pgrouting

Author: digoal

201704/20170409_01.md

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+## 多点最优路径规划 - (商旅问题,拼车,餐饮配送,包裹配送,包裹取件,回程单)  
+                                          
+### 作者                                             
+digoal                                     
+                                      
+### 日期                                                                                                         
+2017-04-09                                    
+                                         
+### 标签                                      
+PostgreSQL , PostGIS , pgrouting , 商旅问题 , 拼车 , 餐饮配送 , 包裹配送 , 包裹取件 , 回程单    
+                                                                                                            
+----                                                                                                      
+                                                                                                               
+## 背景      
+小长假，带着一家人出去旅行，计划好了去几个地方，如何设计旅行线路是最优的？(里面还涉及到路费，路途时间等因素)。  
+  
+![pic](20170409_01_pic_001.jpg)  
+  
+又比如 拼车，餐饮配送，包裹取件、配送，都包含最佳路径计算的共性在里面。   
+  
+PostgreSQL 在GIS领域有这非常丰富的用户和实际案例，路径规划方面，我之前写过一篇关于包裹配送的文章  
+  
+[《聊一聊双十一背后的技术 - 物流、动态路径规划》](../201611/20161114_01.md)  
+  
+在商旅问题，拼车，餐饮配送，包裹取件、配送，等诸多最佳路径计算的需求方面，PostgreSQL又是如何满足需求的呢？  
+  
+## pgrouting 核心功能  
+pgRouting library contains following features:  
+  
+- All Pairs Shortest Path, Johnson’s Algorithm  
+  
+- All Pairs Shortest Path, Floyd-Warshall Algorithm  
+  
+- Shortest Path A*  
+  
+- Bi-directional Dijkstra Shortest Path  
+  
+- Bi-directional A* Shortest Path  
+  
+- Shortest Path Dijkstra  
+  
+- Driving Distance  
+  
+- K-Shortest Path, Multiple Alternative Paths  
+  
+- K-Dijkstra, One to Many Shortest Path  
+  
+- Traveling Sales Person  
+  
+- Turn Restriction Shortest Path (TRSP)  
+  
+## 最佳规划1 - 从一个点出发，经过多点，回到起点  
+解决 旅行、包裹配送、餐饮配送的问题  
+  
+这个问题的定义如下，从一点出发，经过多点，回到起点。  
+  
+Given a collection of cities and travel cost between each pair, find the cheapest way for visiting all of the cities and returning to the starting point.  
+  
+详情  
+  
+http://docs.pgrouting.org/latest/en/TSP-family.html#tsp  
+  
+### 例子1  
+pgr_TSP - Returns a route that visits all the nodes exactly once.  
+  
+从5出发，经过array[-1, 3, 5, 6, -6]，回到5。  
+  
+```  
+SELECT * FROM pgr_TSP(  
+    $$  
+    SELECT * FROM pgr_withPointsCostMatrix(  
+        'SELECT id, source, target, cost, reverse_cost FROM edge_table ORDER BY id',  
+        'SELECT pid, edge_id, fraction from pointsOfInterest',  
+        array[-1, 3, 5, 6, -6], directed := false);  
+    $$,  
+    start_id := 5,  
+    randomize := false  
+);  
+  
+ seq | node | cost | agg_cost   
+-----+------+------+----------  
+   1 |    5 |    1 |        0  
+   2 |    6 |    1 |        1  
+   3 |    3 |  1.6 |        2  
+   4 |   -1 |  1.3 |      3.6  
+   5 |   -6 |  0.3 |      4.9  
+   6 |    5 |    0 |      5.2  
+(6 rows)  
+```  
+  
+### 例子2  
+pgr_eucledianTSP - Returns a route that visits all the coordinates pairs exactly once.  
+  
+```  
+SET client_min_messages TO DEBUG1;  
+SET  
+SELECT* from pgr_eucledianTSP(  
+    $$  
+    SELECT id, st_X(the_geom) AS x, st_Y(the_geom) AS y FROM edge_table_vertices_pgr  
+    $$,  
+    tries_per_temperature := 0,  
+    randomize := false  
+);  
+DEBUG:  pgr_eucledianTSP Processing Information  
+Initializing tsp class ---> tsp.greedyInitial ---> tsp.annealing ---> OK  
+  
+Cycle(100) 	total changes =0	0 were because  delta energy < 0  
+Total swaps: 3  
+Total slides: 0  
+Total reverses: 0  
+Times best tour changed: 4  
+Best cost reached = 18.7796  
+ seq | node |       cost       |     agg_cost       
+-----+------+------------------+------------------  
+   1 |    1 |  1.4142135623731 |                0  
+   2 |    3 |                1 |  1.4142135623731  
+   3 |    4 |                1 | 2.41421356237309  
+   4 |    9 | 0.58309518948453 | 3.41421356237309  
+   5 |   16 | 0.58309518948453 | 3.99730875185762  
+   6 |    6 |                1 | 4.58040394134215  
+   7 |    5 |                1 | 5.58040394134215  
+   8 |    8 |                1 | 6.58040394134215  
+   9 |    7 | 1.58113883008419 | 7.58040394134215  
+  10 |   14 |   1.499999999999 | 9.16154277142634  
+  11 |   15 |              0.5 | 10.6615427714253  
+  12 |   13 |              1.5 | 11.1615427714253  
+  13 |   17 | 1.11803398874989 | 12.6615427714253  
+  14 |   12 |                1 | 13.7795767601752  
+  15 |   11 |                1 | 14.7795767601752  
+  16 |   10 |                2 | 15.7795767601752  
+  17 |    2 |                1 | 17.7795767601752  
+  18 |    1 |                0 | 18.7795767601752  
+(18 rows)  
+```  
+  
+## 最佳规划2 - 从一个点出发，经过多点，到达终点  
+拼车的问题更加复杂一些，  
+  
+从一个点出发（司机位置），经过多点（所有拼车乘客的上车地点），再去到多点（拼车乘客的下车地点）。  
+  
+拼车的问题可以分为两个阶段来解决，  
+  
+第一个阶段，从司机位置到接上所有拼车乘客。  
+  
+第二个阶段，从最后一个乘客上车地点，到达所有乘客的下车地点。  
+  
+两个阶段的规划需求是一样的，从一个点出发，经过多点，到达终点。  
+  
+详情  
+  
+http://docs.pgrouting.org/latest/en/TSP-family.html#tsp  
+  
+### 例子  
+详情  
+  
+http://docs.pgrouting.org/latest/en/pgr_dijkstraVia.html#pgr-dijkstravia  
+  
+Given a list of vertices and a graph, this function is equivalent to finding the shortest path between vertexivertexi and vertexi+1vertexi+1 for all i<size_of(vertexvia)i<size_of(vertexvia).  
+  
+## 参考    
+所有用到的路由函数，点对点成本矩阵函数，请参考  
+  
+http://pgrouting.org/  
+  
+[《聊一聊双十一背后的技术 - 物流、动态路径规划》](../201611/20161114_01.md)  
+    
+http://docs.pgrouting.org/latest/en/TSP-family.html#tsp