# Matlab multi population genetic algorithm

## get ready

Before writing your own code, you should understand the basic structure of the algorithm. For details, please refer to my previous articles outline Or here Simple function optimization Or more advanced nonlinear programming problem and TSP problem

Although the article is simple, it can also understand the basic parameters and specific algorithm structure.

## Multi population genetic algorithm

Although ordinary genetic algorithm can also solve some simple problems, it has many defects and deficiencies, which is similar to the premature problem: all individuals in the population prematurely evolve to the same state and stop evolution.

Add to the traditional genetic algorithm:

- Multiple groups of different control parameters to achieve different search purposes;
- The migration operator realizes the coevolution of multiple groups
- Artificial selection operators are used to preserve the best individuals in each group and form the elite population, and serve as the basis for judging the convergence of the algorithm.

This article focuses on the description of the added content. Please go to the previous article for the basic genetic algorithm.

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Max=sin(π⋅xy)+sin(y2)x,y∈[0,2]

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\left\{ \begin{array}{l} \pi \cdot xy=\dfrac{k_1\pi}{2}\Rightarrow xy=\dfrac{k_1}{2}\ \ y^2=\dfrac{k_2\pi}{2}\Rightarrow y=\sqrt{\dfrac{k_2\pi}{2}}\ \ x,y∈\left[ 0,2 \right]\ \end{array} \right. \,\,\,\,\,\,\,\,k_1,k_2,k_3 is any integer
⎩⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎧π⋅xy=2k1π⇒xy=2k1y2=2k2π⇒y=2k2π
x,y ∈ [0,2] k1, k2, k3 are arbitrary integers

The Matlab genetic algorithm toolbox of Sheffield University is selected to realize the algorithm.

The import of the toolbox is very simple. You can download and import it on the Internet.

Because the operation methods of crossover and mutation in this paper have nothing to do with fitness, only the sorting in the selection operation is related to fitness, so the sorting determines the overall selection value trend (maximum or minimum) of genetic algorithm.

### Population initialization and calculation of initial population fitness

- Initial parameter setting

clc clear close all %% Defining genetic algorithm parameters NIND=40; %Number of individuals NVAR=2; %Dimension of variable MAXGEN=10; %Maximum genetic algebra PRECI=10; %Precision of variables GGAP=0.9; %generation gap MP=10; %Population number of multiple populations Y_max=0; %optimal value px=0.7+(0.9-0.7)*rand(MP,1); %Crossover probability (0).7,0.9) pm=0.001+(0.05-0.001)*rand(MP,1); %Variation probability (0).001,0.05) Scope_individual=[0 0;2 2]; %Individual independent variable range FieldD=[rep(PRECI,[1,NVAR]);Scope_individual;rep([1;0;1;1],[1,NVAR])]; %Area descriptor Chrom=cell(1,MP); ObjV=cell(1,MP); gen=0; %Initial genetic algebra gen_keep=0; %Initial preserving algebra MaxObjV=zeros(MP,1); %Record elite populations MaxChrom=zeros(MP,NVAR*PRECI); %Record the encoding of elite populations FitnV=cell(1,MP); SelCh=cell(1,MP); for i=1:MP Chrom{i}=crtbp(NIND,NVAR*PRECI); %Initial population end for i=1:MP X=bs2rv(Chrom{i},FieldD); %Calculate the decimal conversion of the initial population ObjV{i}=Multi_fun(X); end

Multiple targets are not set for multiple groups here. In the early parameter setting stage:

The crossover probability and mutation probability are transformed into randomly transformed vectors in the corresponding range, representing different parameters of each population.

Add the dimension of the variable and calculate the binary digits of the actual individual
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Set the cell array to store the individual and fitness of each population independently.

### Calculate fitness

- Create a separate. m file to calculate fitness

function ObjV=Multi_fun(X) [m,~]=size(X); ObjV=zeros(m,1); for i=1:m ObjV(i,1)=sin(pi*X(i,1)*X(i,2))+sin(X(i,2)^2); end end

### Single population genetic algorithm

- In this step, it is equivalent to a generation of independent evolution for all populations.

gen=gen+1; for i=1:MP FitnV{i}=ranking(-ObjV{i}); %Assign fitness values SelCh{i}=select('sus',Chrom{i},FitnV{i},GGAP); %choice SelCh{i}=recombin('xovsp',SelCh{i},px(i)); %recombination SelCh{i}=mut(SelCh{i},pm(i)); %variation X=bs2rv(SelCh{i},FieldD); %Calculate the decimal conversion of the initial population ObjVSel=Multi_fun(X); %Calculate objective function value [Chrom{i},ObjV{i}]=reins(Chrom{i},SelCh{i},1,1,ObjV{i},ObjVSel); %Reinsert end

For detailed explanation of related functions, see Simple function optimization . Although they all seek the maximum value, different from the process of simple function optimization, the optimization objective function is not modified inside the fitness function, but a negative sign is taken for the fitness in the sorting operation, which is actually the same as the effect of changing inside the fitness.

### immigrant

- Migration operation makes the connection between various populations, which is also the most important part of multi population genetic algorithm

[Chrom,ObjV]=Multi_immigration(Chrom,ObjV); %Immigration operation

- Select the best individual in each population for migration. Replace the worst individual in the immigrant population with the immigrant individual.
- M u l t i _ i m m i g r a t i o n Multi\_immigration Multi_immigration

function [Chrom,ObjV]=Multi_immigration(Chrom,ObjV) %%Immigration operator MP=length(Chrom); for i=1:MP [~,MaxI]=max(ObjV{i}); Total_target=i+1; if Total_target>MP;Total_target=mod(Total_target,MP);end %Guaranteed less than MP [~,MinI]=min(ObjV{Total_target}); %%The worst individual of the target population is replaced by the best individual of the source population Chrom{Total_target}(MinI,:)=Chrom{i}(MaxI,:); ObjV{Total_target}(MinI,:)=ObjV{i}(MaxI,:); end end

### Manual selection

- The optimal individuals of each population are selected to form a new optimal population

[MaxObjV,MaxChrom]=Artificial_selection(Chrom,ObjV,MaxObjV,MaxChrom); %Manual selection

- A r t i f i c i a l _ s e l e c t i o n Artificial\_selection Artificial_selection

function [MaxObjV,MaxChrom]=Artificial_selection(Chrom,ObjV,MaxObjV,MaxChrom) %%Manual selection operator MP=length(Chrom); for i=1:MP [MaxY,MaxI]=max(ObjV{i}); if MaxY>MaxObjV(i) MaxObjV(i)=MaxY; MaxChrom(i,:)=Chrom{i}(MaxI,:); %It forms a population with the same length and population number end end end

### Record optimal solution

- Find and record the contemporary optimal individual and update the optimal solution.

%Find and record the optimal value of each generation Y_current(gen)=max(MaxObjV); %Finding the best individual in the elite population if Y_current(gen)>Y_max Y_max=Y_current(gen); %Update optimal value gen_keep=0; else gen_keep=gen_keep+1; %Optimal value holding times plus 1 end

For the total cycle, it is the degree of current evolution rather than the total algebra of evolution. If the optimal value remains unchanged in the MAXGEN cycle, it indicates that it has evolved to a high degree. No amount of evolution can shake the degree of the current optimal value evolution. At this time, exit evolution and get a better solution.

### Algorithm calculation results

- Optimal solution and optimal value

x y xy xy | y 2 y^2 y2 |
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0.04998 0.04998 0.04998 | 1.57051 1.57051 1.57051 |

1 / 2 1/2 1/2 | π / 2 \pi/2 π/2 |

The results are consistent with the predicted results.

- The optimal value varies with evolutionary algebra

Here is just a simple example. Even without using multi population genetic algorithm, genetic algorithm alone can have better results. The focus is on the improvement of multi population algorithm to traditional genetic algorithm, and the specific problems should be analyzed in detail.

## Code address

Full code in GitHub website Yes, if you have conditions, you can support it. Now pay attention to me. You're an old fan

## Reference articles

Please refer to the following articles for the content of this article. If you have any questions, please contact this account

[1] Shi Feng. Analysis of 30 cases of MATLAB intelligent algorithm [M]. Beijing University of Aeronautics and Astronautics Press, 2011