A Bi-level Method for Shape and Member Sizing Optimization of Frame Structures

摘要

This paper describes a new optimization method for truss and frame structures that offers significant performance improvements compared to existing approaches. The proposed formulation partitions the problem into two hierarchical levels: shape and sizing. For each configuration of shape variables generated, a specialized deterministic algorithm attempts to find an optimal configuration of discrete section size variables for that particular geometry. The sizing results are then used to inform a gradient-based search that operates on continuous shape variables to find the 'best' overall solution. The proposed method is compared to other optimization approaches using standard minimum-weight truss problems. Results indicate that the bi-level method is capable of finding superior quality solutions (2.8% on average) in an order of magnitude less computational time. The suitability of the method to larger design problems is discussed and further research is proposed to test the scalability of the method.