Sampling Laws for Multi-Objective Simulation Optimization on Finite Sets
Abstract
We consider the multi-objective ranking and selection (MORS) problem, which is a multi-objective optimization problem where the multiple conflicting performance measures can only be observed via Monte Carlo simulation. The MORS problem is a special case of the multi-objective simulation optimization problem in which the decision space or number of systems is finite, and each system can be sampled to some extent. The solution to the MORS problem is a non-dominated set of systems called the Pareto set. When the computational resources required to run the Monte Carlo simulations are expensive, strategically allocating the simulation budget to efficiently and correctly identify the Pareto set is crucial. Motivated by this problem, we propose a simulation budget allocation strategy that maximizes the large deviation rate of decay of the probability of the misclassification event. This allocation strategy is asymptotically optimal, and allows us to model correlated light-tailed random vectors underlying the performance measures. To simplify computation, we develop approximate allocations based on the SCORE (Sampling Criteria for Optimization using Rate Estimators) framework. Due to the computational complexity in obtaining SCORE allocations in MORS problems with more than three objectives, we provide an alternative SCORE allocation strategy that attempts to maximize the rate of decay of the probability of a hybrid misclasification event, where false inclusions occur via scalarization. Since the allocation strategies require knowledge of unknown parameters, we also provide sequential algorithms for implementation. Numerical experiments on problems with multivariate normal objectives indicate that the resulting allocations are fast and perform well.
Degree
Ph.D.
Advisors
Pasupathy, Purdue University.
Subject Area
Statistics|Industrial engineering
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