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Maximum satisfiability: anatomy of the fitness landscape for a hard combinatorial optimisation problem

Maximum satisfiability: anatomy of the fitness landscape for a hard combinatorial optimisation problem
Maximum satisfiability: anatomy of the fitness landscape for a hard combinatorial optimisation problem
The fitness landscape of MAX-3-SAT is investigated for random instances above the satisfiability phase transition. This paper includes a scaling analysis 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 size and relative positions of the global optima, the mean distance between the local and global optima, the expected fitness as a function of the Hamming distance from an optimum and their basins of attraction. These analyses show why the problem becomes hard for local search algorithms as the system size increases. The paper also shows how a recently proposed algorithm can exploit long-range correlations in the fitness landscape to improve on the state-of-the-art heuristic algorithms.
fitness landscape, long-range correlation, maxsat, scaling analysis
319-338
Prugel-Bennett, A.
b107a151-1751-4d8b-b8db-2c395ac4e14e
Tayarani-Najaran, M.-H.
f11092df-dd7d-49df-8625-658dd3f234ba
Prugel-Bennett, A.
b107a151-1751-4d8b-b8db-2c395ac4e14e
Tayarani-Najaran, M.-H.
f11092df-dd7d-49df-8625-658dd3f234ba

Prugel-Bennett, A. and Tayarani-Najaran, M.-H. (2012) Maximum satisfiability: anatomy of the fitness landscape for a hard combinatorial optimisation problem. IEEE Transactions on Evolutionary Computation, 16 (3), 319-338. (doi:10.1109/TEVC.2011.2163638).

Record type: Article

Abstract

The fitness landscape of MAX-3-SAT is investigated for random instances above the satisfiability phase transition. This paper includes a scaling analysis 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 size and relative positions of the global optima, the mean distance between the local and global optima, the expected fitness as a function of the Hamming distance from an optimum and their basins of attraction. These analyses show why the problem becomes hard for local search algorithms as the system size increases. The paper also shows how a recently proposed algorithm can exploit long-range correlations in the fitness landscape to improve on the state-of-the-art heuristic algorithms.

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e-pub ahead of print date: 17 October 2011
Published date: June 2012
Keywords: fitness landscape, long-range correlation, maxsat, scaling analysis
Organisations: Southampton Wireless Group

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Local EPrints ID: 272653
URI: http://eprints.soton.ac.uk/id/eprint/272653
PURE UUID: d131a76f-47f2-47ef-94e3-6c99724fcd16

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Date deposited: 09 Aug 2011 12:53
Last modified: 21 Oct 2019 19:32

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Contributors

Author: A. Prugel-Bennett
Author: M.-H. Tayarani-Najaran

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