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An analysis of the fitness landscape of travelling salesman problem

An analysis of the fitness landscape of travelling salesman problem
An analysis of the fitness landscape of travelling salesman problem
The fitness landscape of the travelling salesman problem is investigated for 11 different types of the problem. The types differ in how the distances between cities are generated. Many different properties of the landscape are studied. The properties chosen are all potentially relevant to choosing an appropriate search algorithm. The analysis includes a scaling study of the time to reach a local optimum, the number of local optima, the expected probability of reaching a local optimum as a function of its fitness, the expected fitness found by local search and the best fitness, the probability of reaching a global optimum, the distance between the local optima and the global optimum, the expected fitness as a function of the distance from an optimum, their basins of attraction and a principal component analysis of the local optima. The principal component analysis shows the correlation of the local optima in the component space. We show how the properties of the principal components of the local optima change from one problem type to another.
1063-6560
347-384
Tayarani Najaran, Mohammad
da003cbc-3d35-4aaa-aa8d-9437b720bfec
Prugel-Bennett, Adam
b107a151-1751-4d8b-b8db-2c395ac4e14e
Tayarani Najaran, Mohammad
da003cbc-3d35-4aaa-aa8d-9437b720bfec
Prugel-Bennett, Adam
b107a151-1751-4d8b-b8db-2c395ac4e14e

Tayarani Najaran, Mohammad and Prugel-Bennett, Adam (2016) An analysis of the fitness landscape of travelling salesman problem. Evolutionary Computation, 24 (2), 347-384. (doi:10.1162/EVCO_a_00154).

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Abstract

The fitness landscape of the travelling salesman problem is investigated for 11 different types of the problem. The types differ in how the distances between cities are generated. Many different properties of the landscape are studied. The properties chosen are all potentially relevant to choosing an appropriate search algorithm. The analysis includes a scaling study of the time to reach a local optimum, the number of local optima, the expected probability of reaching a local optimum as a function of its fitness, the expected fitness found by local search and the best fitness, the probability of reaching a global optimum, the distance between the local optima and the global optimum, the expected fitness as a function of the distance from an optimum, their basins of attraction and a principal component analysis of the local optima. The principal component analysis shows the correlation of the local optima in the component space. We show how the properties of the principal components of the local optima change from one problem type to another.

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e-pub ahead of print date: 13 June 2016
Additional Information: This is AM, however copy has slightly different title. Checking with author if he is aware.

Identifiers

Local EPrints ID: 412228
URI: http://eprints.soton.ac.uk/id/eprint/412228
ISSN: 1063-6560
PURE UUID: d730de6e-bfc3-4d21-a924-609d5f171281

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Date deposited: 14 Jul 2017 16:30
Last modified: 09 Dec 2019 18:45

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Author: Mohammad Tayarani Najaran
Author: Adam Prugel-Bennett

University divisions

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