[WSN communication] optimize HWSN energy-saving clustering protocol based on MATLAB biogeography [including Matlab source code, 1989]

One 、 Introduction to biogeographic algorithm

1 The basic idea
BBO The algorithm originated from biogeography , It simulates the distribution of multiple species in different habitats 、 transfer 、 Mutation and other laws to solve the optimization problem , It is widely used in the field of multi-objective planning . Habitat is considered to be an independent area , Different habitats have different suitability indexes HSI（Habitat suitability index）. HSI Higher habitat species richness is higher , As the population becomes saturated , Its emigration rate has increased , Decrease in immigration rate , and HIS Lower habitats are the opposite , The immigration rate has increased , The emigration rate has decreased . When the habitat encounters an emergency such as disaster or plague ,HIS Will mutate , Break the dynamic balance , For low HIS Add unpredictability to our habitat , It increases the probability of searching the target solution 2.2 There are specific physical models for species migration and mutation operation , The most common are linear models 、 Quadratic model 、 Cosine model, etc . In an effort to 3 Take the linear model as an example , When the number of species in a habitat is 0 The time migration rate is the highest , At the moment λ = I, With the increasing number of migratory species , By the sun 、 water 、 Food and other resource constraints , The immigration rate is decreasing , The emigration rate is increasing . When the number of species in the habitat is S0 when , Just to achieve dynamic balance , At this time, the emigration rate is the same as the emigration rate . And when the habitat reaches saturation , The number of species reaches the maximum Smax , There are no more species moving in at this time , Emigration rate μ = E. Mutation operation is based on biogeographic statistical formula ：


In style ：ms Is the probability of habitat mutation ,mmax Is the maximum mutation rate , The user can set . ps Accommodate... For habitat s Probability of species , pmax Represents the probability of accommodating the largest population .

Two 、 Partial source code

%%  


clc;

[bestfit, averagefit,CHNum,STATISTICS]=start();
function [Chromosome,Fitness,CHNum] = BBO(ProbFlag,Fitness,PopulationSize,NumberOfNodes,Chromosome,Sensor,Sink,ETX,ERX,Efs,Emp,EDA,do,NumofCH,Totenergy)

if ~exist('ProbFlag', 'var')
    ProbFlag = true;
end
pmodify = 1; % habitat modification probability
pmutate = 0.5; % initial mutation probability

Keep = 2; % elitism parameter: how many of the best habitats to keep from one generation to the next
lambdaLower = 0.0; % lower bound for immigration probabilty per gene
lambdaUpper = 1; % upper bound for immigration probabilty per gene
dt = 1; % step size used for numerical integration of probabilities
I = 1; % max immigration rate for each island
E = 1; % max emigration rate, for each island
P = PopulationSize; %max species count, for each island

for j = 1 : size(Chromosome,1)
    Prob(j) = 1 / size(Chromosome,1);
end

% Begin the optimization loop
for GenIndex = 1 : 20
%     GenIndex
    % Sorting of population
    [Chromosome,indices,Fitness]=PopSort(Chromosome,Fitness);
    MinFitness = [Fitness(1)];
    % Compute the average cost
   [AverageFitness] = ComputeAveCost(Chromosome,Fitness);
    AvgFitness = [AverageFitness];
    % Save the best habitats in a temporary array.
    for j = 1 : Keep
        chromKeep(j,:) = Chromosome(j,:);
        costKeep(j) = Fitness(j);
    end
    
    % Map cost values to species counts.
    
    for i = 1 : size(Chromosome,1)
        if Fitness(i)< inf
            SpeciesCount(i) = P - i;
        else
            SpeciesCount(i) = 0;
        end
    end

    % Compute immigration rate and emigration rate for each species count.
    for i = 1 : size(Chromosome,1)
        lambda(i) = I * (1 - SpeciesCount(i) / P);
        mu(i) = E * SpeciesCount(i) / P;
    end
    
    if ProbFlag
        % Compute the time derivative of Prob(i) for each habitat i.
        for j = 1 : size(Chromosome,1)
            
            lambdaMinus = I * (1 - (SpeciesCount(j) - 1) / P);
            muPlus = E * (SpeciesCount(j) + 1) / P;
            if j < size(Chromosome,1)
                ProbMinus = Prob(j+1);
            else
                ProbMinus = 0;
            end
            if j > 1
                ProbPlus = Prob(j-1);
            else
                ProbPlus = 0;
            end
            ProbDot(j) = -(lambda(j) + mu(j)) * Prob(j) + lambdaMinus * ProbMinus + muPlus * ProbPlus;
        end
        % Compute the new probabilities for each species count.
        Prob = Prob + ProbDot * dt;
        Prob = max(Prob, 0);
        Prob = Prob / sum(Prob);
    end
    % Now use lambda and mu to decide how much information to share between habitats.
    lambdaMin = min(lambda);
    lambdaMax = max(lambda);
    for k = 1 : size(Chromosome,1)
        if rand > pmodify
            continue;
        end
        % Normalize the immigration rate.
        lambdaScale = lambdaLower + (lambdaUpper - lambdaLower) * (lambda(k) - lambdaMin) / (lambdaMax - lambdaMin);
        % Probabilistically input new information into habitat i
        for j = 1 : NumberOfNodes
            if (Chromosome(k,j) ~= -1) && rand < lambdaScale
                % Pick a habitat from which to obtain a feature
                RandomNum = rand * sum(mu);
                Select = mu(1);
                SelectIndex = 1;
                while (RandomNum > Select) && (SelectIndex < PopulationSize)
                    SelectIndex = SelectIndex + 1;
                    Select = Select + mu(SelectIndex);
                end
                Chromosome(k,j) = Chromosome(SelectIndex,j);
            else
                Chromosome(k,j) = Chromosome(k,j);
            end
        end
    end
    if ProbFlag
        % Mutation
        Pmax = max(Prob);
        MutationRate = pmutate * (1 - Prob / Pmax);
        
        % Sorting of population
        [Chromosome,indices,Fitness]=PopSort(Chromosome,Fitness);
        
        % Mutate only the worst half of the solutions
        for k = 1 : size(Chromosome,1)
            for parnum = 1 : NumberOfNodes
                if (Chromosome(k,parnum) ~= -1) && MutationRate(k) > rand
                    if( Chromosome(k,parnum) == 0)
                        Chromosome(k,parnum)= 1;
                    else
                        Chromosome(k,parnum) = 0;
                    end
                end
            end
        end
        

3、 ... and 、 Running results

Four 、matlab Edition and references

1 matlab edition
2014a

2 reference
[1] Baoziyang , Yu Jizhou , Poplar . Intelligent optimization algorithm and its application MATLAB example （ The first 2 edition ）[M]. Electronic industry press ,2016.
[2] Zhang Yan , Wu Shuigen .MATLAB Optimization algorithm source code [M]. tsinghua university press ,2017.

3 remarks
This part of the introduction is taken from the Internet , For reference only , If infringement , Contact deletion