Multi-objective Ranking and Selection: Optimal Sampling Laws and Tractable Approximations via SCORE
Eric A. Applegate (applegaepurdue.edu)
Abstract: Consider the multi-objective ranking and selection (MORS) problem in which we select the Pareto-optimal set from a finite set of systems evaluated on three or more stochastic objectives. Solving this problem is difficult because we must determine how to allocate a simulation budget among the systems to minimize the probability that any systems are misclassified. Toward determining such a simulation budget allocation, we characterize the exact asymptotically optimal sample allocation that maximizes the misclassification-probability decay rate, and we provide an implementable allocation called MO-SCORE. The MO-SCORE allocation has three salient features: (a) it simultaneously controls the probabilities of misclassification by exclusion and inclusion; (b) it uses a fast dimension-sweep algorithm to identify phantom Pareto systems crucial for computational efficiency; and (c) it models dependence between the objectives. The MO-SCORE allocation is fast and accurate for problems with three objectives or a small number of systems. For problems with four or more objectives and a large number of systems, where modeling dependence has diminishing returns relative to computational speed, we propose independent MO-SCORE (iMO-SCORE). Our numerical experience is extensive and promising: MO-SCORE and iMO-SCORE successfully solve MORS problems involving several thousand systems in three and four objectives.
Keywords: multi-objective ranking and selection; simulation optimization
Category 1: Other Topics (Optimization of Simulated Systems )
Category 2: Other Topics (Multi-Criteria Optimization )
Citation: Under review.
Entry Submitted: 07/30/2018
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