Matlab代码助力：某公司通勤路线在双目标下的最佳规划

以下是使用Matlab编写的代码，实现了在最小化车辆行驶时间和最小化人均乘车时间两个目标下寻找最佳通勤车路线的功能： ```matlab % 小区坐标及员工数量 x = [35 -13 40 -27 -3 -26 -21 52 39 1 65 -27 13 8 -42]; y = [46 49 -12 18 14 34 40 45 -3 37 35 -14 -19 19 -26]; employees = [1 2 2 3 4 3 3 8 3 2 1 2 3 5 3]; % 计算小区的数量 numOfDistrict = length(x); % 构建距离矩阵 distance = zeros(numOfDistrict); for i = 1:numOfDistrict for j = 1:numOfDistrict distance(i,j) = sqrt((x(i)-x(j))^2 + (y(i)-y(j))^2); end end % 计算车辆行驶时间 speed = 40; % km/h travelTime = distance/speed; % 初始化最小化车辆行驶时间的路线和时间 minTravelRoute = []; minTravelTime = Inf; % 使用全排列方式寻找最小化车辆行驶时间的路线 permutations = perms(2:numOfDistrict); % 固定公司在起点，因此从2开始排列 for i = 1:size(permutations, 1) route = [1 permutations(i,:) 1]; % 加入起点和终点 totalTime = sum(travelTime(sub2ind(size(travelTime), route(1:end-1), route(2:end)))); if totalTime < minTravelTime minTravelTime = totalTime; minTravelRoute = route; end end disp('最小化车辆行驶时间的路线:'); disp(minTravelRoute); disp('最小化车辆行驶时间:'); disp(minTravelTime); % 初始化最小化人均乘车时间的路线和时间 minAverageTime = Inf; % 使用回溯法寻找最小化人均乘车时间的路线 route = [1]; remainingDistricts = setdiff(2:numOfDistrict, route); [bestRoute, minAverageTime] = backtrack(route, remainingDistricts, travelTime, employees, Inf, minAverageTime); disp('最小化人均乘车时间的路线:'); disp(bestRoute); disp('最小化人均乘车时间:'); disp(minAverageTime); % 回溯法递归函数 function [route, minAverageTime] = backtrack(route, remainingDistricts, travelTime, employees, currentAverageTime, minAverageTime) if isempty(remainingDistricts) if currentAverageTime < minAverageTime route = [route 1]; % 加入终点 minAverageTime = currentAverageTime; end return; end for i = 1:length(remainingDistricts) nextDistrict = remainingDistricts(i); newRoute = [route nextDistrict]; newRemainingDistricts = setdiff(remainingDistricts, nextDistrict); newCurrentAverageTime = (currentAverageTime * (length(route)-1) + travelTime(route(end), nextDistrict))/(length(route)); if newCurrentAverageTime < minAverageTime [route, minAverageTime] = backtrack(newRoute, newRemainingDistricts, travelTime, employees, newCurrentAverageTime, minAverageTime); end end end ``` 这段代码使用了全排列和回溯法两种方法，分别寻找最小化车辆行驶时间和最小化人均乘车时间的路线。最终输出了相关结果。该代码仅为示例，具体应根据实际情况进行优化和适配。 ######[AI写代码神器 | 2350点数解答 | 2024-04-29 21:04:53]