Adaptive Pareto Set Estimation for Stochastic Mixed Variable Design Problems

by Christopher D. Arendt

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 work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.