Test and Validation of the Surrogate-Based, Multi-Objective GOMORS Algorithm against the NSGA-II Algorithm in Structural Shape Optimization

Abstract

Nowadays, product development times are constantly decreasing, while the requirements for the products themselves increased significantly in the last decade. Hence, manufacturers use Computer-Aided Design (CAD) and Finite-Element (FE) Methods to develop better products in shorter times. Shape optimization offers great potential to improve many high-fidelity, numerical problems such as the crash performance of cars. Still, the proper selection of optimization algorithms provides a great potential to increase the speed of the optimization time. This article reviews the optimization performance of two different algorithms and frameworks for the structural behavior of a b-pillar. A b-pillar is the structural component between a car’s front and rear door, loaded under static and crash requirements. Furthermore, the validation of the algorithm includes a feasibility constraint. Recently, an optimization routine was implemented and validated for a Non-dominated Sorting Genetic Algorithm (NSGA-II) implementation. Different multi-objective optimization algorithms are reviewed and methodically ranked in a comparative study by given criteria. In this case, the Gap Optimized Multi-Objective Optimization using Response Surfaces (GOMORS) framework is chosen and implemented into the existing Institut für Konstruktionstechnik Optimizes Shapes (IKOS) framework. Specifically, the article compares the NSGA-II and GOMORS directly for a linear, non-linear, and feasibility optimization scenario. The results show that the GOMORS outperforms the NSGA-II vastly regarding the number of function calls and Pareto-efficient results without the feasibility constraint. The problem is reformulated to an unconstrained, three-objective optimization problem to analyze the influence of the constraint. The constrained and unconstrained approaches show equal performance for the given scenarios. Accordingly, the authors provide a clear recommendation towards the surrogate-based GOMORS for costly and multi-objective evaluations. Furthermore, the algorithm can handle the feasibility constraint properly when formulated as an objective function and as a constraint.