Reference : Parallel hybrid optimization methods for permutation based problems
Dissertations and theses : Doctoral thesis
Engineering, computing & technology : Computer science
Parallel hybrid optimization methods for permutation based problems
Mehdi, Malika [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)]
University of Luxembourg, ​Luxembourg, ​​Luxembourg
Université des sciences et technologies de Lille, ​​France
Docteur en Informatique
Bouvry, Pascal mailto
Talbi, El-Ghazali
[en] Combinatorial optimization ; Permutations ; Branch and bound ; Genetic algorithms ; Hybrid methods ; quadratic assignment problem ; metaheuristics ; parallel methods
[en] Solving efficiently large benchmarks of NP-hard permutation-based problems requires the development of hybrid methods combining different classes of optimization algorithms. The key challenge here is how to find connections between the divergent search strategies used in each class of methods in order to build efficient hybridization strategies. Genetic algorithms (GAs) are very popular population-based metaheuristics based on stochastic evolutionary operators. The hybridization of GAs with tree-based exact methods such as Branch-and-Bound is a promising research trend. B&B algorithms are based on an implicit enumeration of the solution space represented as a tree. Our hybridization approach consists in providing a common solution and search space coding and associated search operators enabling an efficient cooperation between the two methods. The tree-based representation of the solution space is traditionally used
in B&B algorithms to enumerate the solutions of the problem at hand. In this thesis, this special representation is adapted
to metaheuristics. The encoding of permutations as natural numbers, which refer to their lexicographic enumeration in the tree, is proposed as a new way to represent the solution space of permutation problems in metaheuristics. Mapping functions between the two representations and special search operators are defined for general permutation problems. This common representation allows the design of efficient cooperation strategies between GAs and B&B algorithms.
The proposed hybrid schemes have been parallelized and validated on standard benchmarks of the 3D quadratic assignment problem (Q3AP) using the computational grid Grid5000.

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