基于C-W节约算法的车辆路径规划问题的Java实现

• VRP问题概述
• 解决算法分类
• 项目描述
• 算法结果

车辆路线问题（VRP）最早是由Dantzig和Ramser于1959年首次提出，它是指一定数量的客户，各自有不同数量的货物需求，配送中心向客户提供货物，由一个车队负责分送货物，组织适当的行车路线，目标是使得客户的需求得到满足，并能在一定的约束下，达到诸如路程最短、成本最小、耗费时间最少等目的。

VRP问题有很多子问题：

• the capacitated vehicle routing problem (CVRP) , 即classical VRP

• the vehicle routing problem with time windows (VRPTW) , 带时间窗 - VRPHTW 硬时间窗   ｜   VRPSTW 软时间窗   ｜   VRPTD（VRP with Time Deadlines）带顾客最迟服务时间

• the Multiple Depot Vehicle Routing Problem (MDVRP) , 多车场

• the Period Vehicle Routing Problem (PVRP) , 周期车辆路径问题

一般使用精确算法 或 启发式算法

• 精确算法适用于小规模问题，能得到最优解。
  • 　direct tree search , 直接树搜索   |   dynamic programming , 动态规划   |   integer linear programming , 整数线性规划

• 启发式算法用于大规模问题，能快速找出可行解。
  • Simulated Annealing 模拟退火
  • Tabu Search 禁忌搜索
  • Genetic Algoritm 遗传算法    |    Genetic Programming 遗传规划
  • Genetic Network Programming 遗传网络规划
  • ACS, Ant Colony System 蚁群算法

我主要是研究了蚁群算法和CW节约算法，发现后者思路比较清晰，并且我们项目的需求也不复杂，所以基于后者的思想来实现。

考虑这样的需求：

某集散中心管辖10个邮局，已知集散中心和各营业点的经纬度，寄达各支局和各支局收寄的邮件， 时间窗口。

邮车装载邮件数不同。邮车的运行成本为3元/公里， 速度为30km每小时。试用最少邮车，并规划邮车的行驶路线使总费用最省。

那么输入参数需要包括：

1. 各个节点的经纬度，邮件收寄数，邮件送达数，时间窗（如果有要求的话，包括最早、最晚到达时间），装卸货时间
2. 可用车辆的载重

输出结果就是算法形成的路径，每条路径中包括到达邮局的先后次序。

问题的解决步骤是： 读入数据、构建路径 、合并路径、优化。

优化阶段对 可行解 进行了节点的调整，缩短行车路线。

目前已经基于CW节约算法，实现 载重量 约束 以及 时间窗口约束，使用Java作为实现。

邮局类

 package vrp;

 import java.util.Objects;

 /**
  * @author <a herf="chenhy@itek-china.com">陈海越</a>
  * @version 1.0
  * @since 新标准版5.0
  */
 public class PostOffice implements Cloneable {

     public PostOffice(int index, String name, float x, float y,
                       float receive, float sendOut,
                       int earliestTime, int latestTime, int duration,
                       int type) {
         this.index = index;
         this.name = name;
         this.x = x;
         this.y = y;
         this.receive = receive;
         this.sendOut = sendOut;
         this.earliestTime = earliestTime;
         this.latestTime = latestTime;
         this.duration = duration;
         this.type = type;
     }

     /**
      * 序号
      */
     private int index;

     private String name;

     private float x;

     private float y;

     private float receive;

     private float sendOut;

     /**
      * 最早到达时间
      */
     private int earliestTime;

     /**
      * 最晚到达时间
      */
     private int latestTime;

     /**
      * 到达时间
      */
     private int arrivedTime;

     private int duration;

     private int type;

     private Route currentRoute;

     private PostOffice previousNode;

     private PostOffice nextNode;

     public String getName() {
         return name;
     }

     public void setName(String name) {
         this.name = name;
     }

     public float getSendOut() {
         return sendOut;
     }

     public void setSendOut(float sendOut) {
         this.sendOut = sendOut;
     }

     public PostOffice getPreviousNode() {
         return previousNode;
     }

     public void setPreviousNode(PostOffice previousNode) {
         this.previousNode = previousNode;
     }

     public PostOffice getNextNode() {
         return nextNode;
     }

     public void setNextNode(PostOffice nextNode) {
         this.nextNode = nextNode;
     }

     public int getArrivedTime() {
         return arrivedTime;
     }

     public void setArrivedTime(int arrivedTime) {
         this.arrivedTime = arrivedTime;
     }

     public Route getCurrentRoute() {
         return currentRoute;
     }

     public void setCurrentRoute(Route currentRoute) {
         this.currentRoute = currentRoute;
     }

     public int getIndex() {
         return index;
     }

     public float getX() {
         return x;
     }

     public float getY() {
         return y;
     }

     public float getReceive() {
         return receive;
     }

     public int getEarliestTime() {
         return earliestTime;
     }

     public int getLatestTime() {
         return latestTime;
     }

     public int getDuration() {
         return duration;
     }

     public int getType() {
         return type;
     }

     public float distanceTo(PostOffice p2) {
         return distanceTo(y, x, p2.y, p2.x, 'K');
     }

     /**
      * 使用经纬度计算，返回距离
      * @param lat1 纬度1
      * @param lon1 经度1
      * @param lat2 纬度2
      * @param lon2 经度2
      * @param unit 'K' 公里 ，默认 英里
      * @return
      */
     private float distanceTo(double lat1, double lon1, double lat2, double lon2, char unit) {
         double theta = lon1 - lon2;
         double dist = Math.sin(deg2rad(lat1)) * Math.sin(deg2rad(lat2)) + Math.cos(deg2rad(lat1)) * Math.cos(deg2rad(lat2)) * Math.cos(deg2rad(theta));
         dist = Math.acos(dist);
         dist = rad2deg(dist);
         dist = dist * 60 * 1.1515;
         if (unit == 'K') {
             dist = dist * 1.609344;
         }
         return (float)(dist);
     }

     private double deg2rad(double deg) {
         return (deg * Math.PI / 180.0);
     }

     private double rad2deg(double rad) {
         return (rad * 180.0 / Math.PI);
     }

     public int getDepartTime() {
         return arrivedTime + duration;
     }

     @Override
     public boolean equals(Object o) {
         if (this == o) return true;
         if (o == null || getClass() != o.getClass()) return false;
         PostOffice that = (PostOffice) o;
         return Float.compare(that.x, x) == 0 &&
                 Float.compare(that.y, y) == 0;
     }

     @Override
     public String toString() {
         return "PostOffice{" + index +
                 " (" + x +
                 ", " + y +
                 ")}";
     }

     @Override
     public Object clone() throws CloneNotSupportedException {
         PostOffice clone = (PostOffice) super.clone();
         clone.setCurrentRoute(currentRoute == null ? null :
                 (Route) currentRoute.clone());
         return clone;
     }

     public String getTimeInterval() {
         return index + " [到达时间：" + convertHHmm(arrivedTime) +
                 ", 出发时间：" + convertHHmm(getDepartTime()) +
                 "]";
     }

     public String convertHHmm(int mins) {
         return (mins < 60 ? "0:" : mins/60 + ":") + mins%60 + "";
     }

     public String getCoordinate() {
         return index + " [" + y + ", " + x + "]";
     }

     @Override
     public int hashCode() {
         return Objects.hash(x, y);
     }
 }

PostOffice.java

路径类

 package vrp;

 import java.util.Collections;
 import java.util.Comparator;
 import java.util.LinkedList;
 import java.util.List;
 import java.util.stream.Collectors;

 /**
  * @author <a herf="chenhy@itek-china.com">陈海越</a>
  * @version 1.0
  * @since 新标准版5.0
  *
  * <pre>
  * 历史：
  *      建立: 2019/9/3 陈海越
  *        </pre>
  */
 public class Route implements Cloneable{

     public static final double DEFAULT_DELTA = 0.0001;
     private LinkedList<PostOffice> nodes;

     private Float capacity = 0f;

     private Float totalReceive = 0f;

     private Float totalSendOut = 0f;

     private Float length = 0f;

     /**
      *  公里每分钟
      */
     private Float speed = 0.5f;

     public void setNodesAndUpdateLoad(List<PostOffice> nodes) {
         this.nodes = new LinkedList<>(nodes);
         for (int i = 0; i < nodes.size(); i++) {
             PostOffice node = nodes.get(i);
             addReceive(node.getReceive());
             addSendOut(node.getSendOut());
         }
     }

     public void setCapacity(Float capacity) {
         this.capacity = capacity;
     }

     public Float getSpeed() {
         return speed;
     }

     public void setSpeed(Float speed) {
         this.speed = speed;
     }

     public void setTotalReceive(Float totalReceive) {
         this.totalReceive = totalReceive;
     }

     public Float getTotalReceive() {
         return totalReceive;
     }

     public Float getTotalSendOut() {
         return totalSendOut;
     }

     public void setTotalSendOut(Float totalSendOut) {
         this.totalSendOut = totalSendOut;
     }

     public Float getCapacity() {
         return capacity;
     }

     public LinkedList<PostOffice> getNodes() {
         return nodes;
     }

     public Float getLength() {
         return length;
     }

     public void setLength(Float length) {
         this.length = length;
     }

     public void addReceive(Float receive) {
         totalReceive += receive;
     }

     public void addSendOut(Float sendOut) {
         totalSendOut += sendOut;
     }

     public Float calcLength(LinkedList<PostOffice> nodes) {
         Float length = 0f;
         if (!nodes.isEmpty()) {
             PostOffice firstNode = nodes.getFirst();
             for (int i=1;i<nodes.size();i++) {
                 PostOffice next = nodes.get(i);
                 length += next.distanceTo(firstNode);
                 firstNode = next;
             }
         }
         return length;
     }

     public boolean twoOptOptimise(){
         //交换中间路径 任意两点，尝试优化路径
         boolean optimised = false;
         for (int i = 1; i < nodes.size()-1; i++) {
             for (int j = i+1; j < nodes.size()-1; j++) {
                 LinkedList<PostOffice> tempList = (LinkedList<PostOffice>) nodes.clone();
                 int k = i, l = j;
                 while (k < l) {
                     Collections.swap(tempList, k, l);
                     k++;l--;
                 }
                 Float tempLength = calcLength(tempList);
                 if (length - tempLength > DEFAULT_DELTA) {
                     //优化成功
                     nodes = tempList;
                     length = tempLength;
                     updateNodeTracing();
                     updateArrivedTime();
                     optimised = true;
                 }
             }
         }
         return optimised;
     }

     /**
      * 更新路径上点的前后关系
      */
     public void updateNodeTracing() {
         PostOffice previous = nodes.get(0);
         for (int i = 1; i < nodes.size(); i++) {
             PostOffice node = nodes.get(i);
             //设置点的前后关系
             node.setPreviousNode(previous);
             previous.setNextNode(node);
             previous = node;
         }
     }

     public void updateArrivedTime() {
         PostOffice previous = nodes.get(0);
         previous.setArrivedTime(previous.getEarliestTime());
         for (int i = 1; i < nodes.size(); i++) {
             PostOffice node = nodes.get(i);
             // 节点到达时间为 离开上一节点时间加上路程时间
             int arrivedTime = previous.getDepartTime() + (int)((node.distanceTo(previous)) / speed);
             node.setArrivedTime(arrivedTime);
             previous = node;
         }

     }

     @Override
     public String toString() {
         return (nodes == null ? "[]" : nodes.stream().map(PostOffice::getCoordinate).collect(Collectors.toList()).toString()) +
                 ", 车辆载重=" + capacity +
                 ", 总送达=" + totalReceive +
                 ", 总收寄=" + totalSendOut +
                 ", 总长度=" + length + "公里" +
                 ", 速度=" + speed * 60 + "公里每小时";
     }

     public String timeSchedule() {
         return "到达时间{" +
                 "邮局=" + (nodes == null ? "[]" : nodes.stream().map(PostOffice::getTimeInterval).collect(Collectors.toList()).toString());
     }

     @Override
     public Object clone() throws CloneNotSupportedException {
         return super.clone();
     }

     /**
      * 硬时间窗限制
      * 到达时间 不能早于最早时间，不能晚于最晚时间
      * @param p1
      * @return
      */
     public boolean hardTimeWindowFeasible(PostOffice p1) {
         PostOffice previous = p1;
         int lastDepart = previous.getDepartTime();
         for (PostOffice node : nodes) {
             int arrivedTime = lastDepart + (int)((node.distanceTo(previous)) / speed);
             if (arrivedTime < node.getEarliestTime() || arrivedTime > node.getLatestTime() ) {
                 return false;
             }
             lastDepart = arrivedTime + node.getDuration();
             previous = node;
         }
         return true;
     }

     public boolean vehicleOptimise(LinkedList<Float> vehicleCapacityList, LinkedList<Float> usedVehicleList) {

         vehicleCapacityList.sort(Comparator.naturalOrder());
         for (Float temp : vehicleCapacityList) {
             if (temp < this.capacity) {
                 if (temp > this.totalReceive) {
                     Float curLoad = totalReceive;
                     boolean cando = true;
                     for (PostOffice node : nodes) {
                         if ( curLoad - node.getReceive() + node.getSendOut() > temp) {
                             cando = false;
                             break;
                         }
                         curLoad = curLoad - node.getReceive() + node.getSendOut();
                     }
                     if (cando) {
                         vehicleCapacityList.remove(temp);
                         vehicleCapacityList.add(capacity);
                         usedVehicleList.remove(capacity);
                         usedVehicleList.add(temp);
                         this.capacity = temp;
                         return true;
                     }
                 }

             }
         }
         return false;
     }
 }

Route.java

节约距离类

 package vrp;

 /**
  * @author <a herf="chenhy@itek-china.com">陈海越</a>
  * @version 1.0
  * @since 新标准版5.0
  *
  * <pre>
  * 历史：
  *      建立: 2019/9/3 陈海越
  *        </pre>
  */
 public class SavedDistance implements Comparable {

     private PostOffice p1;
     private PostOffice p2;
     private float savedDistance;

     public SavedDistance(PostOffice p1, PostOffice p2, float savedDistance) {
         this.p1 = p1;
         this.p2 = p2;
         this.savedDistance = savedDistance;
     }

     public PostOffice getP1() {
         return p1;
     }

     public PostOffice getP2() {
         return p2;
     }

     public PostOffice getAnother(PostOffice p) {
         if (p.equals(p1)) {
             return p2;
         } else if (p.equals(p2)) {
             return p1;
         }
         return null;
     }

     public float getSavedDistance() {
         return savedDistance;
     }

     @Override
     public String toString() {
         return "SD{" +
                 "(" + p1 +
                 " -> " + p2 +
                 "), saved=" + savedDistance +
                 '}';
     }

     @Override
     public int compareTo(Object o) {
         return Float.compare(savedDistance, ((SavedDistance) o).savedDistance);
     }

     public PostOffice nodeAt(Route existRoute) throws Exception {
         if (existRoute.getNodes().contains(p1)) {
             return p1;
         } else if (existRoute.getNodes().contains(p2)) {
             return p2;
         }

         throw new Exception("p1:" + p1 + ", p2:" + p2 +". 均不存在于路径：" + existRoute);
     }
 }

SaveDistance.java

程序入口

 package vrp;

 import java.io.BufferedReader;
 import java.io.File;
 import java.io.FileNotFoundException;
 import java.io.FileReader;
 import java.io.IOException;
 import java.util.ArrayList;
 import java.util.Arrays;
 import java.util.Collections;
 import java.util.Comparator;
 import java.util.LinkedList;
 import java.util.List;

 /**
  * @author <a herf="chenhy@itek-china.com">陈海越</a>
  * @version 1.0
  * @since 新标准版5.0
  *
  * <pre>
  * 历史：
  *      建立: 2019/9/2 陈海越
  *        </pre>
  */
 public class VRPTest {

     public static final String KONGGE = "\\s+|\r";
     public static final int FACTOR = 1;
     private int vehicleNumber;
     private int totalPointNumber;
     private LinkedList<Float> vehicleCapacityList = new LinkedList<>();
     private LinkedList<Float> usedVehicleList = new LinkedList<>();
     private List<PostOffice> postOfficeList = new ArrayList<>();
     private List<Route> routeList = new ArrayList<>();
     private float[][] distMatrix;
     private List<SavedDistance> savingList = new ArrayList<>();

     public static void main(String[] args) throws Exception {
         VRPTest vrpTest = new VRPTest();
         vrpTest.readFromFile("C:\\Users\\Administrator\\Documents\\vrp_data\\test3.txt");
         vrpTest.vrp();
     }

     /**
      * 从文件中读取数据
      */
     public void readFromFile(String fileName) {
         File file = new File(fileName);
         try {
             BufferedReader br = new BufferedReader(new FileReader(
                     file));
             constructGeneral(br);
             constructVehicle(br);
             constructNodes(br);
         } catch (FileNotFoundException e) {
             e.printStackTrace();
         } catch (IOException e) {
             e.printStackTrace();
         }
     }

     private void constructGeneral(BufferedReader br) throws IOException {
         String first = br.readLine().trim();
         String[] firstLineArr = first.split(KONGGE);
         vehicleNumber = Integer.parseInt(firstLineArr[0]);
         totalPointNumber = Integer.parseInt(firstLineArr[1]);
     }

     private void constructVehicle(BufferedReader br) throws IOException {
         String vehicleCapacity = br.readLine().trim();
         for (String s : vehicleCapacity.split(KONGGE)) {
             vehicleCapacityList.add(Float.parseFloat(s));
         }
     }

     private void constructNodes(BufferedReader br) throws IOException {
         for (int i = 0; i < totalPointNumber; i++) {
             String postStr = br.readLine().trim();
             String[] postArr = postStr.split(KONGGE);
             PostOffice postOffice =
                     new PostOffice(Integer.parseInt(postArr[0]), postArr[1],
                             Float.parseFloat(postArr[2]),
                             Float.parseFloat(postArr[3]),
                             Float.parseFloat(postArr[4]),
                             Float.parseFloat(postArr[5]),
                             Integer.parseInt(postArr[6]),
                             Integer.parseInt(postArr[7]),
                             Integer.parseInt(postArr[8]),
                             isDepot(i));
             postOfficeList.add(postOffice);
         }
     }

     private int isDepot(int i) {
         //第一条记录为仓库
         return i == 0 ? 0 : 1;
     }

     public void vrp() throws Exception {
         calcDistMatrix();
         calcSavingMatrix();
         calcRoute();
         cwSaving();
         //optimise
         twoOptOptimise();
         capacityOptimise();

         printGeneral();
         printRoute();
 //        printTimeSchedule();
     }

     /**
      * 计算距离矩阵
      */
     private void calcDistMatrix() {
         int length = postOfficeList.size();
         distMatrix = new float[length][length];
         for (int i = 0; i < totalPointNumber; i++) {
             for (int j = 0; j < i; j++) {
                 distMatrix[i][j] = postOfficeList.get(i).distanceTo(postOfficeList.get(j));
                 distMatrix[j][i] = distMatrix[i][j];
             }
             distMatrix[i][i] = 0;
         }
     }

     /**
      * 计算节约距离列表
      */
     private void calcSavingMatrix() {
         for (int i = 2; i < totalPointNumber; i++) {
             for (int j = 1; j < i; j++) {
                 PostOffice pi = postOfficeList.get(i);
                 PostOffice pj = postOfficeList.get(j);
                 PostOffice depot = postOfficeList.get(0);
                 float dist = pi.distanceTo(pj);
                 float saving =
                         pi.distanceTo(depot) + pj.distanceTo(depot) - dist;
                 savingList.add(new SavedDistance(postOfficeList.get(i), postOfficeList.get(j), saving));
             }
         }
         savingList.sort(Collections.reverseOrder());
     }

     private boolean twoOptOptimise() {
         for (Route route : routeList) {
             if (route.twoOptOptimise()) {
                 return true;
             }
         }
         return false;
     }

     private boolean capacityOptimise() {
         for (Route route : routeList) {
             if (route.vehicleOptimise(vehicleCapacityList, usedVehicleList)) {
                 return true;
             }
         }
         return false;
     }

     /**
      * 构建基础路径
      */
     private void calcRoute() throws CloneNotSupportedException {
         //将所有点单独与集散中心组成一条路径，路径对象中包含集散中心
         PostOffice depot = postOfficeList.get(0);
         for(int i = 1 ; i<postOfficeList.size(); i++) {
             Route r = new Route();
             //更新点 所在路径
             PostOffice startNode = (PostOffice) depot.clone();
             startNode.setCurrentRoute(r);
             PostOffice endNode = (PostOffice) depot.clone();
             endNode.setCurrentRoute(r);
             postOfficeList.get(i).setCurrentRoute(r);
             //更新路径 上的点
             r.setNodesAndUpdateLoad(new LinkedList<>(Arrays.asList(startNode, postOfficeList.get(i), endNode)));

             //更新到达时间
             r.updateArrivedTime();
             //更新路径长度
             r.setLength(r.calcLength(r.getNodes()));
             //更新原路径上点的前后关系
             r.updateNodeTracing();
             //更新载重
             routeList.add(r);
         }
     }

     /**
      * CW节约算法构建路程
      * @throws Exception
      */
     private void cwSaving() throws Exception {
         //取出save值最大的路径，尝试加入当前路径
         for (SavedDistance savedDistance : savingList) {
             mergeSavedDistance(savedDistance);
         }
     }

     /**
      * 合并路径规则：
      * 两点中有一点在路径尾部，一点在路径头部，并且路径总容积满足车辆容积限制
      * 先单独判断 是为了防止 已经分配了车辆的路径没有充分负载
      * @param savedDistance
      */
     private void mergeSavedDistance(SavedDistance savedDistance) throws Exception {
         Route r1 = savedDistance.getP1().getCurrentRoute();
         Route r2 = savedDistance.getP2().getCurrentRoute();
         PostOffice p1 = savedDistance.getP1();
         PostOffice p2 = savedDistance.getP2();

         if (r1.equals(r2)) return;

         if (r1.getCapacity() != 0 ) {
             //如果r1已分配车辆， 计算 容积限制
             tryMergeToRoute(savedDistance, r1, r2, p1, p2);
             return;
         }

         if (r2.getCapacity() != 0) {
             //如果r2已分配车辆，计算 容积限制
             tryMergeToRoute(savedDistance, r2, r1, p2, p1);
             return;
         }

         //如果都没有分配过车辆, 给r1分配 目前容积最大的车辆
         if (r1.getCapacity() == 0) {
             if (vehicleCapacityList.isEmpty()) throw new Exception("汽车已经分配完了");
             //设置车辆总容积
             Float capacity = vehicleCapacityList.pop();
             usedVehicleList.add(capacity);
             r1.setCapacity(capacity * FACTOR);

             tryMergeToRoute(savedDistance, r1, r2, p1, p2);
             return;
         }

         //超过r1容积限制，尝试r2。如果没有分配过车辆, 给r2分配 目前容积最大的车辆
         if (r2.getCapacity() == 0) {
             if (vehicleCapacityList.isEmpty()) throw new Exception("汽车已经分配完了");
             //设置车辆总容积
             Float capacity = vehicleCapacityList.pop();
             usedVehicleList.add(capacity);
             r2.setCapacity(capacity * FACTOR);

             tryMergeToRoute(savedDistance, r2, r1, p2, p1);
         }
     }

     private void tryMergeToRoute(SavedDistance savedDistance,
                                  Route existRoute,
                                  Route mergedRoute,
                                  PostOffice existNode,
                                  PostOffice mergedNode) throws Exception {
         if (appendMergedRoute(existRoute, mergedRoute, existNode,
                 mergedNode)) {
             if (capacityFeasible(existRoute, mergedRoute, false)) {
                 //合并到现有路径之后
                 if (mergedRoute.hardTimeWindowFeasible(existNode)) {
                     mergeRoute(existRoute, mergedRoute, savedDistance
                             , existNode, false);
                 }
             }
         } else if (insertMergedRoute(existRoute, mergedRoute,
                 existNode, mergedNode)) {
             if (capacityFeasible(existRoute, mergedRoute, true)) {
                 //合并到现有路径之前
                 if (existRoute.hardTimeWindowFeasible(mergedNode)) {
                     mergeRoute(existRoute, mergedRoute, savedDistance
                             , existNode, true);
                 }
             }
         }
     }

     private boolean insertMergedRoute(Route existRoute,
                                       Route mergedRoute,
                                       PostOffice existNode,
                                       PostOffice mergedNode) throws Exception {
         if (mergedRoute.getNodes().size() < 3 || existRoute.getNodes().size() < 3)
             throw new Exception("合并路径 节点少于3个");
         return existRoute.getNodes().indexOf(existNode) == 1 && mergedRoute.getNodes().indexOf(mergedNode) == mergedRoute.getNodes().size() - 2;
     }

     private boolean appendMergedRoute(Route existRoute,
                                       Route mergedRoute,
                                       PostOffice existNode,
                                       PostOffice mergedNode) throws Exception {
         if (mergedRoute.getNodes().size() < 3 || existRoute.getNodes().size() < 3)
             throw new Exception("合并路径 节点少于3个");
         return existRoute.getNodes().indexOf(existNode) == existRoute.getNodes().size() - 2 && mergedRoute.getNodes().indexOf(mergedNode) == 1;
     }

     private boolean capacityFeasible(Route existRoute,
                                      Route mergedRoute,
                                      boolean isInsert) throws Exception {
         if (existRoute.getCapacity() > (mergedRoute.getTotalReceive() + existRoute.getTotalReceive()) ) {
             if (isInsert) {
                 Float curLoad = mergedRoute.getTotalSendOut() + existRoute.getTotalReceive();
                 for (PostOffice node : existRoute.getNodes()) {
                     if (curLoad - node.getReceive() + node.getSendOut() > existRoute.getCapacity()) {
                         return false;
                     }
                     curLoad = curLoad - node.getReceive() + node.getSendOut();
                     if (curLoad < 0)
                         throw new Exception("isInsert=true, 当前载重出错，小于0");
                 }
             } else {
                 Float curLoad = existRoute.getTotalSendOut() + mergedRoute.getTotalReceive();
                 for (PostOffice node : mergedRoute.getNodes()) {
                     if (curLoad - node.getReceive() + node.getSendOut() > existRoute.getCapacity()) {
                         return false;
                     }
                     curLoad = curLoad - node.getReceive() + node.getSendOut();
                     if (curLoad < 0)
                         throw new Exception("isInsert=false, 当前载重出错，小于0");
                 }
             }
             return true;
         }

         return false;
     }

     /**
      * 合并路径 算法
      * @param existRoute
      * @param mergedRoute
      * @param savedDistance
      * @param p
      * @param beforeP
      * @throws Exception
      */
     private void mergeRoute(Route existRoute, Route mergedRoute,
                             SavedDistance savedDistance, PostOffice p
             , Boolean beforeP) throws Exception {
         //合并点在p1之前
         LinkedList<PostOffice> mergedNodes = mergedRoute.getNodes();
         mergedNodes.removeFirst();
         mergedNodes.removeLast();

         //从合并处 插入 被合并路径中所有营业点
         existRoute.getNodes().addAll(existRoute.getNodes().indexOf(p) + (beforeP ? 0 : 1), mergedRoute.getNodes());
         //更新 原有路径上所有营业点 所在路径
         mergedNodes.forEach(node -> {
             node.setCurrentRoute(existRoute);
         });
         //更新原路径上点的前后关系
         existRoute.updateNodeTracing();
         //更新到达时间
         existRoute.updateArrivedTime();
         //更新载重
         existRoute.addReceive(mergedRoute.getTotalReceive());
         existRoute.addSendOut(mergedRoute.getTotalSendOut());
         //更新路径长度
         existRoute.setLength(existRoute.calcLength(existRoute.getNodes()));
         //清除 被合并路径
         if (mergedRoute.getCapacity() != 0f) {
             vehicleCapacityList.push(mergedRoute.getCapacity() / FACTOR);
             vehicleCapacityList.sort(Comparator.reverseOrder());
             usedVehicleList.remove(mergedRoute.getCapacity() / FACTOR);
         }
         routeList.remove(mergedRoute);
     }

     private void printGeneral() {
         System.out.println("车辆总数: " + vehicleNumber);
         System.out.println("邮局总数: " + totalPointNumber);
         System.out.println("使用车辆: " + usedVehicleList);
         System.out.println("剩余车辆: " + vehicleCapacityList);
 //        System.out.println("邮局位置: " + postOfficeList);
 //        if (savingList.size() >= 5) {
 //            System.out.println("\n节约距离 top 5: " + savingList.subList(0, 5).toString());
 //        }
     }

     private void printRoute() {
         System.out.println("\n路径: ");
         for (int i = 0; i < routeList.size(); i++) {
             Route r = routeList.get(i);
             System.out.println(i + " " + r.toString());
         }
     }

     private void printTimeSchedule() {
         System.out.println("\n到达时间 ");
         for (int i = 0; i < routeList.size(); i++) {
             Route r = routeList.get(i);
             System.out.println(i + " " + r.timeSchedule());
         }
     }

     public int getTotalPointNumber() {
         return totalPointNumber;
     }

     public LinkedList<Float> getUsedVehicleList() {
         return usedVehicleList;
     }

     public List<PostOffice> getPostOfficeList() {
         return postOfficeList;
     }

     public List<Route> getRouteList() {
         return routeList;
     }

 }

程序入口

测试数据

12 32
20 20 20 8 7.5 19 18.5 3 2 2 15 15
 0 邮件处理中心 113.401158 22.937741 0 0 360 1200 0
 1 市桥营业部 113.400252 22.938145 1.5 2.0 360 1200 30
 2 南村营业部 113.401893 23.018498 1.5 2.0 360 1200 30
 3 南沙营业部 113.506397 22.816508 1.5 2.0 360 1200 30
 4 大石营业部 113.314550 23.003639 1.5 2.0 360 1200 30
 5 洛溪营业部 113.326329 23.039990 1.5 2.0 360 1000 30
 6 石基营业部 113.442812 22.958920 2.0 1.5 360 1200 30
 7 桥南营业部 113.341478 22.928405 2.0 1.5 360 1200 30
 9 金山营业部 113.357242 22.987939 2.0 1.5 360 1200 30
10 德兴投递部 113.385036 22.941521 2.0 1.5 360 1200 30
11 禺山投递部 113.371736 22.940598 2.0 1.5 360 1200 30
12 富都投递部 113.374778 22.962895 2.0 1.5 360 1200 30
13 桥南投递部 113.376950 22.928157 2.0 1.5 360 1200 30
14 石基投递部 113.442540 22.958869 2.0 1.5 360 1200 30
15 大石投递部 113.312418 23.029387 2.0 1.5 360 1200 30
16 丽江投递部 113.308222 23.041347 2.0 1.5 360 1200 30
17 钟村投递部 113.323570 22.983256 2.0 1.5 360 1200 30
18 沙湾投递部 113.346612 22.907224 2.0 1.5 360 1200 30
19 祈福投递部 113.343419 22.973618 2.0 1.5 360 1200 30
20 南村投递部 113.391632 23.002452 2.0 1.5 360 1200 30
21 石楼投递部 113.323820 22.983377 2.0 1.5 360 1200 30
22 新造投递部 113.424587 23.041629 2.0 1.5 360 1200 30
23 化龙投递部 113.472498 23.033740 2.0 1.5 360 1200 30
24 东涌投递部 113.461433 22.891050 2.0 1.5 360 1200 30
25 鱼窝头投递部 113.465328 22.856062 2.0 1.5 360 1200 30
26 南沙投递部 113.538039 22.792315 2.0 1.5 360 1200 30
27 黄阁投递部 113.516492 22.829905 2.0 1.5 360 1200 30
28 大岗投递部 113.412975 22.806085 2.0 1.5 360 1200 30
29 榄核投递部 113.346429 22.844289 2.0 1.5 360 1200 30
30 万顷沙投递部 113.558386 22.712772 2.0 1.5 360 1200 30
31 新垦投递部 113.613264 22.650771 2.0 1.5 360 1200 30
32 横沥投递部 113.494007 22.737961 2.0 1.5 360 1200 30

测试数据