【优化算法】多目标水母搜索优化算法 (MOJS) 【含Matlab源码 248期】

一、获取代码方式

获取代码方式1：
完整代码已上传我的资源：【优化算法】多目标水母搜索优化算法 (MOJS) 【含Matlab源码 248期】

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二、水母搜索优化算法简介

这项研究发展了一个新的元启发式算法，它是受水母在海洋中的行为启发，被称为人工水母搜索(JS)优化器。
水母搜索行为的模拟包括它们跟随洋流、它们在水母群中的运动(主动运动和被动运动)、在这些运动之间切换的时间控制机制，以及收敛到水母花的状态。新算法在基准函数和优化问题上得到了成功的测试。值得注意的是，JS只有两个控制参数，即群体规模和迭代数。因此，JS的使用非常简单，并且可能是解决优化问题的一个优秀的元启发式算法。

三、部分源代码

%% Main MOJS optimizer
function ARCH = MOJS(params,MultiObj)
% Parameters
Np      = params.Np;
Nr      = params.Nr;
MaxIt   = params.maxiter;
ngrid   = params.ngrid;
fun     = MultiObj.fun;
nVar    = MultiObj.nVar;
var_min = MultiObj.var_min(:);
var_max = MultiObj.var_max(:);
it=1;
% Initialization by Eq. 25
POS=initialchaos(7,Np,nVar,var_max',var_min');
POS_fit      = fun(POS);
ELI_POS      = POS;
ELI_POS_fit  = POS_fit;
DOMINATED    = checkDomination(POS_fit);
ARCH.pos     = POS(~DOMINATED,:);
ARCH.pos_fit = POS_fit(~DOMINATED,:);
ARCH         = updateGrid(ARCH,ngrid);

display(['Iteration #0 - Archive size: ' num2str(size(ARCH.pos,1))]);
%% Main MOJS loop
stopCondition = false;
while ~stopCondition
    % Select leader by Eq. 16
    h = selectLeader(ARCH);
    % Calculate time control by Eq. 15
    Ct=abs((1-it*((1)/MaxIt))*(2*rand-1));
    if Ct>=0.5
        Meanvl=mean(ELI_POS);
        for i=1:Np
            % The new position is determined by Eq.19 and Eq.20
            POS(i,:) = ELI_POS(i,:) + Levy(nVar).*(ARCH.pos(h,:) - 3*rand([1 nVar]).*Meanvl);
        end
    else
        for i=1:Np
            if rand<(1-Ct)
                % Jellyfish follow type B
                % Determine the direction by Eq. 24
                j=i;
                while j==i
                    j=randperm(Np,1);
                end
                Step = ELI_POS(i,:) - ELI_POS(j,:);
                if dominates(ELI_POS_fit(j,:),ELI_POS_fit(i,:))
                    Step = -Step;
                end
                % The new position is determined by Eq. 22
                POS(i,:) =ARCH.pos(h,:) + rand([1 nVar]).*Step;
            else
                % Jellyfish follow type A
                % The new position is determined by Eq. 21
                POS(i,:)=ARCH.pos(h,:)+Levy(nVar).*(ELI_POS(i,:)-ARCH.pos(h,:));
            end
        end
    end
    %% Update new position by opposition-based jumping using Eq. 26
    if rand <(it/MaxIt)
        [POS] = OPPOS(POS,var_max,var_min);
    end
    %% Check boundaries
    if rand>=0.5
        POS=checksimplebounds(POS,var_min',var_max');
    else
        POS = checkBoundaries(POS,var_max,var_min);
    end
    %% Evaluate the population
    POS_fit = fun(POS);
    pos_best = dominates(POS_fit, ELI_POS_fit);
    best_pos = ~dominates(ELI_POS_fit, POS_fit);
    best_pos(rand(Np,1)>=0.5) = 0;
    if(sum(pos_best)>1)
        ELI_POS_fit(pos_best,:) = POS_fit(pos_best,:);
        ELI_POS(pos_best,:) = POS(pos_best,:);
    end
    if(sum(best_pos)>1)
        ELI_POS_fit(best_pos,:) = POS_fit(best_pos,:);
        ELI_POS(best_pos,:) = POS(best_pos,:);
    end
    %% Update the archive 
    if size(ARCH.pos,1)==1
        ARCH.pos= POS;
        ARCH.pos_fit= POS_fit;
        ARCH = updateArchive(ARCH,ELI_POS,ELI_POS_fit,ngrid);
    else
        ARCH = updateArchive(ARCH,ELI_POS,ELI_POS_fit,ngrid);
        if size(ARCH.pos,1)==1
            ARCH.pos= ELI_POS;
            ARCH.pos_fit= ELI_POS_fit;
        end
    end
    if(size(ARCH.pos,1)>Nr)
        % Delete the worst members from archive by Eq. 18
        ARCH = deleteFromArchive(ARCH,size(ARCH.pos,1)-Nr,ngrid);
    end
    display(['Iteration #' num2str(it) ' - Archive size: ' num2str(size(ARCH.pos,1))]);
    it=it+1;
    if(it>MaxIt), stopCondition = true; end
end
%% Plotting paretofront
if(size(ARCH.pos_fit,2)==2)
    plot(ARCH.pos_fit(:,1),ARCH.pos_fit(:,2),'or'); hold on;
    grid on; xlabel('f1'); ylabel('f2');
end
if(size(ARCH.pos_fit,2)==3)
    plot3(ARCH.pos_fit(:,1),ARCH.pos_fit(:,2),ARCH.pos_fit(:,3),'or'); hold on;
    grid on; xlabel('f1'); ylabel('f2'); zlabel('f3');
end
end

%% This function calucates the leader performance by a roulette wheel selection
% based on the quality of each hypercube
function selected = selectLeader(ARCH)
% Roulette wheel
prob    = cumsum(ARCH.quality(:,2));     % Cumulated probs
sel_hyp = ARCH.quality(find(rand(1,1)*max(prob)<=prob,1,'first'),1); % Selected hypercube
% Select the index leader as a random selection inside that hypercube
idx      = 1:1:length(ARCH.grid_idx);
selected = idx(ARCH.grid_idx==sel_hyp);
selected = selected(randi(length(selected)));
end

%% This function returns 1 if x dominates y and 0 otherwise
function d = dominates(x,y)
d = all(x<=y,2) & any(x<y,2);
end

%% This function checks the domination inside the population.
function domi_vector = checkDomination(fitness)
Np = size(fitness,1);
if Np>2
    domi_vector = zeros(Np,1);
    all_perm = nchoosek(1:Np,2);    % Possible permutations
    all_perm = [all_perm; [all_perm(:,2) all_perm(:,1)]];
    
    d = dominates(fitness(all_perm(:,1),:),fitness(all_perm(:,2),:));
    dominated_particles = unique(all_perm(d==1,2));
    domi_vector(dominated_particles) = 1;
else
    domi_vector=ones(Np,1);
end
end

%% This function updates the archive given a new population 
function ARCH = updateArchive(ARCH,POS,POS_fit,ngrid)
% Domination between jellyfish
DOMINATED  = checkDomination(POS_fit);
ARCH.pos    = [ARCH.pos; POS(~DOMINATED,:)];
ARCH.pos_fit= [ARCH.pos_fit; POS_fit(~DOMINATED,:)];
% Domination between nondominated jellyfish and the last archive 
DOMINATED  = checkDomination(ARCH.pos_fit);
ARCH.pos_fit= ARCH.pos_fit(~DOMINATED,:);
ARCH.pos    = ARCH.pos(~DOMINATED,:);
% Updating the grid
ARCH        = updateGrid(ARCH,ngrid);
end

%% Function that updates the hypercube grid, the hypercube where belongs
function ARCH = updateGrid(ARCH,ngrid)
% Computing the  hypercube limitation
ndim = size(ARCH.pos_fit,2);
ARCH.hypercube_limits = zeros(ngrid+1,ndim);
for dim = 1:1:ndim
    ARCH.hypercube_limits(:,dim) = linspace(min(ARCH.pos_fit(:,dim)),max(ARCH.pos_fit(:,dim)),ngrid+1)';
end
% Computing where belongs each jellyfish
npar = size(ARCH.pos_fit,1);
ARCH.grid_idx = zeros(npar,1);
ARCH.grid_subidx = zeros(npar,ndim);
for n = 1:1:npar
    idnames = [];
    for d = 1:1:ndim
        ARCH.grid_subidx(n,d) = find(ARCH.pos_fit(n,d)<=ARCH.hypercube_limits(:,d)',1,'first')-1;
        if(ARCH.grid_subidx(n,d)==0), ARCH.grid_subidx(n,d) = 1; end
        idnames = [idnames ',' num2str(ARCH.grid_subidx(n,d))];
    end
    ARCH.grid_idx(n) = eval(['sub2ind(ngrid.*ones(1,ndim)' idnames ');']);
end
% Quality based on the number of jellyfish in each hypercube
ARCH.quality = zeros(ngrid,2);
ids = unique(ARCH.grid_idx);
for i = 1:length(ids)
    ARCH.quality(i,1) = ids(i);                       
    ARCH.quality(i,2) = 10/sum(ARCH.grid_idx==ids(i)); 
end
end

%% This function deletes an excess of jellyfish inside the archive using crowding distances
function ARCH = deleteFromArchive(ARCH,n_extra,ngrid)
% Compute the crowding distances
crowding = zeros(size(ARCH.pos,1),1);
for m = 1:1:size(ARCH.pos_fit,2)
    [m_fit,idx] = sort(ARCH.pos_fit(:,m),'ascend');
    m_up     = [m_fit(2:end); Inf];
    m_down   = [Inf; m_fit(1:end-1)];
    distance = (m_up-m_down)./(max(m_fit)-min(m_fit));
    [~,idx]  = sort(idx,'ascend');
    crowding = crowding + distance(idx);
end
crowding(isnan(crowding)) = Inf;
% This function deletes the extra jellyfish with the smallest crowding distances
[~,del_idx] = sort(crowding,'ascend');
del_idx = del_idx(1:n_extra);
ARCH.pos(del_idx,:) = [];
ARCH.pos_fit(del_idx,:) = [];
ARCH = updateGrid(ARCH,ngrid);
end

%% This function checks the boundary of jellyfish search space
function [POS] = checkBoundaries(POS,var_max,var_min)
% Useful matrices
Np = size(POS,1);
MAXLIM   = repmat(var_max(:)',Np,1);
MINLIM   = repmat(var_min(:)',Np,1);
POS(POS>MAXLIM) = MAXLIM(POS>MAXLIM);
POS(POS<MINLIM) = MINLIM(POS<MINLIM);
end
function POS=checksimplebounds(POS,Lb,Ub)
for i=1:size(POS,1)
    ns_tmp=POS(i,:);
    I=ns_tmp<Lb;
    while sum(I)~=0
        ns_tmp(I)=Ub(I)+(ns_tmp(I)-Lb(I));
        I=ns_tmp<Lb;
    end
    J=ns_tmp>Ub;
    while sum(J)~=0
        ns_tmp(J)=Lb(J)+(ns_tmp(J)-Ub(J));
        J=ns_tmp>Ub;
    end
    POS(i,:)=ns_tmp;
end
end

  

 

  
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四、运行结果

五、matlab版本及参考文献

1 matlab版本
2014a

2 参考文献
[1] 包子阳,余继周,杨杉.智能优化算法及其MATLAB实例（第2版）[M].电子工业出版社，2016.
[2]张岩,吴水根.MATLAB优化算法源代码[M].清华大学出版社，2017.

文章来源: qq912100926.blog.csdn.net，作者：海神之光，版权归原作者所有，如需转载，请联系作者。

原文链接：qq912100926.blog.csdn.net/article/details/120274682