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Analysis of the fitness landscape for the class of combinatorial optimisation problems

Analysis of the fitness landscape for the class of combinatorial optimisation problems
Analysis of the fitness landscape for the class of combinatorial optimisation problems
Anatomy of the fitness landscape for a group of well known combinatorial optimisation problems is studied in this research and the similarities and the differences between their landscapes are pointed out. In this research we target the analysis of the fitness landscape for MAX-SAT, Graph-Colouring, Travelling Salesman and Quadratic Assignment problems. Belonging to the class of NP-Hard problems, all these problems become exponentially harder as the problem size grows. We study a group of properties of the fitness landscape for these problems and show what properties are shared by different problems and what properties are different. The properties we investigate here include the time it takes for a local search algorithm to find a local optimum, the number of local and global optima, distance between local and global optima, expected cost of found optima, probability of reaching a global optimum and the cost of the best configuration in the search space. The relationship between these properties and the system size and other parameters of the problems are studied, and it is shown how these properties are shared or differ in different problems. We also study the long-range correlation within the search space, including the expected cost in the Hamming sphere around the local and global optima, the basin of attraction of the local and global optima and the probability of finding a local optimum as a function of its cost. We believe these information provide good insight for algorithm designers.
Tayarani-Najaran, M.-H.
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Tayarani-Najaran, M.-H.
f11092df-dd7d-49df-8625-658dd3f234ba
Prugel-Bennett, Adam
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(2013) Analysis of the fitness landscape for the class of combinatorial optimisation problems. University of Southampton, Faculty of Physical Sciences and Engineering, Doctoral Thesis, 199pp.

Record type: Thesis (Doctoral)

Abstract

Anatomy of the fitness landscape for a group of well known combinatorial optimisation problems is studied in this research and the similarities and the differences between their landscapes are pointed out. In this research we target the analysis of the fitness landscape for MAX-SAT, Graph-Colouring, Travelling Salesman and Quadratic Assignment problems. Belonging to the class of NP-Hard problems, all these problems become exponentially harder as the problem size grows. We study a group of properties of the fitness landscape for these problems and show what properties are shared by different problems and what properties are different. The properties we investigate here include the time it takes for a local search algorithm to find a local optimum, the number of local and global optima, distance between local and global optima, expected cost of found optima, probability of reaching a global optimum and the cost of the best configuration in the search space. The relationship between these properties and the system size and other parameters of the problems are studied, and it is shown how these properties are shared or differ in different problems. We also study the long-range correlation within the search space, including the expected cost in the Hamming sphere around the local and global optima, the basin of attraction of the local and global optima and the probability of finding a local optimum as a function of its cost. We believe these information provide good insight for algorithm designers.

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Published date: May 2013
Organisations: University of Southampton, Southampton Wireless Group

Identifiers

Local EPrints ID: 355534
URI: http://eprints.soton.ac.uk/id/eprint/355534
PURE UUID: 75069ce4-8fde-4216-adc8-068277eab309

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Date deposited: 11 Nov 2013 14:21
Last modified: 18 Jul 2017 03:47

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Contributors

Author: M.-H. Tayarani-Najaran
Thesis advisor: Adam Prugel-Bennett

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