pgr_TSPeuclidean¶
pgr_TSPeuclidean
- Using Simulated Annealing approximation algorithm
Availability
- Version 3.0.0
- Name change from pgr_eucledianTSP
- Version 2.3.0
- New Official function
Support
Description¶
The travelling salesman problem (TSP) or travelling salesperson problem asks the following question:
Given a list of cities and the distances between each pair of cities, which is the shortest possible route that visits each city exactly once and returns to the origin city?
See Simulated Annealing Algorithm for a complete description of this implementation
Signatures¶
Summary
pgr_TSPeuclidean(Coordinates SQL,
[start_id], [end_id],
[max_processing_time],
[tries_per_temperature], [max_changes_per_temperature], [max_consecutive_non_changes],
[initial_temperature], [final_temperature], [cooling_factor],
[randomize])
RETURNS SETOF (seq, node, cost, agg_cost)
Example: | Not having a random execution |
---|
SELECT * FROM pgr_TSPeuclidean(
$$
SELECT id, st_X(the_geom) AS x, st_Y(the_geom)AS y FROM edge_table_vertices_pgr
$$,
randomize := false);
seq | node | cost | agg_cost
-----+------+-------------------+------------------
1 | 1 | 1.4142135623731 | 0
2 | 3 | 1 | 1.4142135623731
3 | 4 | 1 | 2.41421356237309
4 | 9 | 1 | 3.41421356237309
5 | 6 | 0.58309518948453 | 4.41421356237309
6 | 16 | 0.860232526704263 | 4.99730875185763
7 | 12 | 1.11803398874989 | 5.85754127856189
8 | 17 | 1.11803398874989 | 6.97557526731178
9 | 11 | 1 | 8.09360925606168
10 | 10 | 0.5 | 9.09360925606168
11 | 15 | 0.5 | 9.59360925606168
12 | 13 | 1.58113883008419 | 10.0936092560617
13 | 14 | 1.58113883008419 | 11.6747480861459
14 | 7 | 1 | 13.2558869162301
15 | 8 | 1 | 14.2558869162301
16 | 5 | 1 | 15.2558869162301
17 | 2 | 1 | 16.2558869162301
18 | 1 | 0 | 17.2558869162301
(18 rows)
Parameters¶
Parameter | Description |
---|---|
Coordinates SQL | an SQL query, described in the Inner query |
Optional Parameters¶
Parameter | Type | Default | Description |
---|---|---|---|
start_vid | BIGINT |
0 | The greedy part of the implementation will use this identifier. |
end_vid | BIGINT |
0 | Last visiting vertex before returning to start_vid. |
max_processing_time | FLOAT |
+infinity | Stop the annealing processing when the value is reached. |
tries_per_temperature | INTEGER |
500 | Maximum number of times a neighbor(s) is searched in each temperature. |
max_changes_per_temperature | INTEGER |
60 | Maximum number of times the solution is changed in each temperature. |
max_consecutive_non_changes | INTEGER |
100 | Maximum number of consecutive times the solution is not changed in each temperature. |
initial_temperature | FLOAT |
100 | Starting temperature. |
final_temperature | FLOAT |
0.1 | Ending temperature. |
cooling_factor | FLOAT |
0.9 | Value between between 0 and 1 (not including) used to calculate the next temperature. |
randomize | BOOLEAN |
true | Choose the random seed
|
Inner query¶
Coordinates SQL: an SQL query, which should return a set of rows with the following columns:
Column | Type | Description |
---|---|---|
id | BIGINT |
(optional) Identifier of the coordinate.
|
x | FLOAT |
X value of the coordinate. |
y | FLOAT |
Y value of the coordinate. |
Result Columns¶
Returns SET OF (seq, node, cost, agg_cost)
Column | Type | Description |
---|---|---|
seq | INTEGER |
Row sequence. |
node | BIGINT |
Identifier of the node/coordinate/point. |
cost | FLOAT |
|
agg_cost | FLOAT |
|
Additional Examples¶
Example: | Try \(3\) times per temperature with cooling factor of \(0.5\), not having a random execution |
---|
SELECT* from pgr_TSPeuclidean(
$$
SELECT id, st_X(the_geom) AS x, st_Y(the_geom) AS y FROM edge_table_vertices_pgr
$$,
tries_per_temperature := 3,
cooling_factor := 0.5,
randomize := false);
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)
Example: | Skipping the Simulated Annealing & showing some process information |
---|
SET client_min_messages TO DEBUG1;
SET
SELECT* from pgr_TSPeuclidean(
$$
SELECT id, st_X(the_geom) AS x, st_Y(the_geom) AS y FROM edge_table_vertices_pgr
$$,
tries_per_temperature := 0,
randomize := false);
DEBUG: 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)
The queries use the Sample Data network.