Review on ranking and selection: A new perspective

In this paper,we briefly review the development of ranking and selection(R&S)in the past 70 years,especially the theoretical achievements and practical applications in the past 20 years.Different from the frequentist and Bayesian classifications adopted by Kim and Nelson(2006b)and Chick(2006)in their review articles,we categorize existing R&S procedures into fixed-precision and fixed-budget procedures,as in Hunter and Nelson(2017).We show that these two categories of procedures essentially differ in the underlying methodological formulations,i.e.,they are built on hypothesis testing and dynamic programming,respectively.In light of this variation,we review in detail some well-known procedures in the literature and show how they fit into these two formulations.In addition,we discuss the use of R&S procedures in solving various practical problems and propose what we think are the important research questions in the field.

DESIGN SAMPLING AND REPLICATION ASSIGNMENT UNDER FIXED COMPUTING BUDGET

For many real world problems, when the design space is huge and unstructured, and time consuming simulation is needed to estimate the performance measure, it is important to decide how many designs to sample and how long to run for each design alternative given that we have only a fixed amount of computing time. In this paper, we present a simulation study on how the distribution of the performance measures and distribution of the estimation errors/noises will affect the decision. From the analysis, it is observed that when the underlying distribution of the noise is bounded and if there is a high chance that we can get the smallest noise, then the decision will be to sample as many as possible, but if the noise is unbounded, then it will be important to reduce the noise level first by assigning more replications for each design. On the other hand, if the distribution of the performance measure indicates that we will have a high chance of getting good designs, the suggestion is also to reduce the noise level, otherwise, we need to sample more designs so as to increase the chances of getting good designs. For the special case when the distributions of both the performance measures and noise are normal, we are able to estimate the number of designs to sample, and the number of replications to run in order to obtain the best performance.

Efficient learning for decomposing and optimizing random networks

In this study,we consider the problem of node ranking in a random network.A Markov chain is defined for the network,and its transition probability matrix is unknown but can be learned by sampling random interactions among nodes.Our objective is to decompose the Markov chain into several ergodic classes and select the best node in each ergodic class.We propose a dynamic sampling procedure,which gives a probability guarantee on correct decomposition and maximizes a weighted probability of correct selection of the best node in each ergodic class.Numerical experiment results demonstrate the efficiency of the proposed sampling procedure.

Stochastic systems simulation optimization

With the advance of new computational technology,stochastic systems simulation and optimization has become increasingly a popular subject in both academic research and industrial applications.This paper presents some of recent developments about the problem of optimizing a performance function from a simulation model.We begin by classifying different types of problems and then provide an overview of the major approaches,followed by a more in-depth presentation of two specific areas:optimal computing budget allocation and the nested partitions method.