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On the landscape of combinatorial optimization problems

On the landscape of combinatorial optimization problems
On the landscape of combinatorial optimization problems
This paper carries out a comparison of the fitness landscape for four classic optimization problems: Max-Sat, graph-coloring, traveling salesman, and quadratic assignment. We have focused on two types of properties, local average properties of the landscape, and properties of the local optima. For the local optima we give a fairly comprehensive description of the properties, including the expected time to reach a local optimum, the number of local optima at different cost levels, the distance between optima, and the expected probability of reaching the optima. Principle component analysis is used to understand the correlations between the local optima. Most of the properties that we examine have not been studied previously, particularly those concerned with properties of the local optima. We compare and contrast the behavior of the four different problems. Although the problems are very different at the low level, many of the long-range properties exhibit a remarkable degree of similarity.
420-434
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 (2013) On the landscape of combinatorial optimization problems. IEEE Transactions on Evolutionary Computation, 18 (3), 420-434. (doi:10.1109/TEVC.2013.2281502).

Record type: Article

Abstract

This paper carries out a comparison of the fitness landscape for four classic optimization problems: Max-Sat, graph-coloring, traveling salesman, and quadratic assignment. We have focused on two types of properties, local average properties of the landscape, and properties of the local optima. For the local optima we give a fairly comprehensive description of the properties, including the expected time to reach a local optimum, the number of local optima at different cost levels, the distance between optima, and the expected probability of reaching the optima. Principle component analysis is used to understand the correlations between the local optima. Most of the properties that we examine have not been studied previously, particularly those concerned with properties of the local optima. We compare and contrast the behavior of the four different problems. Although the problems are very different at the low level, many of the long-range properties exhibit a remarkable degree of similarity.

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Accepted/In Press date: 25 July 2013
Published date: 11 September 2013
Organisations: Vision, Learning and Control

Identifiers

Local EPrints ID: 397016
URI: http://eprints.soton.ac.uk/id/eprint/397016
PURE UUID: 171a5c6d-88b8-4603-aa14-0544a417280d

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Date deposited: 12 Jul 2016 15:34
Last modified: 02 Dec 2019 20:08

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Contributors

Author: Mohammad Tayarani Najaran
Author: Adam Prugel-Bennett

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