Genetic Algorithm Stuck to the Same Results

Hello. I have an optimization problem, that aims to schedule the machinery to redue the travelling distance of 5 parts. The problems consists of 8 machines and 5 parts. The machines should be organized in a serial way.

I created the functions that calculates the distances.

The two function work fine. If I enter a feasible sılution it comes with the right output.

Whereas the genetic algorithm part given below, always ends with the results of 79 and schedule to be converted in 5-4-3-2-1-8-7-6 in machine orders.

a(1:9:64)=1; Even this solution is better than 79 as it gives 67. Practically it is 1-2-3-4-5-6-7-8 in machine orders.

No matter how many runs, it always ends with the same results.

I don't know the reason but even manually I have multiple better solutions. Would you please help me figure the reason why it is stuck with a single solution?

++

clc; clear all; close all;

lb = zeros(1, 64);

ub = ones(1, 64);

beq=[1;1;1;1;1;1;1;1;1;1;1;1;1;1;1;1]; %Equal Part of the Equality Constraint

j=0;

for j=1:8

Aeq(j, 1+j-1:8:64+j-1)=1; %Equality Constraint

end

for j=1:8

Aeq(j+8, (j-1)*8+1:(j-1)*8+8)=1;

end

options = optimoptions('ga','PlotFcn', @gaplotbestf);

[x,fval,exitflag,output,population,scores] = ga(@TotalDistanceTravelledv2,64, [], [], Aeq, beq, lb, ub, [], 1, options)

z=0;

for s=1:8

z=z+1;

Results(z) = find(x((s-1)*8+1:(s-1)*8+8)==1);

end

++

%The first function that uses binary values as inputs.

function [TotalDistanceTravelled] = TotalDistanceTravelledv2(MachineInput)

ProductSchedule = readmatrix("UrunSira.xlsx");

z=0;

for s=1:8

z=z+1;

MachineRevised(z) = find(MachineInput((s-1)*8+1:(s-1)*8+8)==1);

end

MachineInput = MachineRevised;

for j=1:8

Sequence = MachineInput(j);

MachineLayout(j,Sequence)= 1;

end

TotalDistanceTravelled = DistanceTravelledCalculation(ProductSchedule, MachineLayout);

end

%The second function to calculate the distance

function [TotalDistanceTravelled] = DistanceTravelledCalculation(ProductSchedule, MachineLayout)

%Machine Layout eye(8) Dersteki Örnek

%ProductSchedule ise Dosyadan Alınıyor excel dosyası

%Machine Index

for s=1:8

MachineIndex(s) = find(MachineLayout(s,:)==1);

end

%Sure Hesabı

for i=1:5

for j=1:8

t = ProductSchedule(i, j); %Verinin Al?nmas?

if t==0

t=Schedule(i,j-1); %Arada "0" Varsa Onun Duzeltilmesi

end

Schedule(i,j)= find(MachineLayout(t,:)==1);

end

end

ScheduleBackup = Schedule;

%Distance Travelled Calculation

for j=1:5

for i=1:7

if Schedule(j,i+1)==0

Schedule(j,i+1)= Schedule(j,i);

end

DistanceTravelled(j,i) = abs(Schedule(j,i+1) - Schedule(j,i));

end

end

TotalDistanceTravelled = sum(DistanceTravelled,"all");

end

Answer 1

[Xinzhi Jiang]

Hi Fatih,

I didn't go through your code, but one tip that may help avoid a previous solution is to formulate that solution as constraints in your next run,

e.g.

abs(x(i) - your_undesirable_value_of_x(i)) - tolerence <= 0

Hope that helps.

[Fatih Yigit]

Strange that didn't wrok either. It brought a new result even worse. When I used initial population 1,2,3,...8, the result is 67. And there was no violation.

I don't know the reason but even the problem is not that complex. only 8!.

Thanks anyway. I hope someone will come with a solution.

[Xinzhi Jiang]

Hi,

I ran the files and it showed the error "GA does not solve problems with integer and equality constraints." If I understand correctly, the 64 variables are binary and there is Aeq at the same time. Did that not give an error as you ran your file?

[Fatih Yigit]

I believe it is the version of Matlab. Mine didn't give such feedback and there is no such information in Matlab website.

https://www.mathworks.com/help/gads/ga.html?s_tid=srchtitle_ga_1

Thanks anyway.