pgr_TSPeuclidean

  • pgr_TSPeuclidean - Aproximation using metric algorithm.

_images/boost-inside.jpeg

Boost Graph Inside

Availability:

  • Version 3.2.1

    • Metric Algorithm from Boost library

    • Simulated Annealing Algorithm no longer supported

      • The Simulated Annealing Algorithm related parameters are ignored: max_processing_time, tries_per_temperature, max_changes_per_temperature, max_consecutive_non_changes, initial_temperature, final_temperature, cooling_factor, randomize

  • Version 3.0.0

    • Name change from pgr_eucledianTSP

  • Version 2.3.0

    • New Official function

Description

Problem Definition

The travelling salesperson problem (TSP) 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?

Characteristics

  • This problem is an NP-hard optimization problem.

  • Metric Algorithm is used

  • Implementation generates solutions that are twice as long as the optimal tour in the worst case when:

    • Graph is undirected

    • Graph is fully connected

    • Graph where traveling costs on edges obey the triangle inequality.

  • On an undirected graph:

    • The traveling costs are symmetric:

    • Traveling costs from u to v are just as much as traveling from v to u

  • Any duplicated identifier will be ignored. The coordinates that will be kept

    is arbitrarly.

    • The coordinates are quite similar for the same identifier, for example

      1, 3.5, 1
      1, 3.499999999999 0.9999999
      
    • The coordinates are quite different for the same identifier, for example

      2, 3.5, 1.0
      2, 3.6, 1.1
      

Signatures

Summary

pgr_TSPeuclidean(Coordinates SQL, [start id], [end_id])
RETURNS SETOF (seq, node, cost, agg_cost)
Example:

With default values

SELECT * FROM pgr_TSPeuclidean(
  $$
  SELECT id, st_X(geom) AS x, st_Y(geom)AS y  FROM vertices
  $$);
 seq | node |      cost      |   agg_cost
-----+------+----------------+---------------
   1 |    1 |              0 |             0
   2 |    6 |   2.2360679775 |  2.2360679775
   3 |    5 |              1 |  3.2360679775
   4 |   10 |  1.41421356237 | 4.65028153987
   5 |    7 |  1.41421356237 | 6.06449510225
   6 |    2 |  2.12132034356 | 8.18581544581
   7 |    9 |  1.58113883008 | 9.76695427589
   8 |    4 |            0.5 | 10.2669542759
   9 |   14 |  1.58113883009 |  11.848093106
  10 |   17 |  1.11803398875 | 12.9661270947
  11 |   16 |              1 | 13.9661270947
  12 |   15 |              1 | 14.9661270947
  13 |   11 |  1.41421356237 | 16.3803406571
  14 |   13 | 0.583095189485 | 16.9634358466
  15 |   12 | 0.860232526704 | 17.8236683733
  16 |    8 |              1 | 18.8236683733
  17 |    3 |  1.41421356237 | 20.2378819357
  18 |    1 |              1 | 21.2378819357
(18 rows)

Parameters

Parameter

Type

Description

Coordinates SQL

TEXT

Coordinates SQL as described below

TSP optional parameters

Column

Type

Default

Description

start_id

ANY-INTEGER

0

The first visiting vertex

  • When 0 any vertex can become the first visiting vertex.

end_id

ANY-INTEGER

0

Last visiting vertex before returning to start_vid.

  • When 0 any vertex can become the last visiting vertex before returning to start_id.

  • When NOT 0 and start_id = 0 then it is the first and last vertex

Inner Queries

Coordinates SQL

Coordinates SQL: an SQL query, which should return a set of rows with the following columns:

Column

Type

Description

id

ANY-INTEGER

Identifier of the starting vertex.

x

ANY-NUMERICAL

X value of the coordinate.

y

ANY-NUMERICAL

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

Cost to traverse from the current node to the next node in the path sequence.

  • 0 for the last row in the tour sequence.

agg_cost

FLOAT

Aggregate cost from the node at seq = 1 to the current node.

  • 0 for the first row in the tour sequence.

Additional Examples

Test 29 cities of Western Sahara

This example shows how to make performance tests using University of Waterloo’s example data using the 29 cities of Western Sahara dataset

Creating a table for the data and storing the data

CREATE TABLE wi29 (id BIGINT, x FLOAT, y FLOAT, geom geometry);
INSERT INTO wi29 (id, x, y) VALUES
(1,20833.3333,17100.0000),
(2,20900.0000,17066.6667),
(3,21300.0000,13016.6667),
(4,21600.0000,14150.0000),
(5,21600.0000,14966.6667),
(6,21600.0000,16500.0000),
(7,22183.3333,13133.3333),
(8,22583.3333,14300.0000),
(9,22683.3333,12716.6667),
(10,23616.6667,15866.6667),
(11,23700.0000,15933.3333),
(12,23883.3333,14533.3333),
(13,24166.6667,13250.0000),
(14,25149.1667,12365.8333),
(15,26133.3333,14500.0000),
(16,26150.0000,10550.0000),
(17,26283.3333,12766.6667),
(18,26433.3333,13433.3333),
(19,26550.0000,13850.0000),
(20,26733.3333,11683.3333),
(21,27026.1111,13051.9444),
(22,27096.1111,13415.8333),
(23,27153.6111,13203.3333),
(24,27166.6667,9833.3333),
(25,27233.3333,10450.0000),
(26,27233.3333,11783.3333),
(27,27266.6667,10383.3333),
(28,27433.3333,12400.0000),
(29,27462.5000,12992.2222);

Adding a geometry (for visual purposes)

UPDATE wi29 SET geom = ST_makePoint(x,y);

Total tour cost

Getting a total cost of the tour, compare the value with the length of an optimal tour is 27603, given on the dataset

SELECT *
FROM pgr_TSPeuclidean($$SELECT * FROM wi29$$)
WHERE seq = 30;
 seq | node |     cost      |   agg_cost
-----+------+---------------+---------------
  30 |    1 | 2266.91173136 | 28777.4854127
(1 row)

Getting a geometry of the tour

WITH
tsp_results AS (SELECT seq, geom FROM pgr_TSPeuclidean($$SELECT * FROM wi29$$) JOIN wi29 ON (node = id))
SELECT ST_MakeLine(ARRAY(SELECT geom FROM tsp_results ORDER BY seq));
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    st_makeline
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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
(1 row)

Visual results

Visualy, The first image is the optimal solution and the second image is the solution obtained with pgr_TSPeuclidean.

_images/wi29optimal.png _images/wi29Solution.png

See Also

Indices and tables