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)
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)。
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
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/
http://docs.pgrouting.org/latest/en/TSP-family.html#tsp