Similarity-based Sampling for Simulation with Binary Outcomes

AbstractAbstract–We consider a feasibility determination problem via simulation with stochastic binary outcomes, in which the design space can be either discrete or continuous, and outcomes can be predicted through a functional relationship that depends on linear combinations of design variables. The goal is to identify all the feasible designs with means (i.e., probabilities) no smaller than a threshold. A logistic model is used to capture the relationship between the probability and design variables. Traditional binary rewards often conceal the numbers of correct and false determinations, thereby being inefficient in large and continuous design spaces. We thus propose a similarity measure to smooth binary rewards. Then, a sampling policy that optimizes a so-called similarity differential (SD) is developed. Under some mild conditions, we show that the SD policy is capable of identifying all the feasible designs as the sampling budget goes to infinity. Two approximate versions of the SD policy are developed to sequentially determine the sampling decisions in large and continuous design spaces. Extensive numerical experiments are conducted to demonstrate the superior performance of our SD policy, document computational savings, and reveal underlying sampling behaviors. Alternatively, we provide a simple but effective heuristic that can be easily used by practitioners.Keywords: simulationfeasibility determinationbinary outcomesoptimal computing budget allocationexperimental designDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgementsWe thank the editors and anonymous reviewers for valuable comments. This paper is supported by the National Science Foundation of China [Grant No. 72301187, 72122019, and 71771202], and by the Fundamental Research Funds for the Central Universities [Grant No. SXYPY202346]Additional informationNotes on contributorsHaitao LiuHaitao Liu received his Ph.D. degree in the Department of Industrial Systems Engineering and Management at National University of Singapore in 2022. He is currently an associate professor in Business School at Sichuan University. His research interests include simulation optimization, statistical learning, and supply chain management.Ping CaoPing Cao received his Ph.D. degree in Operational Research at Academy of Mathematics and Systems Science, Chinese Academy of Science in 2011. He is currently a professor at the School of Management in University of Science and Technology of China. He His research interests include stochastic control, queueing theory, Markov decision process, and dynamic pricing in revenue management.Loo Hay LeeLoo Hay Lee received his Ph.D. degree in Engineering Science from Harvard University, USA. He was a Professor in the Department of Industrial Systems Engineering and Management at National University of Singapore. His research interests include logistics, vehicle routing, supply chain modeling, and simulation-based optimization.Ek Peng ChewEk Peng Chew received his Ph.D. degree in Industrial Engineering from Georgia Institute of Technology, USA. He currently is a Professor in the Department of Industrial Systems Engineering and Management at National University of Singapore. His research areas are in port logistics, maritime transportation, and inventory management.