pgr_TSP

  • pgr_TSP - Using Simulated Annealing approximation algorithm

Availability: 2.0.0

  • Version 2.3.0

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      • Old signature no longer supported

  • Version 2.0.0

    • Official function

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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_TSP(Matrix 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_TSP(
    $$
    SELECT * FROM pgr_dijkstraCostMatrix(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        (SELECT array_agg(id) FROM edge_table_vertices_pgr WHERE id < 14),
        directed := false)
    $$,
    randomize := false);
 seq | node | cost | agg_cost
-----+------+------+----------
   1 |    1 |    1 |        0
   2 |    2 |    1 |        1
   3 |    3 |    1 |        2
   4 |    4 |    1 |        3
   5 |    9 |    1 |        4
   6 |    6 |    1 |        5
   7 |   11 |    1 |        6
   8 |   12 |    2 |        7
   9 |   10 |    1 |        9
  10 |   13 |    4 |       10
  11 |    7 |    1 |       14
  12 |    8 |    1 |       15
  13 |    5 |    2 |       16
  14 |    1 |    0 |       18
(14 rows)

Parameters

Parameter

Description

Matrix 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

  • 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.

Inner query

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

Column

Type

Description

start_vid

BIGINT

Identifier of the starting vertex.

end_vid

BIGINT

Identifier of the ending vertex.

agg_cost

FLOAT

Cost for going from start_vid to end_vid

Can be Used with Cost Matrix - Category functions with directed := false.

If using directed := true, the resulting non symmetric matrix must be converted to symmetric by fixing the non symmetric values according to your application needs.

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 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.

Additional Examples

Example

Start from vertex \(7\)

SELECT * FROM pgr_TSP(
    $$
    SELECT * FROM pgr_dijkstraCostMatrix(
        'SELECT id, source, target, cost, reverse_cost FROM edge_table',
        (SELECT array_agg(id) FROM edge_table_vertices_pgr WHERE id < 14),
        directed := false
    )
    $$,
    start_id := 7,
    randomize := false
);
 seq | node | cost | agg_cost
-----+------+------+----------
   1 |    7 |    1 |        0
   2 |    8 |    1 |        1
   3 |    5 |    1 |        2
   4 |    2 |    1 |        3
   5 |    1 |    2 |        4
   6 |    3 |    1 |        6
   7 |    4 |    1 |        7
   8 |    9 |    1 |        8
   9 |   12 |    1 |        9
  10 |   11 |    1 |       10
  11 |   10 |    1 |       11
  12 |   13 |    3 |       12
  13 |    6 |    3 |       15
  14 |    7 |    0 |       18
(14 rows)

Example

Using with points of interest.

To generate a symmetric matrix:

  • the side information of pointsOfInterset is ignored by not including it in the query

  • and directed := false

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 |  0.3 |        0
   2 |   -6 |  1.3 |      0.3
   3 |   -1 |  1.6 |      1.6
   4 |    3 |    1 |      3.2
   5 |    6 |    1 |      4.2
   6 |    5 |    0 |      5.2
(6 rows)

The queries use the Sample Data network.