如何运用混合K-Means与蚁群算法解决带容量限制的VRP路径规划问题？

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1+内容介绍+随着市场经济的快速发展和现代技术的不断演变，现代物流业也得到了空前的发展。在物流配送的各个环节中，优化配送路径，提高企业服务质量，降低物流成本，提升经济效益。

1 内容介绍

随着市场经济快速发展和现代技术的不断演变,现代物流业也得到了空前的发展.在物流配送活动的各个环节中,配送路径优化对企业提高服务质量,降低物流成本,提高经济效益起到至关重要的作用.蚁群优化算法作为群智能算法的典型代表,在路径规划求解中表现出良好的效果.本文研究了带容量约束车辆路径问题(Capacitated Vehicle Routing Problem,CVRP),并采用蚁群优化算法进行优化求解.实验结果表明,蚁群优化算法能够有效地求解带容量约束车辆路径问题.

2 部分代码

%%%%%%%%%%%%%%%%%%%%蚁群算法求函数极值%%%%%%%%%%%%%%%%%%%%%%%

%%%%%%%%%%%%%%%%%%%%%%%%%初始化%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

clear all; %清除所有变量

close all; %清图

clc; %清屏

m=20; %蚂蚁个数

G_max=200; %最大迭代次数

Rho=0.9; %信息素蒸发系数

P0=0.2; %转移概率常数

XMAX= 5; %搜索变量x最大值

XMIN= -5; %搜索变量x最小值

YMAX= 5; %搜索变量y最大值

YMIN= -5; %搜索变量y最小值

%%%%%%%%%%%%%%%%%随机设置蚂蚁初始位置%%%%%%%%%%%%%%%%%%%%%%

for i=1:m

X(i,1)=(XMIN+(XMAX-XMIN)*rand);

X(i,2)=(YMIN+(YMAX-YMIN)*rand);

Tau(i)=func(X(i,1),X(i,2));

end

step=0.1; %局部搜索步长

for NC=1:G_max

lamda=1/NC;

[Tau_best,BestIndex]=min(Tau);

%%%%%%%%%%%%%%%%%%计算状态转移概率%%%%%%%%%%%%%%%%%%%%

for i=1:m

P(NC,i)=(Tau(BestIndex)-Tau(i))/Tau(BestIndex);

end

%%%%%%%%%%%%%%%%%%%%%%位置更新%%%%%%%%%%%%%%%%%%%%%%%%

for i=1:m

%%%%%%%%%%%%%%%%%局部搜索%%%%%%%%%%%%%%%%%%%%%%

if P(NC,i)<P0

temp1=X(i,1)+(2*rand-1)*step*lamda;

temp2=X(i,2)+(2*rand-1)*step*lamda;

else

%%%%%%%%%%%%%%%%全局搜索%%%%%%%%%%%%%%%%%%%%%%%

temp1=X(i,1)+(XMAX-XMIN)*(rand-0.5);

temp2=X(i,2)+(YMAX-YMIN)*(rand-0.5);

end

%%%%%%%%%%%%%%%%%%%%%边界处理%%%%%%%%%%%%%%%%%%%%%%%

if temp1<XMIN

temp1=XMIN;

end

if temp1>XMAX

temp1=XMAX;

end

if temp2<YMIN

temp2=YMIN;

end

if temp2>YMAX

temp2=YMAX;

end

%%%%%%%%%%%%%%%%%%蚂蚁判断是否移动%%%%%%%%%%%%%%%%%%

if func(temp1,temp2)<func(X(i,1),X(i,2))

X(i,1)=temp1;

X(i,2)=temp2;

end

end

%%%%%%%%%%%%%%%%%%%%%%%更新信息素%%%%%%%%%%%%%%%%%%%%%%%

for i=1:m

Tau(i)=(1-Rho)*Tau(i)+func(X(i,1),X(i,2));

end

[value,index]=min(Tau);

trace(NC)=func(X(index,1),X(index,2));

end

[min_value,min_index]=min(Tau);

minX=X(min_index,1); %最优变量

minY=X(min_index,2); %最优变量

minValue=func(X(min_index,1),X(min_index,2)); %最优值

figure

plot(trace)

xlabel('搜索次数');

ylabel('适应度值');

title('适应度进化曲线')

3 运行结果

4 参考文献

[1]陈廷伟, 施铱鹏, 周敏宣,等. 基于改进蚁群算法的带容量约束车辆路径问题求解[J]. 信息与电脑, 2022, 34(7):4.

部分理论引用网络文献，若有侵权联系博主删除。