Multi-objective optimisation of complex mechanisms using Moving Spheres: An application to suspension elasto-kinematics

This paper presents a new iterative method, called Moving Spheres (MS), for solving multi-objective design optimisation problems involving three-dimensional mechanisms. The method is suited to problems in which most of the design variables belong to the three-dimensional Euclidean space. MS method is able to explore efficiently the design space and identifies the regions where the optimal solutions are located, resulting in a clear spatial representation of optimal solutions. In this paper, MS method is applied to the elasto-kinematic optimisation of an automotive suspension system. The optimal locations of suspension joints are sought within spherical neighbourhoods of a reference suspension. This preserves the kinematic compatibility of the mechanism and facilitates the exploration of the design space through iterative updates of the reference suspension. The rigorous $k$-optimality metric, which introduces a hierarchical sorting in the Pareto-optimal set, is employed to rank optimal design solutions. In the suspension test case, the Pareto-optimal set of approximated through Moving Spheres method is compared with the Pareto-optimal sets resulting from Parameter Space Investigation and multi-objective optimisation Genetic Algorithm with sorting (KEMOGA) methods, considering similar computational time. Moving Spheres method yields a more accurate approximation of the Pareto-optimal set.