Genetic Algorithm and PSO not varying from initial point, regardless of parameters and fitness function

I am trying to compare various algorithms for a predetermined problem. I have solved the algorithms using fmincon and want to compare genetic algorithms and particle swarm optimisation. However, when adapting the code for either, the results don't vary from the initial population. I have played with various paramters and even completely changed the objective function with no result. Can someone please show me where I am going wrong and missing the boat. I would gratly appreciate it.

Here is my main code for the GA (very similar for PSO):

max_28 = 70;
min_28 = 10;
max_21 = 70;
min_21 = 10;

max_28 = max_28/100.*2500000./1200;
min_28 = min_28/100.*2500000./1200;
max_21 = max_21/100.*2000000./1200;
min_21 = min_21/100.*2000000./1200;

flow_decline_out_1 = readtable('Dam flow calculation.xlsx','Sheet','Flows','Range','L2:L97','ReadVariableNames',false);
flow_decline_out = cumsum(table2array([flow_decline_out_1]));
x0 = table2array([readtable('Dam flow calculation.xlsx','Sheet','Flows','Range','S2:S195','ReadVariableNames',false)]);

lb = transpose([10;10;zeros(96*2,1)]);
ub = transpose([70;70;ones(96*2,1).*75]);
% x0 = ub/2;

winter = 0;

if winter == 1
    tariff = table2array(readtable('Dam flow calculation.xlsx','Sheet','Tariff','Range','E3:E98','ReadVariableNames',false));
else
    tariff = table2array(readtable('Dam flow calculation.xlsx','Sheet','Tariff','Range','C3:C98','ReadVariableNames',false));
end 

fun = @(x)Power(x,tariff);

temp = ones(96);

A = [-ones(96,1)./100.*2500000./1200 zeros(96,1) tril(temp) zeros(96,96);
    ones(96,1)./100.*2500000./1200 zeros(96,1) -tril(temp) zeros(96,96);
    zeros(96,1) -ones(96,1)./100.*2000000./1200 -tril(temp) tril(temp);
    zeros(96,1) ones(96,1)./100.*2000000./1200 tril(temp) -tril(temp)];
b = [- min_21.*ones(96,1) + flow_decline_out;
    max_21.*ones(96,1) - flow_decline_out;
    - min_28.*ones(96,1);
    max_28.*ones(96,1)];

Aeq = [zeros(1,1) ones(1,1) ones(1,96) zeros(1,96);
    zeros(1,1) ones(1,1) -ones(1,96) ones(1,96)];
beq = [flow_decline_out(96);
    0];

% initPop = [transpose(x0);transpose(x0);transpose(x0);transpose(x0);transpose(x0);transpose(x0);transpose(x0);transpose(x0);transpose(x0);transpose(x0)];
% options = optimoptions('ga','PenaltyFactor',10000,'CrossoverFcn',{@crossoverintermediate, 1.2},'MutationFcn',@mutationadaptfeasible,'FitnessScalingFcn',@fitscalingrank,'CreationFcn','gacreationlinearfeasible','ConstraintTolerance',1e-6,'Display','iter','PlotFcn',{@gaplotselection, @gaplotbestf},'MaxGenerations',500,'MaxStallGenerations',100);
options = optimoptions("ga",'PlotFcn',{@gaplotbestf,@gaplotstopping},'Display','iter');
X0 = ub; % Start point (row vector)
options.InitialPopulationMatrix = X0;
% options.InitialPopulationMatrix = transpose(x0);
% options.MutationFcn = @mutationuniform;
% options.CrossoverFcn = @crossoverintermediate;
% options.SelectionFcn = @selectionroulette;
% options.CreationFcn = @gacreationuniform;
% options.FitnessScalingFcn = @fitscalingtop;
% options.InitialPopulationRange = [0;7500];
% % options.PopulationSize = 1000;
% options.MigrationDirection = 'forward';
[x,fval] = ga(fun,194,A,b,Aeq,beq,lb,ub,[],[],options);

xlswrite('Dam flow calculation.xlsx',transpose(x),'Flows','P2:P195');
xlswrite('Dam flow calculation.xlsx',1,'Calcs','K1');
winopen('Dam flow calculation.xlsx');

I read the tariff and some flow values from an excel file and use these in the calculations allowing me to have a base to compare the various methods.

And here is the objective function:

function pow = Power(x,tariff)
tariff1 = [zeros(1,2) transpose(tariff) transpose(tariff)];
% pow = tariff1*(transpose(x./eta(x)));
% pow = tariff1*x;
x1 = transpose(x);
pow = tariff1*x1;
% pow = sum(x);
end

Answer 1

[Alan Weiss]

You have a linear objective function and linear constraints. You should use linprog to solve your problem. Typically, a linear programming problem will have a unique solution, though sometimes there is a bounded or semi-bounded portion of an affine subspace of solutions with the same objective function.

ga and particleswarm are not appropriate solvers for this type of problem.

Alan Weiss

MATLAB mathematical toolbox documentation

[Michael Harmse]

Thank you for the reply Alan. I know the answer to the problem but am looking to compare other paramters such as solving rates between the various solvers. Why are GA and PSO not appropriate?

[Alan Weiss]

They are not appropriate because the problem has linear objective and constraints. Both of those algorithms are heuristic, not guaranteed to work in any case. The linprog linear programming solver is much, much faster, can handle much larger problems, and has supporting theory.

For guidance on which solver to choose, see Optimization Decision Table (optimiization toolbox) and Table for Choosing a Solver (global).

Alan Weiss

MATLAB mathematical toolbox documentation