A mean-variance approach to transmission network planning

The limitations of traditional indifference-zone (IZ) ranking and selection procedures stem from their reliance on an IZ parameter, which is often unknown in practice and can lead to inefficiencies. Additionally, since exact evaluation of the probability of correct selection (PCS) is generally unattainable, these approaches commonly rely on a Bonferroni-Inequality-type lower bound to ensure the worst-case PCS, which introduces further conservativeness. To overcome these challenges, we propose fully sequential IZ-free procedures that eliminate the need for an IZ parameter and reduce the conservativeness associated with Bonferroni Inequality approaches. We demonstrate that, in the context of IZ-free procedures, the screening statistic corresponds to the Euclidean distance of a multi-dimensional standard Brownian motion, which behaves as a Bessel process. This connection simplifies the derivation of statistical guarantees for the proposed procedures and facilitates the analytical expressions for key parameters. Our procedures accommodate both known equal variances and unknown unequal variances, with statistical guarantees established in the known equal variance case. Numerical experiments confirm that the proposed procedures outperform existing methods in reducing PCS conservativeness and improving sample size efficiency. These advancements enhance the robustness and practicality of IZ-free procedures for diverse applications.

Selection of planting locations is an important issue in plant breeding and may significantly impact the probability of correctly identifying the desired genotype based on noisy data. This is especially true for early‐stage experimentation where a set of experimental genotypes is observed in very few locations. This study aims to identify locations that are most helpful for discriminating the main effects of two or more genotypes. A regression‐based model is proposed that characterizes the sensitivity of location to the genotype main effect, and locations with significant positive sensitivity are termed discriminative. Comparing or ranking genotypes using these locations results in exaggerated expected differences between genotype main effects, allowing for more accurate comparisons in the presence of noise. Based on the proposed model, an expression for the probability of making correct genotype selection is derived given a set of locations with known location sensitivities. The probability of correct selection is then used to characterize an optimal set of location that maximizes the probability of selecting the genotype with better main effect. These locations are independent of the genotypes being compared and only depend on the number of locations being considered and the sensitivities of these locations to genotype effects. The theoretical implications of the model are validated using data obtained from a commercial soybean breeding program. The results show that by using discriminating locations correct selection is made 76% of the time, versus 67% for all locations and only 63% of the time for non‐discriminating locations.

Subset selection of best simulated systems

The problem of selecting the Bernoulli population which has the highest success probability is considered. It has been noted in several articles that the probability of a correct selection is the same, uniformly in the Bernoulli p-vector (P1,P2,….,Pk), for two or more different selection procedures. We give a general theorem which explains this phenomenon. An application of particular interest arises when curtailment of a single-stage procedure (as introduced by Bechhofer and Kulkarni (1982a) )is employed; the corresponding result for curtailment of a single-stage procedure needs no proof. The use of strong curtailment in place of weak curtailment requires no more (and usually many less) observations to achieve the same.

Convergence rate analysis for optimal computing budget allocation algorithms

In recent years, with the rapid development of computing technology, developing parallel procedures to solve large-scale ranking and selection (R&S) problems has attracted a lot of research attention. In this paper, we take fixed-budget R&S procedure as an example to investigate potential issues of developing parallel procedures. We argue that to measure the performance of a fixed-budget R&S procedure in solving large-scale problems, it is important to quantify the minimal growth rate of the total sampling budget such that as the number of alternatives increases, the probability of correct selection (PCS) would not decrease to zero. We call such a growth rate of the total sampling budget the rate for maintaining correct selection (RMCS). We show that a tight lower bound for the RMCS of a broad class of existing fixed-budget procedures is in the order of [Formula: see text], where k is the number of alternatives. Then, we propose a new type of fixed-budget procedure, namely the fixed-budget knockout-tournament ([Formula: see text]) procedure. We prove that, in terms of the RMCS, our procedure outperforms existing fixed-budget procedures and achieves the optimal order, that is, the order of k. Moreover, we demonstrate that our procedure can be easily implemented in parallel computing environments with almost no nonparallelizable calculations. Last, a comprehensive numerical study shows that our procedure is indeed suitable for solving large-scale problems in parallel computing environments. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: Y. Zhong was supported by the National Natural Science Foundation of China [Grant 72101047]. L. J. Hong was supported by the National Natural Science Foundation of China [Grants 72091211 and 72161160340]. G. Jiang was supported by the National Natural Science Foundation of China [Grants 72121001 and 72171060]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.1221 .

In this study, we consider ranking and selection problems where the simulation model is subject to input uncertainty. Under the input uncertainty, we compare system designs based on their worst-case performance, and seek to maximize the probability of selecting the design with the best performance under the worst-case scenario. By approximating the probability of correct selection (PCS), we develop an asymptotically (as the simulation budget goes to infinity) optimal solution of the resulting problem. An efficient selection procedure is designed within the optimal computing budget allocation (OCBA) framework. Numerical tests show the high efficiency of the proposed method.

The problem of choosing the best of k populations when observations are non-negative and small observations are preferred is considered using a truncated play-the-winner sampling scheme. Upper bounds on the expected sample sizes are derived. The procedure is compared with a fixed sample size procedure on the basis of expected sample size and of risk. It is noted that the probability of correct selection (P.C.S.) is the same for the two procedures so that existing tables may be used.

In a Ranking and Selection problem, the objective of allocation is vital in deriving the rule. However, most of these objectives do not have a closed form. Due to the high cost of a direct approximation, several cheap but biased substitutes were applied to simplify the problem. These simplifications however could potentially affect the optimality of efficiency and therefore influence its finite performance. Fortunately, due to the increasing accessibility of parallel hardware (e.g. GPU), a direct approximation is becoming more tractable. Thus, we want to test the performance of an allocation rule based on an unbiased and direct approximation, expecting an acceleration on the performance. In this paper, we target on one of the famous objectives, the Probability of Correct Selection (PCS). Numerical experiments were done, showing a considerable improvement in finite performance of our algorithm comparing to a traditional one.

We deal with the design problem of early phase dose-finding clinical trials with monotone biologic endpoints, such as biological measurements, laboratory values of serum level, and gene expression. A specific objective of this type of trial is to identify the minimum dose that exhibits adequate drug activity and shifts the mean of the endpoint from a zero dose to the so-called minimum effective dose. Stepwise test procedures for dose finding have been well studied in the context of nonhuman studies where the sampling plan is done in one stage. In this article, we extend the notion of stepwise testing to a two-stage enrollment plan in an attempt to reduce the potential sample size requirement by shutting down unpromising doses in a futility interim. In particular, we examine four two-stage designs and apply them to design a statin trial with four doses and a placebo in patients with Hodgkin's disease. We discuss the calibration of the design parameters and the implementation of these proposed methods. In the context of the statin trial, a calibrated two-stage design can reduce the average total sample size up to 38% (from 125 to 78) from a one-stage step-down test, while maintaining comparable error rates and probability of correct selection. The price for the reduction in the average sample size is the slight increase in the maximum total sample size from 125 to 130.

The problems of i) selecting a subset of size s(⩾t)which contains the t. best cells and ii) selecting a subset of size s(_?t) which consists of any s of the t best cells of a multinomial stributions are considered under the fixed sample-size-indifference zone approach, Methods of strict differentiation with respect to the cell probabilities are used to study the monotonicity properties of the probability of correct selection and to solve the Chen and Hwang's conjecture on the least favorable configuration for the special case that s ≊ t

Discriminating between the log-normal and generalized exponential distributions

SUMMARY For some configurations of the means of k normal populations the probability of selecting the normal population with the largest mean does not increase when the number of observations from a given population is increased. We prove the statement and indicate some incorrect proofs in literature.

In this paper, we introduce a sequential procedure for the Multi-Objective Ranking and Selection (MOR&S) problems that identifies the Pareto front with a guaranteed probability of correct selection (PCS). In particular, the proposed procedure is fully sequential using the test statistics built upon the generalized sequential probability ratio test (GSPRT). The main features of the new proposed procedure are: 1) a unified framework, the new procedure treats the multi-objective problems in the same way as the single-objective problems; 2) an indifference-zone-free formulation, the new procedure eliminates the necessity of indifference-zone parameter; 3) asymptotically optimality, the GSPRT achieves asymptotically the shortest expected sample size among all sequential tests; 4) general distribution, the procedure uses the empirical likelihood for generally distributed observation. A numerical evaluation demonstrates the efficiency of the new procedure.

Optimal Computing Budget Allocation for regression with gradient information