Pareto Set Computation in Convex Multi-objective Design using Adaptive Response Surface Method (ARSM)

Abstract

Optimal design problems normally involve high dimensional design spaces and multiple objective functions. Depending on the complexity of the model, the time required to explore the design space could become excessive. This paper describes the calculation of the Pareto-optimal set based on adaptive surface methodology (ARSM) in order to reduce simulation times given a finite element analysis (FEA) simulation model. The Pareto-optimal strategy consists in the solution of a set of different single-objective problems. Each of this points is found via ARSM. The implementation of ARSM aims to use a few initial simulation points to approximate accurately the set of single-objective functions required. The methodology reduces significantly the number of points required to compute the efficient set compared to other strategies (e.g the exhaustive method), proving to reduce the simulation time of a computationally intensive model.