Adaptive Pareto Set Estimation for Stochastic Mixed Variable Design Problems

Many design problems require the optimization of competing objective functions that may be too complicated to solve analytically. These problems are often modeled in a simulation environment where static input may result in dynamic (stochastic) responses to the various objective functions. System reliability, alloy composition, algorithm parameter selection, and structural design optimization are classes of problems that often exhibit such complex and stochastic properties. Since the physical testing and experimentation of new designs can be prohibitively expensive, engineers need adequate predictions concerning the viability of various designs in order to minimize wasteful testing. Presumably, an appropriate stochastic multi-objective optimizer can be used to eliminate inefficient designs through the analysis of simulated responses. This research develops an adaptation of Walston's Stochastic Multi-Objective Mesh Adaptive Direct Search (SMOMADS) and Paciencia's NMADS based on Kim and de Weck's Adaptive Weighted Sum (AWS) procedure and standard distance to a reference point methods. The main contribution of this paper is a new implementation of MADS for Mixed Variable and Stochastic design problems that drastically reduces dependence on subjective decision maker interaction.