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Mathematical Problems in Engineering
Volume 2015, Article ID 637809, 10 pages
Research Article

A Variable Depth Search Algorithm for Binary Constraint Satisfaction Problems

Department of Technology and Maritime Innovation, Buskerud and Vestfold University College, P.O. Box 4, 3199 Borre, Norway

Received 7 October 2014; Revised 5 March 2015; Accepted 1 April 2015

Academic Editor: Jianming Shi

Copyright © 2015 N. Bouhmala. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The constraint satisfaction problem (CSP) is a popular used paradigm to model a wide spectrum of optimization problems in artificial intelligence. This paper presents a fast metaheuristic for solving binary constraint satisfaction problems. The method can be classified as a variable depth search metaheuristic combining a greedy local search using a self-adaptive weighting strategy on the constraint weights. Several metaheuristics have been developed in the past using various penalty weight mechanisms on the constraints. What distinguishes the proposed metaheuristic from those developed in the past is the update of k variables during each iteration when moving from one assignment of values to another. The benchmark is based on hard random constraint satisfaction problems enjoying several features that make them of a great theoretical and practical interest. The results show that the proposed metaheuristic is capable of solving hard unsolved problems that still remain a challenge for both complete and incomplete methods. In addition, the proposed metaheuristic is remarkably faster than all existing solvers when tested on previously solved instances. Finally, its distinctive feature contrary to other metaheuristics is the absence of parameter tuning making it highly suitable in practical scenarios.