Pareto optimal solutions for a multi objective optimization problem using Matlab. It is very easy, and minimum programming skill is required.
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Here are the details of the benchmark problem to be solved in this video.
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Let’s see how we find Pareto optimal solutions for this multi objective optimization problem.
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Matlab Code
multi_objective_function.m
function YY = multi_objective_function(X)
for i = 1:2
S1(i) = -10*exp(-0.2*sqrt(X(i).^2+X(i+1).^2));
end
F1 = sum(S1); % objective function 1
for i = 1:3
S2(i) = abs(X(i)).^0.8 + 5*sin(X(i).^3);
end
F2 = sum(S2); % objective function 2
YY = [F1 F2];
solving.m
function [x,fval,exitflag,output,population,score] = solving(nvars,lb,ub,PopulationSize_Data,MaxGenerations_Data)
%% This is an auto generated MATLAB file from Optimization Tool.
%% Start with the default options
options = optimoptions('gamultiobj');
%% Modify options setting
options = optimoptions(options,'PopulationSize', PopulationSize_Data);
options = optimoptions(options,'MaxGenerations', MaxGenerations_Data);
options = optimoptions(options,'CrossoverFcn', { @crossoverintermediate [] });
options = optimoptions(options,'Display', 'off');
options = optimoptions(options,'PlotFcn', { @gaplotpareto });
[x,fval,exitflag,output,population,score] = ...
gamultiobj(@multi_objective_function,nvars,[],[],[],[],lb,ub,[],options);
main_program.m
clc
clear all
close all
nvars = 3;
lb = [-5 -5 -5];
ub = [5 5 5];
PopulationSize_Data = 200;
MaxGenerations_Data = 50;
[x,fval,exitflag,output,population,score] = solving(nvars,lb,ub,PopulationSize_Data,MaxGenerations_Data);
optimal_solution = x
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Thanks alot for your help
Thank you !
Great video …. I would like to invite you to co-author a paper with me in the optimization of a structural engineering subject.
It would be a great honor.
Thank you!
How to solve that same problem of looking for the pareto optimum but using the simulated annealing heristics?
I don’t know multi objective simulated annealing algorithm
hello thank you for sharing, please how to do a multi-lens optimization if one of the variable is an integer 12:1:16
We may use rounding function of the related real number to make it “integer”