Session: DAC-15-02-Multidisciplinary Design Optimization, Multiobjective Optimization, and Sensitivity Analysis

Paper Number: 91343

91343 - Multi-Objective Bayesian Optimization Supported by Gaussian Process Classifiers and Conditional Probabilities 

In the last years, there has been an increasing effort to develop Bayesian methodologies to solve multi-objective optimization problems. Most of these methods can be classified in two groups: infilling criterion-based methods and aggregation-based methods. The first group employs an index that quantifies the gain that a new design can produce in the current Pareto front while the last group uses a (possibly non-linear) aggregation function and a weighting vector to identify a Pareto design. Most infilling-based methods have been developed to solve two-objective optimization problems. Aggregation-based methods enable the solution of many-objective optimization problems but their performance depends on the set of weighting vectors, which are often selected randomly. This study proposes a novel multi-objective Bayesian framework that exploits the rich probabilistic information that can be extracted from Gaussian process (GP) classifiers and the ability of conditional probabilities to capture design preferences. In the proposed framework, a GP classifier is trained to identify design zones that potentially contain Pareto designs. The training process involves the inference of a latent GP that encodes input-space interactions that describe a Pareto design. This latent GP enables the solution of many-objective optimization problems with any standard acquisition function and without the prescription of a weighting vector. Conditional probabilities are utilized to define design goals that promote a uniform expansion of the Pareto front. The proposed approach is demonstrated with two benchmark analytical problems and the design optimization of sandwich composite armors for blast mitigation, which involves expensive finite element simulations.

Presenting Author: Homero Valladares Purdue University

Presenting Author Biography: Homero Valladares is a PhD candidate in Mechanical Engineering at Purdue University and a Research Assistant at and Indiana University – Purdue University Indianapolis (IUPUI). In August 2015, he was awarded a J. William Fulbright Scholarship to pursue his Master’s studies in Mechanical Engineering at IUPUI. Since then, he has been working at the Engineering Design Research Laboratory under the direction of Dr. Andres Tovar.

Authors:

Homero Valladares Purdue University
Andres Tovar IUPUI