how to write multi objective particle swarm optimization?

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harsh Brar
harsh Brar on 30 Apr 2022
Answered: Alan Weiss on 1 May 2022
I have two equation with 13 variables with some lower and upper bound.
function t=strength(x)
t(1) = -118.676+0.167.*x(1)+0.097.*x(2)+0.120.*x(3)+0.659.*x(4)-0.044.*x(5)-0.066.*x(6)+0.042.*x(7)+0.065.*x(8)-8.821.*x(9);
t(2) = -0.804-0.001.*x(1)-0.001.*x(2)+0.0.*x(3)+0.0.*x(4)-0.031.*x(5)+0.005.*x(6)-0.002.*x(7)+0.001.*x(8)-0.735.*x(9)+0.097.*x(10)+0.012.*x(11)+0.078.*x(12)-0.220.*x(13);
If 1st equation's output acts as an inputs for 2nd equation, how to formulate it in PSO.
So that one can evaluate the behavior of both the equations simultaneously.
For example: 1st equation about the cost of the product which should be low/fixed and the 2nd equation about the profit which should be high.
If one can perform the optimization, both the equations should be satisfy simultaneously.
clear all
options = optimoptions('particleswarm','SwarmSize',100,'HybridFcn',@fmincon);
obj = @(x)strength(x);
lb = [398 0 0 0 0 138 775 954 0.50 0.750 27 23.96 2];
ub = [402 0 0 0 0 142 779 959 0.50 0.750 27 23.96 2];
rng default % For reproducibility
nvars = 13;
[x,fval,exitflag,output] = particleswarm(obj,nvars,lb,ub,options)
i have formulated this code. but its not quite Satisfactorily right. I am novice in matlab. Anybody mind helping in this regard?

Answers (1)

Alan Weiss
Alan Weiss on 1 May 2022
As you probably understand, particleswarm is for single-objective optimization. You can fake the multiobjective part by taking a convex combination of objectives as your single objective, and then sweeping through the convex combinations, as done in this example. The idea is to take for α going from 0 to 1 and minimize that single objective. You have one objective to minimize and one to maximize, so if is the one to minimize, then you should minimize .
It might be easiest overall for you to use the Global Optimization Toolbox multiobjective solvers, gamultiobj or paretosearch. But do whatever you like.
Alan Weiss
MATLAB mathematical toolbox documentation




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