CAREER: Multi-Objective Optimization via Simulation: Theory, Methods, and Parallel Computation

Purdue University, West Lafayette IN

Investigators

Abstract

This Faculty Early Career Development (CAREER) grant is developing theory, methods, and algorithms for decision-making under uncertainty in complex systems that are modeled using computer-based simulations. The specific focus will be on developing implementable algorithms that identify optimal decisions with respect to multiple performance measures. Such problems arise frequently in a variety of applications including finance, energy, transportation, facility location, supply chain management, telecommunication, and healthcare management. Though widespread, these problems are under-studied, and current solution methods may be slow, imprecise, or inaccurate. Developing methods to solve such problems with provable guarantees on speed, precision, and accuracy will enable decision-makers to make better, timely decisions across a variety of disciplines. Society will benefit from improved systems, characterized by increased efficiency and reduced cost. This project also supports the PI's educational goal of disseminating clear and engaging educational materials at the interface of probability and optimization that recruit, train, and retain the next generation of professionals who make decisions under uncertainty. This research will develop theory, methods, and parallel algorithms for solving multi-objective optimization via simulation problems. Multi-objective optimization via simulation problems are nonlinear multi-objective optimization problems in which each objective can only be observed with error as output from a Monte Carlo simulation; a solution to this problem is a non-dominated (Pareto) set. Despite its prevalence and mature development in the analogous deterministic context, multi-objective optimization via simulation problems have seen relatively little theoretical and algorithmic development in the optimization via simulation literature. These problems are difficult to solve because of their complexity: the objective functions can only be estimated with error through potentially expensive Monte Carlo simulation, and the Pareto set often grows in the number of objectives. The proposed research will develop the theoretical underpinnings of estimating Pareto sets in the stochastic context. Specifically, the proposed theory and methods include scaling for dimension reduction, asymptotic approximation, optimization frameworks that retrieve fast convergence rates, and parallel implementation. Such understanding will lead to new algorithmic methods that evolve optimally in a provable sense and to implementable, efficient parallel algorithms for solving these difficult problems.