基于混合VNS（变邻域搜索算法）的PSO（粒子群优化算法）的任务分配问题（Matlab代码实现）

news2024/10/6 10:28:24

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⛳️座右铭：行百里者，半于九十。

目录

💥1 概述

📚2 运行结果

🎉3 参考文献

👨‍💻4 Matlab代码实现

💥1 概述

PSO算法最早是由Kennedy和Eberhart提出的;它的基本原理源于对鸟群捕食行为的仿真.目前对PSO算法的研究主要集中在连续型的PSO算法,即描述粒子状态及其运动规律的量都是连续型的.而对离散粒子群优化(Discrete Particle Swarm ()ptimization,DPSO)算法的研究甚少.只有ClerC提出用于求解TSP问题的DPSO算法,但其性能与其它算法(如蚁群算法)相比仍有一定差距.

独立任务的分配问题不仅存在于计算机并行计算、操作系统等计算机技术领域,而且还广泛存在于工农业生产、交通运输及服务行业.它通常以总完成时间最短为目标函数,是一个NP-困难的组合优化问题,不存在多项式时间复杂性的算法以找到全局最优解.尽管文献中已有许多启发式算法试图去获取优质解,但是解的质量还是不能令人满意.本文基于一种混合VNS(变邻域搜索算法)的PSO(粒子群优化算法)用以解决拦截对抗中的任务分配问题，新的算法能够有效地避免粒子群陷入局部收敛，并且解决离散优化问题。

📚2 运行结果

ultimate distribute matrix:
         0         0         0         0         0         0    0.0806    0.9194
         0         0    1.0000         0         0         0         0         0
         0         0         0         0         0         0    1.0000         0
         0         0         0         0         0    1.0000         0         0
         0         0         0    1.0000         0         0         0         0
    1.0000         0         0         0         0         0         0         0
         0    1.0000         0         0         0         0         0         0
         0         0         0         0         0    1.0000         0         0
    1.0000         0         0         0         0         0         0         0
         0         0         0         0    1.0000         0         0         0

ultimate fitness value:
  146.8842

时间已过 4.112748 秒。

部分代码：

maxgen = 100; % number of iterations
sizepop = 50; % Population size
Vmax = 1; % limits of velocity
Vmin = -1;
popmax = 1; % limits of position
popmin = 0;

% original population
for i = 1:sizepop
% obtain a particle swarm randomly
popi = popmin + (popmax - popmin)*rand(numP, numE);
for k = 1:numP
popi(k,:) = popi(k,:)/sum(popi(k,:));
end
pop(i,:,:) = popi; % original postion
V(i,:,:) = Vmin + (Vmax - Vmin)*rand(numP, numE); % original velocity
% caculate fitness value
fitness(i) = fitnessf(squeeze(pop(i,:,:)), P, E);
end

% Individual and global extremums of the initial population
[bestfitness bestindex] = max(fitness);
zbest = pop(bestindex,:,:); % global extremums
gbest = pop; % Individual extremums
fitnessgbest = fitness; % Individual extremums fitness value
fitnesszbest = bestfitness; % global extremums fitness value

% iterations
for i = 1:maxgen
for j = 1:sizepop
% velocity update
V(j,:,:) = omg*V(j,:,:) + c1*rand*(gbest(j,:,:) - pop(j,:,:)) + c2*rand*(zbest - pop(j,:,:));

% position update
pop(j,:,:) = pop(j,:,:) + V(j,:,:);
pop(j,find(pop(j,:,:)<0)) = 0;
popj = squeeze(pop(j,:,:));
for k = 1:numP
popj(k,:) = popj(k,:)/sum(popj(k,:));
end
pop(j,:,:) = popj;

% caculate fitness value
fitness(j) = fitnessf(squeeze(pop(j,:,:)), P, E);

Fhistory(i, j) = fitness(j);


end
for j = 1:sizepop
% individual extremum update
if fitness(j) > fitnessgbest(j)
gbest(j,:,:) = pop(j,:,:);
fitnessgbest(j) = fitness(j);
end

% global extremum update
if fitness(j) > fitnesszbest
zbest = pop(j,:,:);
fitnesszbest = fitness(j);
end
end
% vns strategy
for j = 1:sizepop
popj = squeeze(pop(j,:,:));
if i > 3
if (Fhistory(i, j) - Fhistory(i-1, j)) < 1e-4
if (Fhistory(i, j) - Fhistory(i-2, j)) < 1e-4
if mod(i, 15) == 0
if j == 1
disp('vns going');
end
omg = 0.4;
% vns strategy
[popjn, isupdate] = vns(popj, P, E);
pop(j,:,:) = popjn;
tmptfitness = fitnessf(popjn, P, E);
% individual extremum update
if isupdate
gbest(j,:,:) = popjn;
fitnessgbest(j) = tmptfitness;
end
% global extremum update
if tmptfitness > fitnesszbest
zbest = pop(j,:,:);
fitnesszbest = tmptfitness;
end
end
end
end
end

end

yy(i) = fitnesszbest; % fitness value each iteration
disp(i);
disp(squeeze(pop(1, :, :)));
end