How do I input linear constraints for the genetic algorithm function using discrete variables?

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Samer Alsamadi 2023-7-14

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https://ww2.mathworks.cn/matlabcentral/answers/1996213-how-do-i-input-linear-constraints-for-the-genetic-algorithm-function-using-discrete-variables

编辑： Torsten 2023-7-17

Hello,

I am using the matlab's ga algorithm to solve an optimization problem using discrete variables. My decision variable is set to take only integer values, then using a simple mapping function, my decision variable are transformed to the n'th indexed value in a list of specific values which i provide, where n is the integer value initially assigned to the decision variable. I followed the exact steps of the following link:

https://fr.mathworks.com/help/gads/solving-a-mixed-integer-engineering-design-problem-using-the-genetic-algorithm.html

Within this link, they inputed non-linear constraints using a function. In my case, I am interested in inserting linear constraints of inequality, using the matrices A and b. The algorithm seems to not respect these constraints. This is possible because the algorithm is applying the constraints to the decision variables in the form of integers rather than their transformed form.

How should I inser the A and b matrices in such a scenario?

Thank you.

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Torsten 2023-7-15

在 MATLAB Online 中打开

I just see in your code that you work with random inputs that change during each iteration. This is stochastic optimization and not possible with the usual MATLAB optimizers.

clear all

clc

rng('default') % For reproducibility

N = 10; % Nbr of electric vehicles

eta = 0.9;

C = 50; %kWh

P_ev = 8; %kWh

SoC_i = [0.5, 0.4, 0.6, 0.8, 0.1, 0.2, 0.5, 0.85, 0.55, 0.35];

SoC_f = 1;

time_step = 0.25; % 15 min. planning interval

delta_xi = zeros(1,10);

for i = 1:N

delta_xi_temp = ((SoC_f - SoC_i(i)) * C) / (eta * P_ev);

time_step = 0.25;

delta_xi(i) = ceil(delta_xi_temp / time_step) * time_step;

end

t_ar = [4,5,6,7,8,9,10,11,12,13];

t_dp = t_ar + 8;

A = diag(-1*ones(1,10)); % Arrival time inequality left side

b = [-t_ar(1);

-t_ar(2);

-t_ar(3);

-t_ar(4);

-t_ar(5);

-t_ar(6);

-t_ar(7);

-t_ar(8);

-t_ar(9);

-t_ar(10)]; % Arrival time inequality right side

lb = ones(1,10);

ub = 96*ones(1,10);

nvars = 10;

opts = optimoptions(@ga, ...

'PopulationSize', 150, ...

'MaxGenerations', 10, ...

'EliteCount', 10, ...

'FunctionTolerance', 1e-8, ...

'ConstraintTolerance',1.0000e-06, ...

'PlotFcn', @gaplotbestf);

[xbestDisc, fbestDisc, exitflag] = ga(@EVWithDisc, ...

10, A, b, [], [], lb, ub, [], 1:10, opts);

Optimization terminated: maximum number of generations exceeded.

xbestDisc = EVMapVariables(xbestDisc);

xbestDisc >= t_ar

ans = 1×10 logical array

1 1 0 1 0 0 0 0 0 0

function cost = EVWithDisc(x)

%cantileverVolumeWithDisc Calculate volume of a stepped cantilever

% V = cantileverVolumeWithDisc(x) calculates the volume of the stepped

% cantilever in the "Solving a Mixed Integer Engineering Design Problem

% Using the Genetic Algorithm" example. In this function, the variables

% x(3), x(4), x(5) and x(6) are chosen from a discrete set.

% Map the discrete variables

x = EVMapVariables(x);

% Volume of cantilever beam

cost = EV_fitness_func_(x);

end

function x = EVMapVariables(x)

all_X = 0:0.25:23.75;

x(1) = all_X(x(1));

x(2) = all_X(x(2));

x(3) = all_X(x(3));

x(4) = all_X(x(4));

x(5) = all_X(x(5));

x(6) = all_X(x(6));

x(7) = all_X(x(7));

x(8) = all_X(x(8));

x(9) = all_X(x(9));

x(10) = all_X(x(10));

end

function cost = EV_fitness_func_(chargingTimes)

rng('default')

a_t = 10 * rand(1,96);

N = 10; % Nbr of electric vehicles

eta = 0.9;

C = 50; %kWh

P_ev = 8; %kWh

SoC_i = [0.5, 0.4, 0.6, 0.8, 0.1, 0.2, 0.5, 0.85, 0.55, 0.35];

SoC_f = 1;

time_step = 0.25; % 15 minute time steps for planning

cost = 0;

delta_xi = zeros(1,10);

for i = 1:N

x_i = chargingTimes(i);

sum_internal = 0;

delta_xi(i) = ((SoC_f - SoC_i(i)) * C) / (eta * P_ev);

delta_xi(i) = ceil(delta_xi(i) / time_step) * time_step;

for t = x_i:0.25:x_i+delta_xi(i)

t_temp = t;

if t_temp > 23.75

t_temp = t_temp - 24;

end

index = (t_temp/0.25) + 1;

electricity_price = a_t(index);

sum_internal = sum_internal + P_ev * electricity_price * 0.25;

end

cost = cost + sum_internal;

end

Samer Alsamadi 2023-7-17

I wanted to try that method but read the writing linear constraints in the non-linear constraints part of the algorithm could lead to problems as the algo will mess things up. Do you have an idea if that is true or not? Thanks anyways for providing a code example!

Torsten 2023-7-17

编辑：Torsten 2023-7-17

Your constraints are linear in the transformed variables, but not in the solution variables.

Or are you able to use A (which is multiplied by x, not x_trans) and b to set the constraints you want on x_trans ?

What you did in your code is setting x(1:10) >= t_ar(1:10), not x_trans(1:10) >= t_ar(1:10). And from what you wrote this is what you actually want, isn't it ?

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