How to increase accuracy of optimization using genetic algorithm of the following code? Value obtained by ga = -2360 (approx.) and Actual value is = -2390. Percentage of accuracy by ga = 98.7%

clc

clear

price=[49.52, 47.94, 46.24, 43.34]';

inFlow=[1070,1070,1070 1070]';

x0 = [inFlow; zeros(size(inFlow))];

stor0 = 90000; % initial vol. of water stored in the reservoir (Acre-Feet)

k1 = 0.00003; % K-factor coefficient

k2 = 9; % K-factor offset

MW2kW = 1000; % MW to kW

C2A = 1.98347/24; % Convert from CFS to AF/HR

C = [C2A k1 k2 MW2kW]; % Vector of constants

N = length(inFlow);

DefineConstraints;

X = sym('x',[2*N,1]); % turbine flow and spill flow

F = sym('F',[N,1]); % flow into the reservoir

P = sym('P',[N,1]); % price

s0 = sym('s0'); % initial storage

c = sym({'c1','c2','c3','c4'}.','real'); % constants

TotFlow = X(1:N)+X(N+1:end);

S = cell(N,1);

S{1} = s0 + c(1)*(F(1)-TotFlow(1));

for ii = 2:N

S{ii} = S{ii-1} + c(1)*(F(ii)-TotFlow(ii));

end

k = c(2)*([s0; S(1:end-1)]+ S)/2+c(3);

MWh = k.*X(1:N)/c(4);

R = P.*MWh;

totR = -sum(R);

totR = subs(totR,[c;s0;P;F],[C';stor0;price;inFlow]);

matlabFunction(totR,'vars',{X.'},'file','objFcn_ga','Optimize',false);

PopulationSize_Data = 200;

EliteCount_Data = 2;

CrossoverFraction_Data = 0.4;

MaxGenerations_Data = 5000;

MaxStallGenerations_Data = 500;

InitialPopulationMatrix_Data = zeros(1,2*N);

FunctionTolerance_Data=1e-06;

ConstraintTolerance_Data=1e-3;

options = optimoptions('ga');

options = optimoptions(options,'PopulationSize', PopulationSize_Data);

options = optimoptions(options,'EliteCount', EliteCount_Data);

options = optimoptions(options,'CrossoverFraction', CrossoverFraction_Data);

options = optimoptions(options,'MaxGenerations', MaxGenerations_Data);

options = optimoptions(options,'MaxStallGenerations', MaxStallGenerations_Data);

options = optimoptions(options,'FunctionTolerance', FunctionTolerance_Data);

options = optimoptions(options,'ConstraintTolerance', ConstraintTolerance_Data);

options = optimoptions(options,'InitialPopulationMatrix', InitialPopulationMatrix_Data);

options = optimoptions(options,'SelectionFcn', @selectionroulette);

options = optimoptions(options,'CrossoverFcn', @crossoversinglepoint);

options = optimoptions(options,'MutationFcn', @mutationadaptfeasible);

options = optimoptions(options,'Display', 'iter');

options = optimoptions(options,'PlotFcn', { @gaplotbestf });

tic

[x3,fval3] = ga(@objFcn_ga,2*N,A,b,Aeq,beq,LB,UB,[],options);

toc

x3

fval3

%Define constraint

% Save the following script in the matlab file DefineConstraints.m

LB = zeros(2*N,1); % must have positive flow

UB = [25000*ones(N,1); % maximum turbine flow of 25,000 CFS

Inf(N,1)]; % no bound on spill flow

ot = ones(N,1);

b = -500*ot;

A = spdiags([-ot -ot],[0 N],N,N*2);

A2 = spdiags([ot ot -ot -ot],[0 N -1 N-1],N,N*2);

A2=full(A2);

b2 = 500*ot;

% remove the initial starting condition

A2(1,:) = [];

b2(1,:) = [];

% now add constraints for the -500 condition

A = [A; A2; -A2];

b = [b; b2; b2];

c = stor0 + C2A*cumsum(inFlow); % Convert CFS to AF

b = [b; 100000-c; -50000+c];

s = -C2A*sparse(tril(ones(N)));

s = [s s];

A = [A; s; -s];

Aeq = ones(1,2*N);

beq = sum(inFlow);

A=full(A);

Answer 1

[Alan Weiss]

You are getting a pretty good answer from the wrong solver. Your objective and constraints are all smooth, so you should not be using a Global Optimization Toolbox solver, unless you want to try MultiStart or GlobalSearch. I suggest that you use fmincon for this kind or problem. Here is what I did based on your setup:

rng default
x0 = 1e4*rand(size(LB))';
tic
[x3,fval3] = fmincon(@objFcn_ga,x0,A,b,Aeq,beq,LB,UB);
toc
x3
fval3

Here is what I got:

Local minimum possible. Constraints satisfied.

...

Elapsed time is 0.280546 seconds.

x3 =

1.0e+03 *

1.7600 1.2600 0.7600 0.5000 0.0000 0.0000 0.0000 0.0000

fval3 =

-2.3909e+03

Alan Weiss

MATLAB mathematical toolbox documentation