Hierarchical Optimization-Based Approach for Two-Dimensional Rectangular Layout Design Problems

Abstract

This paper proposes a hierarchical optimization-based approach for two-dimensional rectangular layout design problems. While decomposition-based optimization has been a key approach for the complicated design problems under the trend of multidisciplinary design optimization, it has focused on continuous ones. While various approaches for layout design have been developed, they are based on any evolutionary algorithm for effectively handling its combinatorial nature. This paper aims to bring a new paradigm by combining decomposition-based optimization and evolutionary algorithms toward solving complicated layout design problems. In the approach, the Pareto optimality of subsystem-level layout against the optimality of system-level layout is extracted through two-level hierarchical formulation. Then, a computational design algorithm is developed. It represents the layout topology with sequence-pair and the shape of each subsystem or component with the aspect ratio, and optimizes them with genetic algorithms. The Pareto optimality of sub-levels is handled with multi-objective genetic algorithms, in which a set of Pareto are simultaneously generated. Top-level and sub-level layout problems are coordinated through exchange of preferable ranges of shapes and layout. An implemented approach is applied to an example problem for demonstrating its performance and capability.