Pareto-based branch and bound algorithm for multiobjective optimization of a safety transformer

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Brisset, Stephane | Tran, Tuan-Vu

Edité par HAL CCSD ; Emerald

International audience. The design of electromagnetic devices is mainly expressed in the literature in term of problem with continuous parameters. However, these problems are in the second part of the design process and often limited to the fine-tuning of some parameters corresponding to the structureselected in the first part. Despite recent progress in topological (Stolpe, 2014) and combinatorial (Amoiralis et al., 2008; Hemker et al., 2008; Sourd and Spanjaard, 2008) optimizations, there is a lack of decision tools for the choice of the structure and materials when dealing with conflictinggoals. At this stage, the parameters aremainly discrete and not sorted. Moreover, the production in a very small series practiced by few small and medium firms is supported by standards. It is thus a question of choosing among a great but finite numberof solutions rather than to optimize some dimensions finely.Optimization with discrete variables requires different concept than the conventional continuous one. The computation time of combinatorial optimization is also far more expensive. This is worsening in the design of electromagnetic devices because models are non-linear and time-consuming. Heuristic, Tabu search (Glover and Laguna, 1993) and branch and bound (BB) algorithm (Amoiralis et al., 2008; Hemker et al., 2008; Sourd and Spanjaard, 2008) can solve combinatorial problems. The former computes approximate solutions in an affordable time, while the latter finds the exact solutions with higher computing cost.The first part of the paper is devoted to introducing the context of combinatorial optimization in electrical machines and the main issues for solving this kind of problems. In the second part, the mechanisms of BB algorithm are explained and new criteria for thebranching and the initialization are proposed for multiobjective problems. The Pareto-based BB algorithm is applied to the bi-objective optimization of a safety transformer. Results are compared to those of exhaustive enumeration and non-dominated sorting genetic algorithm.Finally, some conclusions and prospects are given.

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