2012 年 3 巻 2 号 p. 31-46
This paper proposes a multi-start optimization framework for the continuous multi-objective optimization problem (CMOP). Numerical solutions to a CMOP should have a satisfactory level of precision and coverage in order to give a fine representation of the Pareto set or the Pareto front. One successful approach in terms of precision is the descent method, guaranteeing convergence to a Pareto solution if the problem does not have non-Pareto-optimal critical points. However, the coverage of solutions produced by naive multi-start strategies, e.g., choosing initial parameters evenly or at random, would be unsatisfactory. This is because the correspondence between initial parameters, i.e., initial solutions, and weight vectors when a scalarization of objective functions is incorporated, and resulting solutions is usually unknown in advance and may be biased. Our proposal, Adaptive Weighted Aggregation (AWA), is a scalarization-based multi-start framework that employs two novel strategies taking coverage into account: 1) subdivision: a systematic initialization scheme utilizing the correspondence between the set of weight vectors and the Pareto set/front; 2) relocation: an iterative search mechanism for a well-placed Pareto solution that is equidistant from neighboring solutions with an adaptation of weight vectors. Alternately repeating the subdivision and the relocation, AWA approximates the Pareto set/front progressively from the boundary to the interior. We demonstrate the effectiveness of AWA by comparing it to conventional multi-start descent methods on 2- to 6-objective benchmark problems. Several aspects of the computational efficiency and the scalability of AWA are also discussed.
