In this paper we propose a parallel hybrid genetic method for solving . This problem is proved to be computationally NP-hard. The parallelism in our algorithm is of two hierarchical levels. The first level is an insular model where a number of GAs (genetic algorithms) evolve in parallel. The second level is a parallel transformation of individuals in each GA. Implementation has been done using ParadisEO 1 framework, and the experiments have been performed on GRID5000, the French nation-wide computational grid. To evaluate our method, we used three benchmarks derived from QAP instances of QAPLIB and the results are compared with those reported in the literature. The preliminary results show that the method is promising. The obtained solutions are close to the optimal values and the execution is efficient.

Abstract-The quadratic 3-dimensional assignment problem (Q3AP) is an extension of the well-known NP-hard quadratic assignment problem. It has been proved to be one of the most difficult combinatorial optimization problems. Local search (LS) algorithms are a class of heuristics which have been successfully applied to solve such hard optimization problem. These methods handle with a single solution iteratively improved by exploring its neighborhood in the solution space. In this paper, we propose an iterated tabu search for solving the Q3AP. The design of this algorithm is essentially based on a new large neighborhood structure. Indeed, in LS heuristics, designing operators to explore large promising regions of the search space may improve the quality of the obtained solutions. However, designing such neighborhood is at the expense of a highly computationally process. Therefore, the use of graphics processing units (GPUs) provides an efficient complementary way to speed up the search. The proposed GPU-based iterated tabu search has been experimented on 5 different Q3AP instances. The obtained results are convincing both in terms of efficiency, quality and robustness of the provided solutions at run time.Index Terms-Quadratic 3-dimensional assignment problem (Q3AP), GPU-based local search, metaheuristics on GPU, iterated tabu search on graphics processing units.

Pattern set mining is an important part of a number of data mining tasks such as classification, clustering, database tiling, or pattern summarization. Efficiently mining pattern sets is a highly challenging task and most approaches use heuristic strategies. In this paper, we formulate the pattern set mining problem as an optimization task, ensuring that the produced solution is the best one from the entire search space. We propose a method based on integer linear programming (ILP) that is exhaustive, declarative and optimal. ILP solvers can exploit different constraint types to restrict the search space, and can use any pattern set measure (or combination thereof) as an objective function, allowing the user to focus on the optimal result. We illustrate and show the efficiency of our method by applying it to the tiling problem.

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