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：
- 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
- 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。
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
1 package vrp;
2
3 import java.util.Objects;
4
5 /**
6 * @author
7 * @version 1.0
8 * @since 新标准版5.0
9 */
10 public class PostOffice implements Cloneable {
11
12 public PostOffice(int index, String name, float x, float y,
13 float receive, float sendOut,
14 int earliestTime, int latestTime, int duration,
15 int type) {
16 this.index = index;
17 this.name = name;
18 this.x = x;
19 this.y = y;
20 this.receive = receive;
21 this.sendOut = sendOut;
22 this.earliestTime = earliestTime;
23 this.latestTime = latestTime;
24 this.duration = duration;
25 this.type = type;
26 }
27
28 /**
29 * 序号
30 */
31 private int index;
32
33 private String name;
34
35 private float x;
36
37 private float y;
38
39 private float receive;
40
41 private float sendOut;
42
43 /**
44 * 最早到达时间
45 */
46 private int earliestTime;
47
48 /**
49 * 最晚到达时间
50 */
51 private int latestTime;
52
53 /**
54 * 到达时间
55 */
56 private int arrivedTime;
57
58 private int duration;
59
60 private int type;
61
62 private Route currentRoute;
63
64 private PostOffice previousNode;
65
66 private PostOffice nextNode;
67
68 public String getName() {
69 return name;
70 }
71
72 public void setName(String name) {
73 this.name = name;
74 }
75
76 public float getSendOut() {
77 return sendOut;
78 }
79
80 public void setSendOut(float sendOut) {
81 this.sendOut = sendOut;
82 }
83
84 public PostOffice getPreviousNode() {
85 return previousNode;
86 }
87
88 public void setPreviousNode(PostOffice previousNode) {
89 this.previousNode = previousNode;
90 }
91
92 public PostOffice getNextNode() {
93 return nextNode;
94 }
95
96 public void setNextNode(PostOffice nextNode) {
97 this.nextNode = nextNode;
98 }
99
100 public int getArrivedTime() {
101 return arrivedTime;
102 }
103
104 public void setArrivedTime(int arrivedTime) {
105 this.arrivedTime = arrivedTime;
106 }
107
108
109 public Route getCurrentRoute() {
110 return currentRoute;
111 }
112
113 public void setCurrentRoute(Route currentRoute) {
114 this.currentRoute = currentRoute;
115 }
116
117 public int getIndex() {
118 return index;
119 }
120
121 public float getX() {
122 return x;
123 }
124
125 public float getY() {
126 return y;
127 }
128
129 public float getReceive() {
130 return receive;
131 }
132
133 public int getEarliestTime() {
134 return earliestTime;
135 }
136
137 public int getLatestTime() {
138 return latestTime;
139 }
140
141 public int getDuration() {
142 return duration;
143 }
144
145 public int getType() {
146 return type;
147 }
148
149 public float distanceTo(PostOffice p2) {
150 return distanceTo(y, x, p2.y, p2.x, 'K');
151 }
152
153 /**
154 * 使用经纬度计算，返回距离
155 * @param lat1 纬度1
156 * @param lon1 经度1
157 * @param lat2 纬度2
158 * @param lon2 经度2
159 * @param unit 'K' 公里 ，默认 英里
160 * @return
161 */
162 private float distanceTo(double lat1, double lon1, double lat2, double lon2, char unit) {
163 double theta = lon1 - lon2;
164 double dist = Math.sin(deg2rad(lat1)) * Math.sin(deg2rad(lat2)) + Math.cos(deg2rad(lat1)) * Math.cos(deg2rad(lat2)) * Math.cos(deg2rad(theta));
165 dist = Math.acos(dist);
166 dist = rad2deg(dist);
167 dist = dist * 60 * 1.1515;
168 if (unit == 'K') {
169 dist = dist * 1.609344;
170 }
171 return (float)(dist);
172 }
173
174 private double deg2rad(double deg) {
175 return (deg * Math.PI / 180.0);
176 }
177
178 private double rad2deg(double rad) {
179 return (rad * 180.0 / Math.PI);
180 }
181
182 public int getDepartTime() {
183 return arrivedTime + duration;
184 }
185
186 @Override
187 public boolean equals(Object o) {
188 if (this == o) return true;
189 if (o == null || getClass() != o.getClass()) return false;
190 PostOffice that = (PostOffice) o;
191 return Float.compare(that.x, x) == 0 &&
192 Float.compare(that.y, y) == 0;
193 }
194
195 @Override
196 public String toString() {
197 return "PostOffice{" + index +
198 " (" + x +
199 ", " + y +
200 ")}";
201 }
202
203 @Override
204 public Object clone() throws CloneNotSupportedException {
205 PostOffice clone = (PostOffice) super.clone();
206 clone.setCurrentRoute(currentRoute == null ? null :
207 (Route) currentRoute.clone());
208 return clone;
209 }
210
211 public String getTimeInterval() {
212 return index + " [到达时间：" + convertHHmm(arrivedTime) +
213 ", 出发时间：" + convertHHmm(getDepartTime()) +
214 "]";
215 }
216
217 public String convertHHmm(int mins) {
218 return (mins < 60 ? "0:" : mins/60 + ":") + mins%60 + "";
219 }
220
221 public String getCoordinate() {
222 return index + " [" + y + ", " + x + "]";
223 }
224
225 @Override
226 public int hashCode() {
227 return Objects.hash(x, y);
228 }
229 }
路径类
1 package vrp;
2
3 import java.util.Collections;
4 import java.util.Comparator;
5 import java.util.LinkedList;
6 import java.util.List;
7 import java.util.stream.Collectors;
8
9 /**
10 * @author
11 * @version 1.0
12 * @since 新标准版5.0
13 *
14 *
15 * 历史：
16 * 建立: 2019/9/3 陈海越
17 *
18 */
19 public class Route implements Cloneable{
20
21 public static final double DEFAULT_DELTA = 0.0001;
22 private LinkedList<postoffice> nodes;
23
24 private Float capacity = 0f;
25
26 private Float totalReceive = 0f;
27
28 private Float totalSendOut = 0f;
29
30 private Float length = 0f;
31
32 /**
33 * 公里每分钟
34 */
35 private Float speed = 0.5f;
36
37 public void setNodesAndUpdateLoad(List<postoffice> nodes) {
38 this.nodes = new LinkedList<>(nodes);
39 for (int i = 0; i < nodes.size(); i++) {
40 PostOffice node = nodes.get(i);
41 addReceive(node.getReceive());
42 addSendOut(node.getSendOut());
43 }
44 }
45
46 public void setCapacity(Float capacity) {
47 this.capacity = capacity;
48 }
49
50 public Float getSpeed() {
51 return speed;
52 }
53
54 public void setSpeed(Float speed) {
55 this.speed = speed;
56 }
57
58 public void setTotalReceive(Float totalReceive) {
59 this.totalReceive = totalReceive;
60 }
61
62 public Float getTotalReceive() {
63 return totalReceive;
64 }
65
66 public Float getTotalSendOut() {
67 return totalSendOut;
68 }
69
70 public void setTotalSendOut(Float totalSendOut) {
71 this.totalSendOut = totalSendOut;
72 }
73
74 public Float getCapacity() {
75 return capacity;
76 }
77
78 public LinkedList<postoffice> getNodes() {
79 return nodes;
80 }
81
82 public Float getLength() {
83 return length;
84 }
85
86 public void setLength(Float length) {
87 this.length = length;
88 }
89
90 public void addReceive(Float receive) {
91 totalReceive += receive;
92 }
93
94 public void addSendOut(Float sendOut) {
95 totalSendOut += sendOut;
96 }
97
98 public Float calcLength(LinkedList<postoffice> nodes) {
99 Float length = 0f;
100 if (!nodes.isEmpty()) {
101 PostOffice firstNode = nodes.getFirst();
102 for (int i=1;i<nodes.size>103 PostOffice next = nodes.get(i);
104 length += next.distanceTo(firstNode);
105 firstNode = next;
106 }
107 }
108 return length;
109 }
110
111 public boolean twoOptOptimise(){
112 //交换中间路径 任意两点，尝试优化路径
113 boolean optimised = false;
114 for (int i = 1; i < nodes.size()-1; i++) {
115 for (int j = i+1; j < nodes.size()-1; j++) {
116 LinkedList<postoffice> tempList = (LinkedList<postoffice>) nodes.clone();
117 int k = i, l = j;
118 while (k < l) {
119 Collections.swap(tempList, k, l);
120 k++;l--;
121 }
122 Float tempLength = calcLength(tempList);
123 if (length - tempLength > DEFAULT_DELTA) {
124 //优化成功
125 nodes = tempList;
126 length = tempLength;
127 updateNodeTracing();
128 updateArrivedTime();
129 optimised = true;
130 }
131 }
132 }
133 return optimised;
134 }
135
136 /**
137 * 更新路径上点的前后关系
138 */
139 public void updateNodeTracing() {
140 PostOffice previous = nodes.get(0);
141 for (int i = 1; i < nodes.size(); i++) {
142 PostOffice node = nodes.get(i);
143 //设置点的前后关系
144 node.setPreviousNode(previous);
145 previous.setNextNode(node);
146 previous = node;
147 }
148 }
149
150 public void updateArrivedTime() {
151 PostOffice previous = nodes.get(0);
152 previous.setArrivedTime(previous.getEarliestTime());
153 for (int i = 1; i < nodes.size(); i++) {
154 PostOffice node = nodes.get(i);
155 // 节点到达时间为 离开上一节点时间加上路程时间
156 int arrivedTime = previous.getDepartTime() + (int)((node.distanceTo(previous)) / speed);
157 node.setArrivedTime(arrivedTime);
158 previous = node;
159 }
160
161 }
162
163 @Override
164 public String toString() {
165 return (nodes == null ? "[]" : nodes.stream().map(PostOffice::getCoordinate).collect(Collectors.toList()).toString()) +
166 ", 车辆载重=" + capacity +
167 ", 总送达=" + totalReceive +
168 ", 总收寄=" + totalSendOut +
169 ", 总长度=" + length + "公里" +
170 ", 速度=" + speed * 60 + "公里每小时";
171 }
172
173 public String timeSchedule() {
174 return "到达时间{" +
175 "邮局=" + (nodes == null ? "[]" : nodes.stream().map(PostOffice::getTimeInterval).collect(Collectors.toList()).toString());
176 }
177
178 @Override
179 public Object clone() throws CloneNotSupportedException {
180 return super.clone();
181 }
182
183 /**
184 * 硬时间窗限制
185 * 到达时间 不能早于最早时间，不能晚于最晚时间
186 * @param p1
187 * @return
188 */
189 public boolean hardTimeWindowFeasible(PostOffice p1) {
190 PostOffice previous = p1;
191 int lastDepart = previous.getDepartTime();
192 for (PostOffice node : nodes) {
193 int arrivedTime = lastDepart + (int)((node.distanceTo(previous)) / speed);
194 if (arrivedTime < node.getEarliestTime() || arrivedTime > node.getLatestTime() ) {
195 return false;
196 }
197 lastDepart = arrivedTime + node.getDuration();
198 previous = node;
199 }
200 return true;
201 }
202
203
204 public boolean vehicleOptimise(LinkedList<float> vehicleCapacityList, LinkedList<float> usedVehicleList) {
205
206 vehicleCapacityList.sort(Comparator.naturalOrder());
207 for (Float temp : vehicleCapacityList) {
208 if (temp < this.capacity) {
209 if (temp > this.totalReceive) {
210 Float curLoad = totalReceive;
211 boolean cando = true;
212 for (PostOffice node : nodes) {
213 if ( curLoad - node.getReceive() + node.getSendOut() > temp) {
214 cando = false;
215 break;
216 }
217 curLoad = curLoad - node.getReceive() + node.getSendOut();
218 }
219 if (cando) {
220 vehicleCapacityList.remove(temp);
221 vehicleCapacityList.add(capacity);
222 usedVehicleList.remove(capacity);
223 usedVehicleList.add(temp);
224 this.capacity = temp;
225 return true;
226 }
227 }
228
229 }
230 }
231 return false;
232 }
233 }
/<float>/<float>/<postoffice>/<postoffice>/<nodes.size>/<postoffice>/<postoffice>/<postoffice>/<postoffice>
节约距离类
1 package vrp;
2
3 /**
4 * @author
5 * @version 1.0
6 * @since 新标准版5.0
7 *
8 *
9 * 历史：
10 * 建立: 2019/9/3 陈海越
11 *
12 */
13 public class SavedDistance implements Comparable {
14
15 private PostOffice p1;
16 private PostOffice p2;
17 private float savedDistance;
18
19 public SavedDistance(PostOffice p1, PostOffice p2, float savedDistance) {
20 this.p1 = p1;
21 this.p2 = p2;
22 this.savedDistance = savedDistance;
23 }
24
25 public PostOffice getP1() {
26 return p1;
27 }
28
29 public PostOffice getP2() {
30 return p2;
31 }
32
33 public PostOffice getAnother(PostOffice p) {
34 if (p.equals(p1)) {
35 return p2;
36 } else if (p.equals(p2)) {
37 return p1;
38 }
39 return null;
40 }
41
42 public float getSavedDistance() {
43 return savedDistance;
44 }
45
46 @Override
47 public String toString() {
48 return "SD{" +
49 "(" + p1 +
50 " -> " + p2 +
51 "), saved=" + savedDistance +
52 '}';
53 }
54
55 @Override
56 public int compareTo(Object o) {
57 return Float.compare(savedDistance, ((SavedDistance) o).savedDistance);
58 }
59
60 public PostOffice nodeAt(Route existRoute) throws Exception {
61 if (existRoute.getNodes().contains(p1)) {
62 return p1;
63 } else if (existRoute.getNodes().contains(p2)) {
64 return p2;
65 }
66
67 throw new Exception("p1:" + p1 + ", p2:" + p2 +". 均不存在于路径：" + existRoute);
68 }
69 }
程序入口
1 package vrp;
2
3 import java.io.BufferedReader;
4 import java.io.File;
5 import java.io.FileNotFoundException;
6 import java.io.FileReader;
7 import java.io.IOException;
8 import java.util.ArrayList;
9 import java.util.Arrays;
10 import java.util.Collections;
11 import java.util.Comparator;
12 import java.util.LinkedList;
13 import java.util.List;
14
15 /**
16 * @author
17 * @version 1.0
18 * @since 新标准版5.0
19 *
20 *
21 * 历史：
22 * 建立: 2019/9/2 陈海越
23 *
24 */
25 public class VRPTest {
26
27 public static final String KONGGE = "\\\\s+|\\r";
28 public static final int FACTOR = 1;
29 private int vehicleNumber;
30 private int totalPointNumber;
31 private LinkedList<float> vehicleCapacityList = new LinkedList<>();
32 private LinkedList<float> usedVehicleList = new LinkedList<>();
33 private List<postoffice> postOfficeList = new ArrayList<>();
34 private List<route> routeList = new ArrayList<>();
35 private float[][] distMatrix;
36 private List<saveddistance> savingList = new ArrayList<>();
37
38
39 public static void main(String[] args) throws Exception {
40 VRPTest vrpTest = new VRPTest();
41 vrpTest.readFromFile("C:\\\\Users\\\\Administrator\\\\Documents\\\\vrp_data\\\\test3.txt");
42 vrpTest.vrp();
43 }
44
45 /**
46 * 从文件中读取数据
47 */
48 public void readFromFile(String fileName) {
49 File file = new File(fileName);
50 try {
51 BufferedReader br = new BufferedReader(new FileReader(
52 file));
53 constructGeneral(br);
54 constructVehicle(br);
55 constructNodes(br);
56 } catch (FileNotFoundException e) {
57 e.printStackTrace();
58 } catch (IOException e) {
59 e.printStackTrace();
60 }
61 }
62
63 private void constructGeneral(BufferedReader br) throws IOException {
64 String first = br.readLine().trim();
65 String[] firstLineArr = first.split(KONGGE);
66 vehicleNumber = Integer.parseInt(firstLineArr[0]);
67 totalPointNumber = Integer.parseInt(firstLineArr[1]);
68 }
69
70 private void constructVehicle(BufferedReader br) throws IOException {
71 String vehicleCapacity = br.readLine().trim();
72 for (String s : vehicleCapacity.split(KONGGE)) {
73 vehicleCapacityList.add(Float.parseFloat(s));
74 }
75 }
76
77 private void constructNodes(BufferedReader br) throws IOException {
78 for (int i = 0; i < totalPointNumber; i++) {
79 String postStr = br.readLine().trim();
80 String[] postArr = postStr.split(KONGGE);
81 PostOffice postOffice =
82 new PostOffice(Integer.parseInt(postArr[0]), postArr[1],
83 Float.parseFloat(postArr[2]),
84 Float.parseFloat(postArr[3]),
85 Float.parseFloat(postArr[4]),
86 Float.parseFloat(postArr[5]),
87 Integer.parseInt(postArr[6]),
88 Integer.parseInt(postArr[7]),
89 Integer.parseInt(postArr[8]),
90 isDepot(i));
91 postOfficeList.add(postOffice);
92 }
93 }
94
95 private int isDepot(int i) {
96 //第一条记录为仓库
97 return i == 0 ? 0 : 1;
98 }
99
100 public void vrp() throws Exception {
101 calcDistMatrix();
102 calcSavingMatrix();
103 calcRoute();
104 cwSaving();
105 //optimise
106 twoOptOptimise();
107 capacityOptimise();
108
109 printGeneral();
110 printRoute();
111 // printTimeSchedule();
112 }
113
114 /**
115 * 计算距离矩阵
116 */
117 private void calcDistMatrix() {
118 int length = postOfficeList.size();
119 distMatrix = new float[length][length];
120 for (int i = 0; i < totalPointNumber; i++) {
121 for (int j = 0; j < i; j++) {
122 distMatrix[i][j] = postOfficeList.get(i).distanceTo(postOfficeList.get(j));
123 distMatrix[j][i] = distMatrix[i][j];
124 }
125 distMatrix[i][i] = 0;
126 }
127 }
128
129 /**
130 * 计算节约距离列表
131 */
132 private void calcSavingMatrix() {
133 for (int i = 2; i < totalPointNumber; i++) {
134 for (int j = 1; j < i; j++) {
135 PostOffice pi = postOfficeList.get(i);
136 PostOffice pj = postOfficeList.get(j);
137 PostOffice depot = postOfficeList.get(0);
138 float dist = pi.distanceTo(pj);
139 float saving =
140 pi.distanceTo(depot) + pj.distanceTo(depot) - dist;
141 savingList.add(new SavedDistance(postOfficeList.get(i), postOfficeList.get(j), saving));
142 }
143 }
144 savingList.sort(Collections.reverseOrder());
145 }
146
147 private boolean twoOptOptimise() {
148 for (Route route : routeList) {
149 if (route.twoOptOptimise()) {
150 return true;
151 }
152 }
153 return false;
154 }
155
156 private boolean capacityOptimise() {
157 for (Route route : routeList) {
158 if (route.vehicleOptimise(vehicleCapacityList, usedVehicleList)) {
159 return true;
160 }
161 }
162 return false;
163 }
164
165
166
167 /**
168 * 构建基础路径
169 */
170 private void calcRoute() throws CloneNotSupportedException {
171 //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
172 PostOffice depot = postOfficeList.get(0);
173 for(int i = 1 ; i<postofficelist.size>174 Route r = new Route();
175 //更新点 所在路径
176 PostOffice startNode = (PostOffice) depot.clone();
177 startNode.setCurrentRoute(r);
178 PostOffice endNode = (PostOffice) depot.clone();
179 endNode.setCurrentRoute(r);
180 postOfficeList.get(i).setCurrentRoute(r);
181 //更新路径 上的点
182 r.setNodesAndUpdateLoad(new LinkedList<>(Arrays.asList(startNode, postOfficeList.get(i), endNode)));
183
184 //更新到达时间
185 r.updateArrivedTime();
186 //更新路径长度
187 r.setLength(r.calcLength(r.getNodes()));
188 //更新原路径上点的前后关系
189 r.updateNodeTracing();
190 //更新载重
191 routeList.add(r);
192 }
193 }
194
195 /**
196 * CW节约算法构建路程
197 * @throws Exception
198 */
199 private void cwSaving() throws Exception {
200 //取出save值最大的路径，尝试加入当前路径
201 for (SavedDistance savedDistance : savingList) {
202 mergeSavedDistance(savedDistance);
203 }
204 }
205
206 /**
207 * 合并路径规则：
208 * 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
209 * 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
210 * @param savedDistance
211 */
212 private void mergeSavedDistance(SavedDistance savedDistance) throws Exception {
213 Route r1 = savedDistance.getP1().getCurrentRoute();
214 Route r2 = savedDistance.getP2().getCurrentRoute();
215 PostOffice p1 = savedDistance.getP1();
216 PostOffice p2 = savedDistance.getP2();
217
218 if (r1.equals(r2)) return;
219
220 if (r1.getCapacity() != 0 ) {
221 //如果r1已分配车辆， 计算 容积限制
222 tryMergeToRoute(savedDistance, r1, r2, p1, p2);
223 return;
224 }
225
226 if (r2.getCapacity() != 0) {
227 //如果r2已分配车辆，计算 容积限制
228 tryMergeToRoute(savedDistance, r2, r1, p2, p1);
229 return;
230 }
231
232 //如果都没有分配过车辆, 给r1分配 目前容积最大的车辆
233 if (r1.getCapacity() == 0) {
234 if (vehicleCapacityList.isEmpty()) throw new Exception("汽车已经分配完了");
235 //设置车辆总容积
236 Float capacity = vehicleCapacityList.pop();
237 usedVehicleList.add(capacity);
238 r1.setCapacity(capacity * FACTOR);
239
240 tryMergeToRoute(savedDistance, r1, r2, p1, p2);
241 return;
242 }
243
244 //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
245 if (r2.getCapacity() == 0) {
246 if (vehicleCapacityList.isEmpty()) throw new Exception("汽车已经分配完了");
247 //设置车辆总容积
248 Float capacity = vehicleCapacityList.pop();
249 usedVehicleList.add(capacity);
250 r2.setCapacity(capacity * FACTOR);
251
252 tryMergeToRoute(savedDistance, r2, r1, p2, p1);
253 }
254 }
255
256 private void tryMergeToRoute(SavedDistance savedDistance,
257 Route existRoute,
258 Route mergedRoute,
259 PostOffice existNode,
260 PostOffice mergedNode) throws Exception {
261 if (appendMergedRoute(existRoute, mergedRoute, existNode,
262 mergedNode)) {
263 if (capacityFeasible(existRoute, mergedRoute, false)) {
264 //合并到现有路径之后
265 if (mergedRoute.hardTimeWindowFeasible(existNode)) {
266 mergeRoute(existRoute, mergedRoute, savedDistance
267 , existNode, false);
268 }
269 }
270 } else if (insertMergedRoute(existRoute, mergedRoute,
271 existNode, mergedNode)) {
272 if (capacityFeasible(existRoute, mergedRoute, true)) {
273 //合并到现有路径之前
274 if (existRoute.hardTimeWindowFeasible(mergedNode)) {
275 mergeRoute(existRoute, mergedRoute, savedDistance
276 , existNode, true);
277 }
278 }
279 }
280 }
281
282 private boolean insertMergedRoute(Route existRoute,
283 Route mergedRoute,
284 PostOffice existNode,
285 PostOffice mergedNode) throws Exception {
286 if (mergedRoute.getNodes().size() < 3 || existRoute.getNodes().size() < 3)
287 throw new Exception("合并路径 节点少于3个");
288 return existRoute.getNodes().indexOf(existNode) == 1 && mergedRoute.getNodes().indexOf(mergedNode) == mergedRoute.getNodes().size() - 2;
289 }
290
291 private boolean appendMergedRoute(Route existRoute,
292 Route mergedRoute,
293 PostOffice existNode,
294 PostOffice mergedNode) throws Exception {
295 if (mergedRoute.getNodes().size() < 3 || existRoute.getNodes().size() < 3)
296 throw new Exception("合并路径 节点少于3个");
297 return existRoute.getNodes().indexOf(existNode) == existRoute.getNodes().size() - 2 && mergedRoute.getNodes().indexOf(mergedNode) == 1;
298 }
299
300 private boolean capacityFeasible(Route existRoute,
301 Route mergedRoute,
302 boolean isInsert) throws Exception {
303 if (existRoute.getCapacity() > (mergedRoute.getTotalReceive() + existRoute.getTotalReceive()) ) {
304 if (isInsert) {
305 Float curLoad = mergedRoute.getTotalSendOut() + existRoute.getTotalReceive();
306 for (PostOffice node : existRoute.getNodes()) {
307 if (curLoad - node.getReceive() + node.getSendOut() > existRoute.getCapacity()) {
308 return false;
309 }
310 curLoad = curLoad - node.getReceive() + node.getSendOut();
311 if (curLoad < 0)
312 throw new Exception("isInsert=true, 当前载重出错，小于0");
313 }
314 } else {
315 Float curLoad = existRoute.getTotalSendOut() + mergedRoute.getTotalReceive();
316 for (PostOffice node : mergedRoute.getNodes()) {
317 if (curLoad - node.getReceive() + node.getSendOut() > existRoute.getCapacity()) {
318 return false;
319 }
320 curLoad = curLoad - node.getReceive() + node.getSendOut();
321 if (curLoad < 0)
322 throw new Exception("isInsert=false, 当前载重出错，小于0");
323 }
324 }
325 return true;
326 }
327
328 return false;
329 }
330
331 /**
332 * 合并路径 算法
333 * @param existRoute
334 * @param mergedRoute
335 * @param savedDistance
336 * @param p
337 * @param beforeP
338 * @throws Exception
339 */
340 private void mergeRoute(Route existRoute, Route mergedRoute,
341 SavedDistance savedDistance, PostOffice p
342 , Boolean beforeP) throws Exception {
343 //合并点在p1之前
344 LinkedList<postoffice> mergedNodes = mergedRoute.getNodes();
345 mergedNodes.removeFirst();
346 mergedNodes.removeLast();
347
348 //从合并处 插入 被合并路径中所有营业点
349 existRoute.getNodes().addAll(existRoute.getNodes().indexOf(p) + (beforeP ? 0 : 1), mergedRoute.getNodes());
350 //更新 原有路径上所有营业点 所在路径
351 mergedNodes.forEach(node -> {
352 node.setCurrentRoute(existRoute);
353 });
354 //更新原路径上点的前后关系
355 existRoute.updateNodeTracing();
356 //更新到达时间
357 existRoute.updateArrivedTime();
358 //更新载重
359 existRoute.addReceive(mergedRoute.getTotalReceive());
360 existRoute.addSendOut(mergedRoute.getTotalSendOut());
361 //更新路径长度
362 existRoute.setLength(existRoute.calcLength(existRoute.getNodes()));
363 //清除 被合并路径
364 if (mergedRoute.getCapacity() != 0f) {
365 vehicleCapacityList.push(mergedRoute.getCapacity() / FACTOR);
366 vehicleCapacityList.sort(Comparator.reverseOrder());
367 usedVehicleList.remove(mergedRoute.getCapacity() / FACTOR);
368 }
369 routeList.remove(mergedRoute);
370 }
371
372
373
374 private void printGeneral() {
375 System.out.println("车辆总数: " + vehicleNumber);
376 System.out.println("邮局总数: " + totalPointNumber);
377 System.out.println("使用车辆: " + usedVehicleList);
378 System.out.println("剩余车辆: " + vehicleCapacityList);
379 // System.out.println("邮局位置: " + postOfficeList);
380 // if (savingList.size() >= 5) {
381 // System.out.println("\\n节约距离 top 5: " + savingList.subList(0, 5).toString());
382 // }
383 }
384
385 private void printRoute() {
386 System.out.println("\\n路径: ");
387 for (int i = 0; i < routeList.size(); i++) {
388 Route r = routeList.get(i);
389 System.out.println(i + " " + r.toString());
390 }
391 }
392
393 private void printTimeSchedule() {
394 System.out.println("\\n到达时间 ");
395 for (int i = 0; i < routeList.size(); i++) {
396 Route r = routeList.get(i);
397 System.out.println(i + " " + r.timeSchedule());
398 }
399 }
400
401
402 public int getTotalPointNumber() {
403 return totalPointNumber;
404 }
405
406
407 public LinkedList<float> getUsedVehicleList() {
408 return usedVehicleList;
409 }
410
411 public List<postoffice> getPostOfficeList() {
412 return postOfficeList;
413 }
414
415 public List<route> getRouteList() {
416 return routeList;
417 }
418
419 }
/<route>/<postoffice>/<float>/<postoffice>/<postofficelist.size>/<saveddistance>/<route>/<postoffice>/<float>/<float>
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
原文：https://www.cnblogs.com/andrew-chen/p/11498871.html
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