Adaptive Restart Hybrid Genetic Algorithm

Hello everyone!

In this post, I am going to show you my innovative version of Genetic Algorithm, called “Adaptive Restart Hybrid Genetic Algorithm”. This Genetic Algorithm has an adaptive restart mechanism, and please pay a close attention to the effect of the mechanism.

Did you know that Genetic Algorithm (GA) is a very popular optimization algorithm, often used to solve complex large scale optimization problems in many fields. Like other meta-heuristic algorithms, GA can only provide a probabilistic guarantee of the global optimal solution. Having a GA capable of finding the global optimal solution with high success probability is always desirable.

In this research, an innovative GA structure that can enhance the GA’s success probability of finding the global optimal solution is proposed. This version of GA has three innovations.

First, the GA is capable of restarting its search process, based on adaptive condition, to jump out of local optima, if being trapped, to enhance the GA’s exploration.

Second, the GA has a local solution generation module which is integrated in the GA loop to enhance the GA’s exploitation.

Third, a systematic method based on Taguchi Experimental Design is proposed to tune the GA parameter set to balance the exploration and exploitation to enhance the GA capability of finding the global optimal solution.

Effectiveness of the proposed GA is validated in 20 large-scale case study problems in which the proposed GA always outperforms five other algorithms available in the global optimization literature.

Let’s see how it works:

Matlab Code

population.m

function Y=population(p,d,LR,UR)
% d = dimensions of the problem
% p = population size
% LR = Lower bound
% UR = Up bound
Y=(UR-LR)*rand(p,d)+LR;

crossover.m

function Y=crossover(X,n)
% X = population
% n = no of pairs of chromosomes crossover
[x y]=size(X);
E=zeros(2*n,y);
for i= 1:n
    r=randi(x,1,2);
    while r(1)==r(2)
        r=randi(x,1,2);
    end
    % Note: r = selec two chromsomes for crossover
    A=X(r(1),:); % chromosome 1 for crossover
    B=X(r(2),:); % chromosome 2 for crossover
    c=1+randi(y-1); % select cut point
    D=A(1,c:y); % reserve
    A(1,c:y)=B(1,c:y);
    B(1,c:y)=D;
    % NOTE: A and B are chromosomes after crossover
    E(2*i-1,:)=A;
    E(2*i,:)=B;
end
Y=E;

mutation.m

function Y=mutation(X,n)
% X = population
% n = no of pairs of chromosomes crossover
[x y]=size(X);
E=zeros(2*n,y);
for i= 1:n
    r=randi(x,1,2);
    while r(1)==r(2)
        r=randi(x,1,2);
    end
    % Note: r = selec two chromsomes for mutation
    A=X(r(1),:); % chromosome 1 for mutation
    B=X(r(2),:); % chromosome 2 for mutation
    
    c=randi(y); % select cut point
    D=A(1,c); % reserve
    A(1,c)=B(1,c);
    B(1,c)=D;
    % NOTE: A and B are chromosomes after crossover
    E(2*i-1,:)=A;
    E(2*i,:)=B;
end
Y=E;

local_search.m

function YY=local_search(X,n,s,LR,UR)
% X = current best solution
% n = no. of chromosomes seleected
%clc
%clear all
%close all
%X=population(1);
%=====================================================
[x y]=size(X);
A=ones(2*y,1)*X;
j=1;

for i=1:y
...
end
% NOTE: A = LOCAL SOLUTION 
%=======================================================
% Randomly select n local solutions
[x1 y1]=size(A);
Y=zeros(n,y1);
for k = 1:n
...
end
[x2 y2]=size(Y);
for i=1:x2
    for j=1:y2
...
end
YY=Y;

evaluation.m

function Y = evaluation(X)
% X = population
[x y]=size(X);
d=y; % number of dimensions
C=zeros(1,x);
for j=1:x
    P=X(j,:);
    B=zeros(2,d);
    for i=1:d
        x1=P(1,i);
        B(1,i)=x1^2;
        B(2,i)=cos(2*pi*x1);
    end
    Z=-20*exp(-0.2*sqrt(sum(B(1,:))/d))-exp(sum(B(2,:))/d)+20+exp(1);
    C(1,j)=1/Z; % obbjective function
end
Y=C;

selection.m

function [YY1 YY2] = selection(P1,B,p,s)
% P1 - population
% B - fitness value 
% p - population size
% s = select top s chromsomes
%-------------------------------------------------------------------------
% Top selection operation
for i =1:s
    [r1 c1]=find(B==max(B));
    Y1(i,:)=P1(max(c1),:);
    Fn(i)=1/B(max(c1));
    P1(max(c1),:)=[];
    B(:,max(c1))=[];
    clear r1 c1
end
% Determine total fitness for the population
C=sum(B);
% Determine selection probability
D=B/C;
% Determine cumulative probability 
E= cumsum(D);
% Generate a vector constaining normalised random numbers
N=rand(1);
d1=1;
d2=s;
while d2 <= p-1
...
...
end
YY1=Y1;
YY2=Fn;
end

GA.m

clear all
clc
close all
%--------------------------------------------------------------------------
dim = 10; % dimensions of the problem
LR=-15; % Lower bound
UR=30;  % Up bound
%----------------------------------------------------------------
p= 100; % population size
c= 2; % crossover rate
m= 10; % mutation rate
s= 50; % number of generations to restart if getting stuck in local minimum
g= 1; % elite chromosomes
r= 1;% number of initial chromosomes
n= 4; % no of chromosomes RAMDOMLY selected from local (in %)
tg=500; % Total generations
redu=0.1;
%--------------------------------------------------------------------------
P1=population(r,dim,LR,UR); % Initial guess
w=1;
j=1;
K=0;
KK=0;
ww=1;
figure
title('Blue - Minimum         Red - Average');
xlabel('Generation')
ylabel('Objective function value')
hold on
while j <=tg
        P=population(p-r,dim,LR,UR);
        P(p-r+1:p,:)=P1;
        % Extended population
        lp=1;
        t= 15;% initial step size
        while lp==1
...
        end
end
minimum=min(K(:,2))
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Sorry! This is only a half of the Matlab code.

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Download the whole Matlab code here (Membership Code ID: 039)

No need to build the Matlab code from scratch because it’s very time-consuming. My idol, Jim Rohn, once said: “Time is more value than money. You can get more money, but you cannot get more time”. If you think this code can be used in your research/teaching work, you should download it and then customize/modify/apply it to your work, without any obligation of citing the original source if you don’t want. However, redistribution (i.e., downloading the code/script here and then making it available on another site on the Internet) is strictly prohibited.

If you have any question or problem, please contact Dr. Panda by email: learnwithpanda2018@gmail.com

Thank you very much and good luck with your research!

Dr.Panda