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目录
💥1 概述
柔性作业车间调度问题""(flexible job shopscheduling problem，FJSP)是一种研究生产资源的分配与工件工序的加工顺序的问题，具有加工设备不确定和工艺路线柔性等特性。在实际的车间生产环境中，很多工件的工艺流程具有偏序关系，可能会包含工序具有共同前继工序或者多个前继工序的情况。
本文基于变邻域搜索平衡优化算法与粘菌算法的柔性车间调度，这两种很新的算法效果很不错。并用Matlab代码实现。
📚2 算法
% Equilibrium Optimizer and Slime Mould Algorithm with Centroid
% Opposition-based Computation and Variable Neighborhood Search
function [bestFitness,bestPositions,Convergence_curve] = VEOSMA(Pop_size,Max_iter,lb,ub,dim,data)
rand('seed',sum(100 * clock)); % Random number seed
V = 1; a1 = 2; a2 = 1; GP = 0.5; % EO parameters
z = 0.6; % SMA parameter
Jr = 0.3; % Learning rate
% Initialize the population of slime mould
X = initialization(Pop_size,dim,ub,lb);
for i = 1:Pop_size
Fitness(i,1) = fitness(data,X(i,:));
end
weight = ones(Pop_size,dim); % Fitness weight of each slime mould
% Centroid opposition-based computation
M = zeros(1,dim);
for i = 1:dim
M(i) = M(i)+sum(X(:,i));
end
M = M/Pop_size; % Center of mass point
OX = 2*M-X; % Opposite position
for i = 1:Pop_size
AllFitness_OX(i,1) = fitness(data,OX(i,:));
if AllFitness_OX(i) < Fitness(i)
X(i,:) = OX(i,:); Fitness(i) = AllFitness_OX(i);
end
end
C_old = X; fit_old = Fitness;
Convergence_curve = zeros(1,Max_iter);
% Main loop
for it = 1:Max_iter
% Fitness evaluation
for i = 1:Pop_size
Fitness(i,1) = fitness(data,X(i,:));
end
% Centroid opposition-based computation
if rand < Jr
M = zeros(1,dim);
for i = 1:dim
M(i) = M(i)+sum(X(:,i));
end
M = M/Pop_size; % Center of mass point
OX = 2*M-X; % Opposite position
for i = 1:Pop_size
AllFitness_OX(i,1) = fitness(data,OX(i,:));
if AllFitness_OX(i) < Fitness(i)
X(i,:) = OX(i,:); Fitness(i) = AllFitness_OX(i);
end
end
end
% Memory pooling mechanism to preserve the optimal position of individual history
for i = 1:Pop_size
if fit_old(i) < Fitness(i)
Fitness(i) = fit_old(i); X(i,:) = C_old(i,:);
end
end
C_old = X; fit_old = Fitness; % C_old is equivalent to a memory pool, the original SMA has no greedy selection
% Update the equilibrium pool
[Order,Index] = sort(Fitness);
bestPositions = X(Index(1),:); bestFitness = Order(1);
Ceq2 = X(Index(2),:); Ceq3 = X(Index(3),:); Ceq4 = X(Index(4),:);
Ceq_ave = (bestPositions+Ceq2+Ceq3+Ceq4)/4; % Average candidate solution
C_pool = [bestPositions; Ceq2; Ceq3; Ceq4; Ceq_ave]; % Equilibrium pool
worstFitness = Order(Pop_size);
S = bestFitness-worstFitness+eps; % Plus eps to avoid denominator zero
% Calculate the fitness weight of each slime mould
for i = 1:Pop_size
if i <= Pop_size/2
weight(Index(i),:) = 1+rand(1,dim)*log10((bestFitness-Order(i))/S+1);
else
weight(Index(i),:) = 1-rand(1,dim)*log10((bestFitness-Order(i))/S+1);
end
end
% Update EO parameters
t = (1-it/Max_iter)^(a2*it/Max_iter);
lambda = rand(Pop_size,dim);
r1 = rand(Pop_size,1);
r2 = rand(Pop_size,1);
rn = randi(size(C_pool,1),Pop_size,1);
% Update SMA parameters
a = atanh(1-(it/Max_iter));
vb = unifrnd(-a,a,Pop_size,dim);
b = 1-it/Max_iter;
vc = unifrnd(-b,b,Pop_size,dim);
p = tanh(abs(Fitness-bestFitness));
r = rand(Pop_size,dim);
A = randi([1,Pop_size],Pop_size,dim); % Two positions randomly selected from population
B = randi([1,Pop_size],Pop_size,dim);
% Update the Position of search agents
for i = 1:Pop_size
if rand < z
Ceq = C_pool(rn(i,1),:); % Select a solution randomly from the equilibrium pool
F = a1*sign(r(i,:)-0.5).*(exp(-lambda(i,:).*t)-1); % Calculate the exponential term coefficient
GCP = 0.5*r1(i,1)*ones(1,dim)*(r2(i,1)>=GP); % Calculate the mass generation rate
G = (GCP.*(Ceq-lambda(i,:).*X(i,:))).*F;
X(i,:) = Ceq+(X(i,:)-Ceq).*F+(G./lambda(i,:)*V).*(1-F); % Update position
else
for j = 1:dim
if r(i,j) < p(i)
X(i,j) = bestPositions(j)+vb(i,j)*(weight(i,j)*X(A(i,j),j)-X(B(i,j),j));
else
X(i,j) = X(i,j)+vc(i,j)*X(i,j);
end
end
end
end
%% Variable neighborhood search
for i = 1:Pop_size
VNS_X(i,:) = VNS(X(i,:),data); % Self-learning by the VNS
VNS_Fitness(i,1) = fitness(data,VNS_X(i,:));
if VNS_Fitness(i) < Fitness(i) % Greedy selection
X(i,:) = VNS_X(i,:);
Fitness(i) = VNS_Fitness(i);
if Fitness(i) < bestFitness
bestPositions = X(i,:);
bestFitness = Fitness(i);
end
end
end
Convergence_curve(it) = bestFitness;
end
end
% Developer: Shihong Yin
🎉3 参考文献
[1]李长云,林多,何频捷,谷鹏飞.基于等级邻域策略的偏序柔性车间优化调度[J].制造技术与机床,2022(07):165-172.DOI:10.19287/j.mtmt.1005-2402.2022.07.028.
[2]李旻运. 基于改进的NSGA2算法的多目标柔性车间调度问题的研究及应用[D].湖州师范学院,2022.DOI:10.27946/d.cnki.ghzsf.2022.000051.