How can we insert upper and lower bounds in particle swarm optimization for more than one variable parameters that need to be optimized.

Hi sir/ madam,

I am using particle swarm optimization method for optimizing maximum amount of energy dissipated in an absorber (objective function). For this I have to go through solving ODE consists of more than one variable parameters. I am stucked while giving upper and lower bound for the variable parameters in (particleswarm) function for more than one variable. i actually want to know how can i feed upper and lower bound inside the particleswarm function for more than one variable parameter.

Answer 1

[Alan Weiss]

I am not sure that I understand you. You might be asking about bounding some control variables. Generally, all of your control variables are in one vector, typically called x, and your bounds are a vector of lower bounds and a vector of upper bounds. See Writing Scalar Objective Functions and Bound Constraints.

However, you might be asking about how to bound nonlinear functions of your control variables, meaning functions that depend on your control variables but are not, themselves, control variables. Those are called nonlinear inequality constraints, and are not available in the particleswarm solver. See Nonlinear Constraints. You can use patternsearch or ga for those constraints.

Alan Weiss

MATLAB mathematical toolbox documentation

[Rajni kant kumar]

Thank you for your kind attention, My actual question is ( how we can get more than one optimum value of coefficients for maximization of objective function. i am attaching my code below that will help you understand my question. In the code C,lamda1,E1 are required to vary simultaneously to get optimum objective function.

clc
clear all
%% the lower and upper bound working well while i choose only one variable coefficient for example 'C', but it doesn't work when we take two or three variable coefficient (C,lamda1,E1) simultaneously.
lb = 0.01;
ub = 1;

nvars=1;

fun=@myObj_opti;

[K,fval] = particleswarm(fun,nvars,lb,ub);

disp(['PSO: K = ' num2str(K)]);


%% I want to vary all the coefficients simultanously to get optimum of these for maximum objective function 




function obj = myObj_opti(C,lamda1,E1)

tspan=[0:0.1:50];

% Initial condition

y0=[0;0];

% C=1000
%  
% E1=0.01; 
% lmda1=0.05;



 [t,y]=ode45(@(t,y) nonlin_opti(t,y,C,lamda1,E1),tspan,y0);
 
% energy dissipated
 
p1=10;
 
E11=lmda1*y(:,2).*(y(:,2))';

% amount of input energy 

 E2=p1*y(:,2)';
         
 
 
E =E11./E2;

obj=-max(E);


end





function [f]=nonlin_opti(t,y,C,E1,lamda1)

%% sinusoidal force
 
f= zeros(2,1);

f(1)=y(2);
f(2)= -y(1)*lamda1+E1*y(2)+C;


end

[Walter Roberson]

You need to put all of your parameters into a single vector of values. Your code can unpack them from the vector.

function obj = myObj_opti(ClE)
  C = ClE(1);
  lamda1 = ClE(2);
  E1 = ClE(3);
  ...

[Rajni kant kumar]

Ok thanks Walter, i am trying.

[Rajni kant kumar]

And one more question, how can i insert the lb and ub in the particleswarm function for those parameters i.e. vector C1E?

[Walter Roberson]

The ub and lb vectors you pass to particleswarm should be the same length as the number of variables. particleswarm will use the bounds automatically for the creation function.

[Rajni kant kumar]

Thanks Walter Roberson for the help.