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Multi-objective Ranking and Selection: Optimal Sampling Laws and Tractable Approximations via SCORE

Eric A. Applegate (applegae***at***purdue.edu)
Guy Feldman (gfeldman***at***purdue.edu)
Susan R. Hunter (susanhunter***at***purdue.edu)
Raghu Pasupathy (pasupath***at***purdue.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.

Download: [PDF]

Entry Submitted: 07/30/2018
Entry Accepted: 07/30/2018
Entry Last Modified: 05/29/2019

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