Non-gradient methods in MDO - Status and future directions

Abstract

A number of multidisciplinary design optimization (MDO) problems are characterized by the presence of discrete and integer design variables, over and beyond the more traditional continuous variable problems. In some applications, the number of design variables may be quite large. Additionally, the design space in such problems may be nonconvex, and in some situations, even disjointed. The use of conventional mathematical programming methods in such problems is fraught with hazards. First, these gradient-based methods cannot be used directly in the presence of discrete variables. Their use is facilitated by creating multiple equivalent continuous variable problems; in the presence of high-dimensionality, the number of such problems to be solved can be quite large. Finally, it must be borne in mind that these methods have a propensity to convergence to a relative optimum closest to the starting point, and this is a major weakness in the presence of multimodality in the design space. This paper focuses on non-gradient optimization methods such as simulated annealing (SA), and genetic algorithms (GA), Tabu search (TS) and rulebased expert systems. It also examines issues pertinent to using these methods in MDO problems.