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Design and Implementation of a Graph-Based Constraint Model for Local Search

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Publication Type:

Licentiate Thesis

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Mälardalen University


Abstract

Local search has during the last years evolved into a powerful technique for solving large combinatorial problems, often outperforming complete algorithms. The classical approach for generic constraint solving in local search is to provide a set of primitive constraints, which in turn can be used to form more complex combinatorial structures. Unfortunately, for several combinatorial structures there is no decomposition into binary constraints which is acceptable in terms of space and/or time complexity. Global constraints have been introduced in local search as time and space efficient modelling components, capturing the properties of common combinatorial substructures.In this thesis we propose a compositional approach for global constraint design and implementation for local search. Traditionally, global constraints have been implemented as monolithic entities, often using a low-level language and requiring in-depth knowledge of the constraint system itself. In this work we propose to use graph structures, filters and cost components to create global constraints in a high-level C++ framework called Composer. The composed constraints can then be used for constraint solving in a generic, domain-independent local search solver. We show the theoretical model of the framework, and give algorithms for incrementally updating the costs and conflict levels of the constraints. We also show how to compose several well-known global constraints, and demonstrate by experimental results that a compositional approach at global constraint modelling is not only possible in practice, but also highly competitive with existing low-level implementations of constraint-based local search.

Bibtex

@misc{Bohlin629,
author = {Markus Bohlin},
title = {Design and Implementation of a Graph-Based Constraint Model for Local Search},
number = {27},
month = {April},
year = {2004},
publisher = {M{\"a}lardalen University},
url = {http://www.es.mdh.se/publications/629-}
}