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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

      对于物流配送企业来说,想在激烈的竞争环境中获得优势,就需要为客户提供高质量的服务,还要将成本降到最低。高效快速的商品配送能够提高客户的满意度,提高服务质量,但若盲目提高时效性,则人力需求量、运输费用、车辆需求都会大大增加,导致运输成本的增加。如何通过合理化运输来实现既能降低物流成本,又能提高物流配送的服务质量、准时为客户提供服务,对物流企业来说是一个亟待解决的问题。

       正确的选择车辆的行驶路径,制定出切实可行的车辆配送路线方案对降低成本十分关键,这类问题就是车辆路径优化问题(Vehicle Routing Problem,VRP),简称VRP问题。为了增强物流企业时效性,货物配送方和接收方约定送货时间段,若送货迟到,货物接收方有理由提出时间补偿,配送方需要向接收货物的客户支付惩罚费用,这个时间段被称为时间窗(Time Windows),在VRP的基础上加入时间窗因素,就是带时间窗车辆路径问题(Vehicle Routing Problem with Time Windows, VRPTW)。从理论研究方面来看,带时间窗车辆路径优化问题属于复杂的组合优化问题,求解复杂度较高,计算量较大,已被证实属于NP-hard问题。

📚2 运行结果

【ACO-VRPTW】基于蚁群优化算法的时间窗的车辆配送(VRP)优化(Matlab代码实现)_开发语言

【ACO-VRPTW】基于蚁群优化算法的时间窗的车辆配送(VRP)优化(Matlab代码实现)_时间段_02

主函数代码:

clear; clc; close all;
tic
%% input
c101 = importdata('c101.txt');
% c101 = importdata('my_test_data.xlsx');
% depot_time_window1 = c101(1,5); % time window of depot
% depot_time_window2 = c101(1,6);depot_time_window1 = TimeTrans(c101(1,5)); % time window of depot
depot_time_window2 = TimeTrans(c101(1,6));
vertexs = c101(:,2:3);
customer = vertexs(2:end,:); % customer locations
customer_number = size(customer,1);
% vehicle_number = 25;
% time_window1 = c101(2:end,5);
% time_window2 = c101(2:end,6);time_window1 = TimeTrans(c101(2:end,5));
time_window2 = TimeTrans(c101(2:end,6));width = time_window2-time_window1; % width of time window
service_time = c101(2:end,7);
h = pdist(vertexs);
dist = squareform(h); % distance matrix
%% initialize the parameters
ant_number = floor(customer_number * 1.5); % number of ants
alpha = 4; % parameter for pheromone
beta = 5; % paremeter for heuristic information
gamma = 2; % parameter for waiting time
delta = 3; % parameter for width of time window
r0 = 0.5; % a constant to control the movement of ants
rho = 0.85; % pheromone evaporation rate
Q = 5; % a constant to influence the update of pheromene
Eta = 1./dist; % heuristic function
iter = 1; % initial iteration number
iter_max = 200; % maximum iteration numberTau = ones(customer_number+1,customer_number+1); % a matrix to store pheromone
Table = zeros(ant_number,customer_number); % a matrix to save the route
Route_best = zeros(iter_max,customer_number); % the best route
Cost_best = zeros(iter_max,1); % the cost of best routeiter_time = [];
last_dist = 0;
stop_count = 0;%% find the best route
while iter <= iter_max
%tic;
% ConstructAntSolutions
for i = 1:ant_number
for j = 1:customer_number
r = rand;
np = NextPoint(i,Table,Tau,Eta,alpha,beta,gamma,delta,r,r0,time_window1,time_window2,width,service_time,depot_time_window2,dist);
Table(i,j) = np;
end
end
%% calculate the cost for each ant
cost = zeros(ant_number,1);
NV = zeros(ant_number,1);
TD = zeros(ant_number,1);
for i=1:ant_number
VC = decode(Table(i,:),time_window1,time_window2,depot_time_window2,service_time,dist);
[cost(i,1),NV(i,1),TD(i,1)] = CostFun(VC,dist);
end
%% find the minimal cost and the best route
if iter == 1
[min_Cost,min_index] = min(cost);
Cost_best(iter) = min_Cost;
Route_best(iter,:) = Table(min_index,:);
else
% compare the min_cost in this iteration with the last iter
[min_Cost,min_index] = min(cost);
Cost_best(iter) = min(Cost_best(iter - 1),min_Cost);
if Cost_best(iter) == min_Cost
Route_best(iter,:) = Table(min_index,:);
else
Route_best(iter,:) = Route_best((iter-1),:);
end
end
%% update the pheromene
bestR = Route_best(iter,:); % find out the best route
[bestVC,bestNV,bestTD] = decode(bestR,time_window1,time_window2,depot_time_window2,service_time,dist);
Tau = updateTau(Tau,bestR,rho,Q,time_window1,time_window2,depot_time_window2,service_time,dist); %% print
disp(['Iterration: ',num2str(iter)])
disp(['Number of Robots: ',num2str(bestNV),', Total Distance: ',num2str(bestTD)]);
fprintf('\n')
%
iter = iter+1;
Table = zeros(ant_number,customer_number);

%iter_time(iter) = toc;

% if last_dist == bestTD
% stop_count = stop_count + 1;
% if stop_count > 30
% break;
% end
% else
% last_dist = bestTD;
% stop_count = 0;
% end

end
%% draw
bestRoute=Route_best(iter-1,:);
[bestVC,NV,TD]=decode(bestRoute,time_window1,time_window2,depot_time_window2,service_time,dist);
draw_Best(bestVC,vertexs);
figure(2)
plot(1:iter_max,Cost_best,'b')
xlabel('Iteration')
ylabel('Cost')
title('Change of Cost')
%% check the constraints, 1 == no violation
flag = Check(bestVC,time_window1,time_window2,depot_time_window2,service_time,dist)toc

🎉3 参考文献

[1]胡俊桥. 蚁群混合算法求解带时间窗车辆路径问题[D].西安科技大学,2017.

[2]魏志秀. 基于改进蚁群算法研究带时间窗的配送车辆路径优化问题[D].江苏大学,2021.DOI:10.27170/d.cnki.gjsuu.2021.002182.

👨‍💻4 Matlab代码实现