The following working MATLAB code can be used to execute/test the benchmark functions optimization and for future application developments. Each of the below mentioned function need to be in a separate file having the name as described here. The main file called Main_Runner is required to be executed and this will draw services from other functions as well as long as all these are in the same folder with the given name.

%% File Main_Runner

% % Program to optimize 23 test functions%/

clear;close all;clc;

population = 30;

numberOfChances = 500; % Iteration of lifeChoices

numberOfRuns = 1; % number of independent trials

bestCost = zeros(23,numberOfRuns);

for functionNum = 1:23

[xMin,xMax,dimension,objF] = GetFunctionDetails(functionNum);

for currentRun = 1:numberOfRuns

[bestCost(functionNum,currentRun), bestChoice, convergenceCurve]...

= LCO (population, numberOfChances, dimension, xMin, xMax,...

objF);

end

mean(bestCost(functionNum,:))

end

%% File LCO - The main optimizer

function [bestCost, bestChoice, convergenceCurve] = LCO (population,...

numberOfChances, dimension, xMin, xMax, objF)

x = initialise(xMin, xMax, population, dimension);

cost = zeros(1,population);

for i = 1:population

cost(i) = objF(x(i,:));

end

[x, cost] = getSortedPopulationAndCost(x, cost);

bestCost = cost(1);

bestChoice = x(1,:);

convergenceCurve = zeros(1,numberOfChances);

convergenceCurve(1) = bestCost;

r1 = 2.35;

r2 = 0.875;

r3 = 0.70;

n = ceil(sqrt(population));

for currentChance = 2:numberOfChances

f1 = (currentChance-1)/(numberOfChances-1);

f2 = 1-f1;

xn = zeros(1,dimension);

for current = 2:population

z=rand();

if (z > r2)

for currentDim = 1:dimension

random = rand(n,1);

xn(1,currentDim) = sum(random.*x(1:n,currentDim))/n;

end

elseif (z > r3)

if(length(xMax)>1)

for k = 1:dimension

xn(1,k) = xMax(k)-(x(current,k)-xMin(k))*rand();

end

else

xn(1,:) = xMax-(x(current,:)-xMin)*rand();

end

else

betterDiff = f2*r1*(x(current-1,:) - x(current,:));

bestDiff = f1*r1*(x(1,:) - x(current,:));

for currentDim = 1:dimension

xn(currentDim) = x(current,currentDim)...

+ rand()*betterDiff(1,currentDim)...

+ rand()*bestDiff(1,currentDim);

end

end

if(prod(xn >= xMin) && prod(xn <= xMax))

currCost = objF(xn);

if (currCost < cost(current))

x(current,:) = xn;

cost(current) = currCost;

end

end

end

[x, cost] = getSortedPopulationAndCost(x, cost);

bestCost = cost(1);

bestChoice = x(1,:);

convergenceCurve(currentChance) = bestCost;

end

end

function x = initialise(xMin, xMax, population, dimension)

if (size(xMin,2) == 1)

xMin = repmat(xMin, population, dimension);

else

xMin = repmat(xMin, population, 1);

end

if (size(xMax,2) == 1)

xMax = repmat(xMax, population, dimension);

else

xMax = repmat(xMax, population, 1);

end

x = xMin + (xMax - xMin).*rand(population, dimension);

end

function [x, cost] = getSortedPopulationAndCost(x, cost)

[cost, index] = sort(cost, 'ascend');

x = x(index,:);

end

%% Function GetFunctionDetails

function [xMin,xMax,dimension,objF] = GetFunctionDetails(functionNum)

switch functionNum

case 1

objF = @F1;

xMin = -100;

xMax = 100;

dimension = 30;

case 2

objF = @F2;

xMin = -10;

xMax = 10;

dimension = 30;

case 3

objF = @F3;

xMin = -100;

xMax = 100;

dimension = 30;

case 4

objF = @F4;

xMin = -100;

xMax = 100;

dimension = 30;

case 5

objF = @F5;

xMin = -30;

xMax = 30;

dimension = 30;

case 6

objF = @F6;

xMin = -100;

xMax = 100;

dimension = 30;

case 7

objF = @F7;

xMin = -1.28;

xMax = 1.28;

dimension = 30;

case 8

objF = @F8;

xMin = -500;

xMax = 500;

dimension = 30;

case 9

objF = @F9;

xMin = -5.12;

xMax = 5.12;

dimension = 30;

case 10

objF = @F10;

xMin = -32;

xMax = 32;

dimension = 30;

case 11

objF = @F11;

xMin = -600;

xMax = 600;

dimension = 30;

case 12

objF = @F12;

xMin = -50;

xMax = 50;

dimension = 30;

case 13

objF = @F13;

xMin = -50;

xMax = 50;

dimension = 30;

case 14

objF = @F14;

xMin = -65.536;

xMax = 65.536;

dimension = 2;

case 15

objF = @F15;

xMin = -5;

xMax = 5;

dimension = 4;

case 16

objF = @F16;

xMin = -5;

xMax = 5;

dimension = 2;

case 17

objF = @F17;

xMin = [-5,0];

xMax = [10,15];

dimension = 2;

case 18

objF = @F18;

xMin = -2;

xMax = 2;

dimension = 2;

case 19

objF = @F19;

xMin = 0;

xMax = 1;

dimension = 3;

case 20

objF = @F20;

xMin = 0;

xMax = 1;

dimension = 6;

case 21

objF = @F21;

xMin = 0;

xMax = 10;

dimension = 4;

case 22

objF = @F22;

xMin = 0;

xMax = 10;

dimension = 4;

case 23

objF = @F23;

xMin = 0;

xMax = 10;

dimension = 4;

end

end

% F1 begins here

function cost = F1(x)

cost = sum(x.^2);

end

% F2 begins here

function cost = F2(x)

cost = sum(abs(x))+prod(abs(x));

end

% F3 begins here

function cost = F3(x)

dimension = size(x,2);

cost = 0;

for i = 1:dimension

cost = cost + sum(x(1:i))^2;

end

end

% F4 begins here

function cost = F4(x)

cost = max(abs(x));

end

% F5 begins here

function cost = F5(x)

dimension = size(x,2);

cost = sum(100*(x(2:dimension)-(x(1:dimension-1).^2))...

.^2+(x(1:dimension-1)-1).^2);

end

% F6 begins here

function cost = F6(x)

cost = sum(abs((x+.5)).^2);

end

% F7 begins here

function cost = F7(x)

dimension = size(x,2);

cost = sum([1:dimension].*(x.^4))+rand;

end

% F8 begins here

function cost = F8(x)

cost = sum(-x.*sin(sqrt(abs(x))));

end

% F9 begins here

function cost = F9(x)

dimension = size(x,2);

cost = sum(x.^2-10*cos(2*pi.*x))+10*dimension;

end

% F10 begins here

function cost = F10(x)

dimesnion = size(x,2);

cost = -20*exp(-.2*sqrt(sum(x.^2)/dimesnion))...

-exp(sum(cos(2*pi.*x))/dimesnion)+20+exp(1);

end

% F11 begins here

function cost = F11(x)

dimension = size(x,2);

cost = sum(x.^2)/4000-prod(cos(x./sqrt([1:dimension])))+1;

end

% F12 begins here

function cost = F12(x)

dimension = size(x,2);

cost = (pi/dimension)*(10*((sin(pi*(1+(x(1)+1)/4)))^2)...

+sum((((x(1:dimension-1)+1)./4).^2).*(1+10.*...

((sin(pi.*(1+(x(2:dimension)+1)./4)))).^2))+...

((x(dimension)+1)/4)^2)+sum(Ufun(x,10,100,4));

end

% F13 begins here

function cost = F13(x)

dimension = size(x,2);

cost = .1*((sin(3*pi*x(1)))^2+sum((x(1:dimension-1)-1).^2.*...

(1+(sin(3.*pi.*x(2:dimension))).^2))+((x(dimension)-1)^2)*...

(1+(sin(2*pi*x(dimension)))^2))+sum(Ufun(x,5,100,4));

end

% F14 begins here

function cost = F14(x)

aS = [-32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 -32 -16 0 16 32 ...

-32 -16 0 16 32; -32 -32 -32 -32 -32 -16 -16 -16 -16 -16 0 0 0 0 ...

0 16 16 16 16 16 32 32 32 32 32];

for j=1:25

bS(j) = sum((x'-aS(:,j)).^6);

end

cost = (1/500+sum(1./([1:25]+bS))).^(-1);

end

% F15 begins here

function cost = F15(x)

aK = [.1957 .1947 .1735 .16 .0844 .0627 .0456 .0342 .0323 .0235 .0246];

bK = [.25 .5 1 2 4 6 8 10 12 14 16];bK=1./bK;

cost = sum((aK-((x(1).*(bK.^2+x(2).*bK))./(bK.^2+x(3).*bK+x(4)))).^2);

end

% F16 begins here

function cost = F16(x)

cost = 4*(x(1)^2)-2.1*(x(1)^4)+(x(1)^6)/3+x(1)*x(2)-4*(x(2)^2)+...

4*(x(2)^4);

end

% F17 begins here

function cost = F17(x)

cost = (x(2)-(x(1)^2)*5.1/(4*(pi^2))+5/pi*x(1)-6)^2+10*(1-1/(8*pi))*...

cos(x(1))+10;

end

% F18 begins here

function cost = F18(x)

cost =(1+(x(1)+x(2)+1)^2*(19-14*x(1)+3*(x(1)^2)-14*x(2)+6*x(1)*x(2)+...

3*x(2)^2))*(30+(2*x(1)-3*x(2))^2*(18-32*x(1)+12*(x(1)^2)+48*...

x(2)-36*x(1)*x(2)+27*(x(2)^2)));

end

% F19 begins here

function cost = F19(x)

aH = [3 10 30;.1 10 35;3 10 30;.1 10 35];cH=[1 1.2 3 3.2];

pH = [.3689 .117 .2673;.4699 .4387 .747;.1091 .8732 .5547;.03815 ...

.5743 .8828];

cost = 0;

for i = 1:4

cost = cost-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));

end

end

% F20 begins here

function cost = F20(x)

aH = [10 3 17 3.5 1.7 8;.05 10 17 .1 8 14;3 3.5 1.7 10 17 8;17 8 ...

.05 10 .1 14];

cH = [1 1.2 3 3.2];

pH = [.1312 .1696 .5569 .0124 .8283 .5886;.2329 .4135 .8307 .3736 ...

.1004 .9991;.2348 .1415 .3522 .2883 .3047 .6650;.4047 .8828 ...

.8732 .5743 .1091 .0381];

cost = 0;

for i = 1:4

cost = cost-cH(i)*exp(-(sum(aH(i,:).*((x-pH(i,:)).^2))));

end

end

% F21 begins here

function cost = F21(x)

aSH = [4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;8 ...

1 8 1;6 2 6 2;7 3.6 7 3.6];

cSH = [.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

cost = 0;

for i = 1:5

cost = cost-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);

end

end

% F22 begins here

function cost = F22(x)

aSH = [4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;...

8 1 8 1;6 2 6 2;7 3.6 7 3.6];

cSH = [.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

cost = 0;

for i = 1:7

cost = cost-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);

end

end

% F23 begins here

function cost = F23(x)

aSH = [4 4 4 4;1 1 1 1;8 8 8 8;6 6 6 6;3 7 3 7;2 9 2 9;5 5 3 3;...

8 1 8 1;6 2 6 2;7 3.6 7 3.6];

cSH = [.1 .2 .2 .4 .4 .6 .3 .7 .5 .5];

cost = 0;

for i = 1:10

cost = cost-((x-aSH(i,:))*(x-aSH(i,:))'+cSH(i))^(-1);

end

end

function cost = Ufun(x,a,k,m)

cost = k.*((x-a).^m).*(x>a)+k.*((-x-a).^m).*(x<(-a));

end

%% Function Analysis

%% This may not be required is analysis is undesired

format long;

for functionNum = 1:23

fprintf('Analysis for function %d \n', functionNum);

bestBestCost(functionNum) = min(bestCost(functionNum,:));

worstBestCost(functionNum) = max(bestCost(functionNum,:));

meanBestCost(functionNum) = mean(bestCost(functionNum,:));

stdBestCost(functionNum) = std(bestCost(functionNum,:));

fprintf('Best = %f, Worst = %f, Mean = %f, Std = %f \n\n',...

bestBestCost(functionNum), worstBestCost(functionNum),...

meanBestCost(functionNum), stdBestCost(functionNum));

end