Large Barrier Trees for Studying Search
Large Barrier Trees for Studying Search
Barrier trees are a method for representing the landscape structure of high-dimensional discrete spaces such as those that occur in the cost function of combinatorial optimization problems. The leaves of the tree represent local optima and a vertex where subtrees join represents the lowest cost saddle-point between the local optima in the subtrees. This paper introduces an extension to existing Barrier tree methods that make them more useful for studying heuristic optimization algorithms. It is shown that every configuration in the search space can be mapped onto a vertex in the Barrier tree. This provides additional information about the landscape, such as the number of configurations in a local optimum. It also allows the computation of additional statistics such as the correlation between configurations in different parts of the Barrier tree. Furthermore, the mappings allow the dynamic behavior of a heuristic search algorithms to be visualized. This extension is illustrated using an instance of the MAX-3-SAT problem.
Barrier trees MAX-SAT combinatorial optimization cost landscape heuristic search
385-397
Hallam, Jonathan
ad913478-bbc8-46f0-ba3a-8567f609047a
Prügel-Bennett, Adam
b4b5930c-a20c-4f25-acd6-ebc0b0dc4250
2005
Hallam, Jonathan
ad913478-bbc8-46f0-ba3a-8567f609047a
Prügel-Bennett, Adam
b4b5930c-a20c-4f25-acd6-ebc0b0dc4250
Hallam, Jonathan and Prügel-Bennett, Adam
(2005)
Large Barrier Trees for Studying Search.
IEEE Transactions on Evolutionary Computation, 9 (4), .
Abstract
Barrier trees are a method for representing the landscape structure of high-dimensional discrete spaces such as those that occur in the cost function of combinatorial optimization problems. The leaves of the tree represent local optima and a vertex where subtrees join represents the lowest cost saddle-point between the local optima in the subtrees. This paper introduces an extension to existing Barrier tree methods that make them more useful for studying heuristic optimization algorithms. It is shown that every configuration in the search space can be mapped onto a vertex in the Barrier tree. This provides additional information about the landscape, such as the number of configurations in a local optimum. It also allows the computation of additional statistics such as the correlation between configurations in different parts of the Barrier tree. Furthermore, the mappings allow the dynamic behavior of a heuristic search algorithms to be visualized. This extension is illustrated using an instance of the MAX-3-SAT problem.
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Submitted date: 2 February 2005
Accepted/In Press date: 2 February 2005
Published date: 2005
Keywords:
Barrier trees MAX-SAT combinatorial optimization cost landscape heuristic search
Organisations:
Electronics & Computer Science
Identifiers
Local EPrints ID: 261523
URI: http://eprints.soton.ac.uk/id/eprint/261523
PURE UUID: 2e41699a-9b03-4c5b-bd4e-adb88bf1fc4a
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Date deposited: 28 Oct 2005
Last modified: 14 Mar 2024 06:53
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Contributors
Author:
Jonathan Hallam
Author:
Adam Prügel-Bennett
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