Decomposition Templates and Joint Morphing Operators for Genetic Algorithm Optimization of Multi-Component Topology

This paper presents a continuum-based approach for multi-objective topology optimization of multi-component structures. Objectives include minimization of compliance, weight and as cost of assembly and manufacturing. Decision variables are partitioned into two main groups: those pertaining to material allocation within a design domain (base topology problem), and those pertaining to decomposition of a monolithic structure into multiple components (joint allocation problem). Generally speaking, the two problems are coupled in the sense that the decomposition of an optimal monolithic structure is not always guaranteed to produce an optimal multi-component structure. However, for spot-welded sheet-metal structures (such as those often found in automotive applications), certain assumptions can be about the performance of a monolithic structure that favor the adoption of a two-stage approach that decouples the base topology and joint allocation problems. A multi-objective genetic algorithm (GA) is used throughout the studies in this paper. While the problem decoupling in two-stage approaches significantly reduces the size of the search space and allows better performance of the GA, the size of the search space can still be quite enormous in the second stage. To further improve the performance, we propose a new mutation operator based on decomposition templates and localized joints morphing. A cantilever-loaded structure is then used as a metric to study and compare various setups of single and two-stage GA approaches.