In this study, we propose a hierarchical optimization-based approach for two-dimensional rectangular layout design problems. Decomposition-based optimization has been a key approach for complicated design problems in multidisciplinary design optimization (MDO), but the main focus has been design problems where the design variables are continuous. On the other hand, various approaches have been developed for layout design based on evolutionary algorithms, e.g., simulated annealing (SA) and genetic algorithms (GAs) which can handle its combinatorial nature in an effective manner. In the present study, we aim to introduce a new paradigm by combining decomposition-based optimization and evolutionary algorithms for solving complicated layout design problems. In this approach, the original layout problem is decomposed into the top-level layout problem and a set of sublevel layout problems, where the layouts obtained from the sublevel problems are used as components of the top-level problem. Since the preferable shapes of these components are unclear when the sublevel problems are solved, a set of Pareto optima are provided in the sublevel problems and these solutions are used as candidate components in the top-level problem. A computational design algorithm is developed based on this approach, which represents the layout topology with sequence pair and the shape of each subsystem or component with the aspect ratio, and they are optimized using GAs. The Pareto optimality of the sublevels is handled by multi-objective GAs, and a set of Pareto optima is generated simultaneously. The top-level and sublevel layout problems are coordinated via the exchange of preferable ranges for the shapes and layout. This approach was implemented and applied to an example problem to demonstrate its performance and capability.
Interbank lending with benchmark rates: Pareto optima for a class of singular control games
