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On the Complexity of Hierarchical Problem Solving

On the Complexity of Hierarchical Problem Solving
On the Complexity of Hierarchical Problem Solving
Competent Genetic Algorithms can e±ciently address problems in which the linkage between variables is limited to a small order k. Problems with higher order dependencies can only be addressed e±ciently if further problem properties exist that can be exploited. An important class of problems for which this occurs is that of hierarchical problems. Hierarchical problems can contain dependencies between all variables (k = n) while being solvable in polynomial time. An open question so far is what precise properties a hierarchical problem must possess in order to be solvable e±ciently. We study this question by investigating several features of hierarchical problems and determining their e®ect on computational complexity, both analytically and empirically. The analyses are based on the Hierarchical Genetic Algorithm (HGA), which is developed as part of this work. The HGA is tested on ranges of hierarchical problems, produced by a generator for hierarchical problems.
De Jong, Edwin
fa5e78fc-c363-4bc3-b139-9ab5199853ba
Watson, Richard A.
ce199dfc-d5d4-4edf-bd7b-f9e224c96c75
Thierens, Dirk
0f991e11-375d-452b-8613-bbc66a799def
De Jong, Edwin
fa5e78fc-c363-4bc3-b139-9ab5199853ba
Watson, Richard A.
ce199dfc-d5d4-4edf-bd7b-f9e224c96c75
Thierens, Dirk
0f991e11-375d-452b-8613-bbc66a799def

De Jong, Edwin, Watson, Richard A. and Thierens, Dirk (2005) On the Complexity of Hierarchical Problem Solving Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2005)

Record type: Article

Abstract

Competent Genetic Algorithms can e±ciently address problems in which the linkage between variables is limited to a small order k. Problems with higher order dependencies can only be addressed e±ciently if further problem properties exist that can be exploited. An important class of problems for which this occurs is that of hierarchical problems. Hierarchical problems can contain dependencies between all variables (k = n) while being solvable in polynomial time. An open question so far is what precise properties a hierarchical problem must possess in order to be solvable e±ciently. We study this question by investigating several features of hierarchical problems and determining their e®ect on computational complexity, both analytically and empirically. The analyses are based on the Hierarchical Genetic Algorithm (HGA), which is developed as part of this work. The HGA is tested on ranges of hierarchical problems, produced by a generator for hierarchical problems.

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Published date: 2005
Organisations: Agents, Interactions & Complexity

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Local EPrints ID: 262016
URI: http://eprints.soton.ac.uk/id/eprint/262016
PURE UUID: d455228f-6355-4848-ad95-0d9e94b1f883

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Date deposited: 21 Feb 2006
Last modified: 18 Jul 2017 08:56

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Contributors

Author: Edwin De Jong
Author: Dirk Thierens

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