# pgr_TSP¶

• pgr_TSP - Using Simulated Annealing approximation algorithm

Availability: 2.0.0

• Signature changed 2.3.0

## 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 |    3 |        0
2 |    4 |    1 |        3
3 |    9 |    1 |        4
4 |   12 |    1 |        5
5 |   11 |    2 |        6
6 |   13 |    1 |        8
7 |   10 |    1 |        9
8 |    5 |    2 |       10
9 |    7 |    1 |       12
10 |    8 |    2 |       13
11 |    6 |    1 |       15
12 |    3 |    1 |       16
13 |    2 |    1 |       17
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 |    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)



The queries use the Sample Data network.

## See Also¶

Indices and tables