On the Role of Robustness in Multi-Objective Robust Optimization: Application to an IPM Motor Design Problem

This paper discusses the different roles that robustness can assume when solving a multi-objective design optimization problem. A new role for robustness in multi-objective design optimization problems is proposed based on which an approach to conducting multi-objective robust optimization and finding the robust optima is suggested. This new approach is then tested on an internal permanent magnet motor design problem and the results are presented.

I. Introduction

Multi-objective optimization is concerned with optimizing more than one objective function under a set of constraints. The general problem is formulated as

$$\begin{align}&\min _{x}~{F( x )}=[ F_{1}( x ),\ldots ,F_{m}(x ) ]^{T} \\[-3.5pt]&\text {s.t:}~\begin{cases} g_{i}( x )\le 0,& i=1,\ldots ,k \\[-1pt] h_{j}( x )=0,& j=1,\ldots ,l \\ \end{cases} \end{align}$$ where is the number of objectives, is the number of inequality constraints, and is the number of equality constraints. The solution to the above formulation is usually presented in the form of a set of non-dominated points in the feasible region of the objective space. The optima are known as the Pareto front, since this definition of optimality and the relations of dominance were first introduced by Vilfredo Pareto.