How to define a binary decision variable as upper and lower bond in an optimization function?

Hello experts,

I have an optimization problem that i have to solve using improved particle swarm optimization and i want to define the binary variable (x2) in Matlab as constraint.

x2 = 0 for charge of battery

x2 = 1 for discharge of battery

how can i define it thank you in advance.

Answer 1

[Walter Roberson]

https://www.mathworks.com/help/gads/particle-swarm-optimization-algorithm.html

You cannot use integer constraints with the Mathworks provided particle swarm algorithm. You can force the initial positions to match the constraints but the velocity will always be continuous so the first step will move away from the constraints. There is no hook that you can use to confine the range of motion to integers.

[Usman Taya]

I am not using matlab toolbox of particle swarm algorithm. I have write code from scratch. I want to use binary variable in scratch codes. Is it possible to do that.

[Walter Roberson]

You might as well use the same mechanism that is used for ga() and some other optimization routines: use lower bound 0, upper bound 1, and have one of your parameters be a list of indices of which variables are subject to integer constraints.

As for implementation:

After a new position has been created, round() the components of the position that are integer constrained, and then apply normal boundary handling to keep it within lb / ub

[Usman Taya]

Hi Brother,

I didn't understand. Kindly could you explain it in detail with a small simple example.

Thank you very much for your help.

[Walter Roberson]

Code without integer constraints:

position = position + velocity;
position = apply_bounds_constraints(positions, constraint_information);

Code with integer constraints:

position = position + velocity;
position(integer_constraint_index) = round(position(integer_constraint_index));
position = apply_bounds_constraints(positions, constraint_information);

[Lahiru Ransara]

When I use Walter's code my Best Cost is getting same value for all the iterations. :( What I'm missing?

[Walter Roberson]

@Lahiru Ransara

As this situation was for the case of user-provided code for doing all of the genetic optimization, instead of using MATLAB Library functions, then it is difficult for us to know what is in the rest of the code.

Also, the velocity might come out to be less than +/- 1/2 in each component, so round() might be returning you to the same position.