Parallel Hybrid Optimization Methods For Permutation Based Problems

Solving efficiently large benchmarks of NP-hard permutation-based problems requires the development of hybrid methods combining different classes of optimization methods. Indeed, it is now acknowledged that such methods perform better than traditional optimization methods when used separately. The key challenge 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. This encoding approach is based on the mathematical properties of permutations (Lehmer codes, inversion tables, etc.). Mapping functions between the two representations (permutations and numbers) and special search operators adapted to the encoding are defined for general permutation problems, with respect to the theory of representation. This common representation allows the design of efficient cooperation strategies between GAs and B&B algorithms. In this thesis, two hybridization schemes combining GAs with B&B based on this common representation are proposed. The two hybridization approaches HGABB/HAGABB (Hybrid Adaptive GA-B&B) and COBBIGA (cooperative B&B interval-based GA), have been validated on standard benchmarks of one of the hardest permutation-based problems, the three dimensional quadratic assignment problem (Q3AP). In order to solve large benchmarks of permutationbased problems, a parallelization for computational grids is also proposed for the two hybrid schemes. This parallelization is based on space decomposition techniques (the decomposition by intervals) used in parallel B&B algorithms. From the implementation point of view, in order to facilitate further design and implementation of hybrid methods combining metaheuristics with tree-based exact methods, a hybridization C++ framework integrated to the framework for metaheuristics ParadisEO is developed. The new framework is used to conduct extensive experiments over the computational grid Grid’5000.