Multi-Objective Pareto Concurrent Subspace Optimization for Multidisciplinary Design

Abstract

Most real-world design problems are complex and multidisciplinary, with almost always more than one objective (cost) function to be extremized simultaneously. The primary goal of this research is to develop a framework to enable multi-objective optimization of multidisciplinary design applications, wherein each discipline is able to retain substantial autonomous control during the process. To achieve this end, we have extended the capability of the concurrent subspace optimization method to handle multi-objective optimization problems in a multidisciplinary design optimization context Although the conventional concurrent subspace optimization approach is easily able to deal with multi-objective optimization problems by applying the weighted sum approach, the main disadvantage is that the weighted sum cannot capture Pareto points on any nonconvex part of the Pareto frontier. Moreover, an aggregate objective function simply cannot reflect the true spirit of the concurrent subspace optimization method, which was developed to allow groups of specialists to independently have more control over their own design criteria and goals, even while maintaining system level coordination. In this paper, the multi-objective Pareto concurrent subspace optimization method is proposed in which each discipline has substantial control over its own objective function during the design process, while still ensuring responsibility for constraint satisfaction in coupled subspaces. The proposed approach is particularly useful given the realities of geographical distribution, computational platform variation, and dependence upon legacy codes within individual disciplines that so predominates the design of large-scale products such as aircraft and automobiles. As part of the multi-objective Pareto concurrent subspace optimization method developed here, it is demonstrated that the endpoints of the Pareto frontier can be easily identified, together with an ability to generate Pareto points within prescribed limits to ensure a reasonably even distribution across the entire frontier. The approach is validated (using three multidisciplinary design optimization test problems) against Pareto frontiers generated using the weighted sum approach.