pgr_eucledianTSP¶

Name¶

• pgr_eucledianTSP - Returns a route that visits all the coordinates pairs exactly once.

Synopsis¶

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, what is the shortest possible route that visits each city exactly once and returns to the origin city?

This implementation uses simulated annealing to return the approximate solution when the input is given in the form of coordinates.

Signature Summary¶

pgr_eucledianTSP(coordinates_sql)
pgr_eucledianTSP(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)


Signatures¶

Minimal Signature¶

pgr_eucledianTSP(coordinates_sql)
RETURNS SETOF (seq, node, cost, agg_cost)


Because the documentation examples are auto generated and tested for non changing results, and the default is to have random execution, the example is wrapping the actual call.

WITH
query AS (
SELECT * FROM pgr_eucledianTSP(
$$SELECT id, st_X(the_geom) AS x, st_Y(the_geom)AS y FROM edge_table_vertices_pgr$$
)
)
SELECT agg_cost < 20 AS under_20 FROM query WHERE seq = 18;
under_20
----------
t
(1 row)


Complete Signature¶

pgr_eucledianTSP(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:

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 := 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)


Description of the Signatures¶

Description of the coordinates SQL query¶

Column Type Description
id BIGINT Identifier of the coordinate. (optional)
x FLOAT X value of the coordinate.
y FLOAT Y value of the coordinate.

When the value of id is not given then the coordinates will receive an id starting from 1, in the order given.

Description Of the Control parameters¶

The control parameters are optional, and have a default value.

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

• true: Use current time as seed
• false: Use 1 as seed. Using this value will get the same results with the same data in each execution.

Description of the return values¶

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
Cost to traverse from the current node ito the next node in the path sequence.
• 0 for the last row in the path sequence.
agg_cost FLOAT
Aggregate cost from the node at seq = 1 to the current node.
• 0 for the first row in the path sequence.

Examples¶

Example: Skipping the Simulated Annealing & showing some process information
SET client_min_messages TO NOTICE;
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
);
NOTICE:  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)


The queries use the Sample Data network.

History

• New in version 2.3.0