Noise-Tolerant Techniques for Decomposition-Based Multiobjective Evolutionary Algorithms

Kinematics Design of a MacPherson Suspension Architecture Based on Bayesian Optimization

Engineering design is traditionally performed by hand: an expert makes design proposals based on past experience, and these proposals are then tested for compliance with certain target specifications. Testing for compliance is performed first by computer simulation using what is called a discipline model. Such a model can be implemented by finite element analysis, multibody systems approach, etc. Designs passing this simulation are then considered for physical prototyping. The overall process may take months and is a significant cost in practice. We have developed a Bayesian optimization (BO) system for partially automating this process by directly optimizing compliance with the target specification with respect to the design parameters. The proposed method is a general framework for computing the generalized inverse of a high-dimensional nonlinear function that does not require, for example, gradient information, which is often unavailable from discipline models. We furthermore develop a three-tier convergence criterion based on: 1) convergence to a solution optimally satisfying all specified design criteria; 2) detection that a design satisfying all criteria is infeasible; or 3) convergence to a probably approximately correct (PAC) solution. We demonstrate the proposed approach on benchmark functions and a vehicle chassis design problem motivated by an industry setting using a state-of-the-art commercial discipline model. We show that the proposed approach is general, scalable, and efficient and that the novel convergence criteria can be implemented straightforwardly based on the existing concepts and subroutines in popular BO software packages.

A Multiobjective Framework for Many-Objective Optimization

It is known that many-objective optimization problems (MaOPs) often face the difficulty of maintaining good diversity and convergence in the search process due to the high-dimensional objective space. To address this issue, this article proposes a novel multiobjective framework for many-objective optimization (Mo4Ma), which transforms the many-objective space into multiobjective space. First, the many objectives are transformed into two indicative objectives of convergence and diversity. Second, a clustering-based sequential selection strategy is put forward in the transformed multiobjective space to guide the evolutionary search process. Specifically, the selection is circularly performed on the clustered subpopulations to maintain population diversity. In each round of selection, solutions with good performance in the transformed multiobjective space will be chosen to improve the overall convergence. The Mo4Ma is a generic framework that any type of evolutionary computation algorithm can incorporate compatibly. In this article, the differential evolution (DE) is adopted as the optimizer in the Mo4Ma framework, thus resulting in an Mo4Ma-DE algorithm. Experimental results show that the Mo4Ma-DE algorithm can obtain well-converged and widely distributed Pareto solutions along with the many-objective Pareto sets of the original MaOPs. Compared with seven state-of-the-art MaOP algorithms, the proposed Mo4Ma-DE algorithm shows strong competitiveness and general better performance.