Optimal Computing Budget Allocation Research Articles

Ranking and selection with two-stage decision

Ranking & selection (R&S) is concerned with the selection of the best decision from a finite set of alternative decisions when the outcome of the decision has to be estimated using stochastic simulation. In this paper, we extend the R&S problem to a two-stage setting where after a first-stage decision has been made, some information may be observed and a second-stage decision then needs to be made based on the observed information to achieve the best outcome. We then extend two popular single-stage R&S algorithms, expected value of information (EVI) and optimal computing budget allocation (OCBA), to efficiently solve the new two-stage R&S problem. We prove the consistency of the new two-stage EVI (2S-EVI) and OCBA (2S-OCBA) algorithms. Experiment results on benchmark test problems and a two-stage multi-product assortment problem show that both algorithms outperform applying single-stage EVI and OCBA in the two-stage setting. Between 2S-EVI and 2S-OCBA, numerical results suggest that 2S-EVI tends to perform better with smaller number of decisions at first and second stage while 2S-OCBA has better performance for larger problems.

Adaptive budget allocation in simheuristics applied to stochastic home healthcare routing and scheduling

The organization of home care is of pivotal importance in response to the trend of delivering more care directly to clients’ residences. With more vulnerable clients residing at home, variability in care durations needs careful consideration. This paper addresses the operational home healthcare routing and scheduling problem (HHCRSP) with uncertainty in travel and service times. The quality of the routes is evaluated based on the expected objective function, incorporating travel time, waiting time, and shift overtime. Due to the complexity of the problem, a simheuristic approach is applied that carefully integrates the optimization of the deterministic HHCRSP with simulation. This study proposes a new framework, based on optimal computing budget allocation and the expected opportunity costs, to dynamically determine when to employ optimization and when to use simulation. A practical case study demonstrates the effectiveness of the approach and reveals the substantial impact of accounting for randomness in the HHCRSP.

A Combined OCBA–AIC Method for Stochastic Variable Selection in Data Envelopment Analysis

This study introduces a novel approach to enhance variable selection in Data Envelopment Analysis (DEA), especially in stochastic environments where efficiency estimation is inherently complex. To address these challenges, we propose a game cross-DEA model to refine efficiency estimation. Additionally, we integrate the Akaike Information Criterion (AIC) with the Optimal Computing Budget Allocation (OCBA) technique, creating a hybrid method named OCBA–AIC. This innovative method efficiently allocates computational resources for stochastic variable selection. Our numerical analysis indicates that OCBA–AIC surpasses existing methods, achieving a lower AIC value. We also present two real-world case studies that demonstrate the effectiveness of our approach in ranking suppliers and tourism companies under uncertainty by selecting the most suitable partners. This research enriches the understanding of efficiency measurement in DEA and makes a substantial contribution to the field of performance management and decision-making in stochastic contexts.

Accelerated Driving-Training-Based Optimization for Solving Constrained Bi-Objective Stochastic Optimization Problems

The constrained bi-objective stochastic optimization problem (CBSOP) considers the optimization problem with stochastic bi-objective functions subject to deterministic constraints. The CBSOP is part of a set of hard combinatorial optimization problems regarding time complexity. Ordinal optimization (OO) theory provides a commonly recognized structure to handle hard combinatorial optimization problems. Although OO theory may solve hard combinatorial optimization problems quickly, the deterministic constraints will critically influence computing performance. This work presents a metaheuristic approach that combines driving-training-based optimization (DTBO) with ordinal optimization (OO), abbreviated as DTOO, to solve the CBSOP with a large design space. The DTOO approach comprises three major components: the surrogate model, diversification, and intensification. In the surrogate model, the regularized minimal-energy tensor product with cubic Hermite splines is utilized as a fitness estimation of design. In diversification, an accelerated driving-training-based optimization is presented to determine N remarkable designs from the design space. In intensification, a reinforced optimal computing budget allocation is used to find an extraordinary design from the N remarkable designs. The DTOO approach is applied to a medical resource allocation problem in the emergency department. Simulation results obtained by the DTOO approach are compared with three heuristic approaches to examine the performance of the DTOO approach. Test results show that the DTOO approach obtains an extraordinary design with higher solution quality and computational efficiency than the three heuristic approaches.

Optimal Computing Budget Allocation for Operations of a Zone-Picking System

Optimal Computing Budget Allocation for Operations of a Zone-Picking System

Virtual Material Quality Investigation System

It is often difficult to inspect the material quality in the procurement process. In many cases, the true quality may only be revealed after several manufacturing processes or at the final test of the finished goods. This study employs a hybrid strategy consisting of predictive analytics and prescriptive analytics. The former considers the production characteristics and estimates the probability distribution of the material quality using a simulation optimization technique known as optimal computing budget allocation. The latter optimizes the feeding portfolio of the material allocation into the production line according to the customer's order specification. This study develops a virtual material quality investigation (VMQI) system considering the hybrid strategy and including four modules. An empirical study of a solar cell manufacturer in Taiwan validates the proposed VMQI system. The results show that the VMQI system improves the solution quality by at least 30% and potentially reduces the production cost by 19.8%.

Advanced golden jackal optimization for solving the constrained integer stochastic optimization problems

Constrained integer stochastic optimization problems (CISOP) are optimization problems where the cost function is stochastic and the constraints are deterministic. Solving the CISOP using conventional optimization techniques is time-consuming when the design space is huge. Ordinal optimization offers an efficient technique suitable for solving the CISOP. In this paper, an approach that uses golden jackal optimization assisted by ordinal optimization (GJOO) is developed for resolving the CISOP in a relatively short time. The GJOO is composed of three phases: metamodel, global search, and ranking and selection. At first, the polynomial chaos expansion is used as a metamodel to rapidly assess a solution. Next, advanced golden jackal optimization is adopted to determine N excellent solutions from the entire design space. At last, the modified optimal computing budget allocation is adopted to determine a distinguished solution from the N excellent solutions. The GJOO is utilized to the shipping/receiving docks optimization problem of a container freight station in air cargo. The performances of the GJOO are compared with those of five meta-heuristic methods. Empirical results demonstrate the efficiency and robustness of the GJOO algorithm.

Strategy Optimization for Range Gate Pull-Off Track-Deception Jamming Under Black-Box Circumstance

In this paper, we study the strategy optimization problem of black-box range gate pull-off (RGPO) jamming. In the black-box RGPO jamming, the jammer does not have extensive knowledge about the tracking model of the threat radar, which makes it difficult to accurately estimate the performance of candidate jamming strategies. To address the issue, this paper proposes a multi-mode black-box RGPO jamming method, which uses a set of local elemental simulation models to cover the possible tracking model of the threat radar, and the overall performance estimate of the candidate jamming strategies are obtained by a certain combination of the sampling results from the local elemental simulation models. To obtain the desired RGPO jamming strategy, a particle swarm optimization with optimal computing budget allocation scheme (PSO-OCBA) based multi-mode black-box RGPO jamming strategy optimization algorithm is proposed. In addition, we construct several most widely used tracking problems as the benchmark problems to test the performance of the proposed method. Experimental results demonstrate that the proposed method is highly competitive to deal with the strategy optimization problem of the black-box RGPO jamming.

A Stochastic Simulation Optimization-Based Range Gate Pull-Off Jamming Method

Range gate pull-off (RGPO) jamming is an electronic countermeasure widely used to fool radar tracking systems. Nevertheless, the research on its strategy optimization has only been tepid. Optimization model, appropriate performance metrics, as well as efficient algorithms are required to further the research in this field. The algebraic description for the objective function of the optimization of the RGPO jamming strategy is difficult to obtain, and the jamming results are not deterministic under the influence of the input noise. To address these issues, this paper models the generation of the RGPO jamming strategy as a stochastic simulation optimization (SSO) problem, and proposes an optimization algorithm of the RGPO jamming strategy with the help of SSO technologies. We propose the committee based active learning (CAL) assisted optimal computing budget allocation based particle swarm optimization (CALPSO-OCBA) to alleviate the competition between solution space search and candidate solution performance evaluation by embedding CAL into PSO-OCBA. To improve the feasibility of the proposed algorithm, a scoring scheme that does not rely on the internal knowledge of the radar tracking system (i.e., tracking model, tracking method and tracking parameters) is designed. In addition, we use four most widely used tracking problems as the benchmarks for testing the proposed optimization algorithm of the RGPO jamming strategy. Experimental results demonstrate that the proposed algorithm is highly competitive in solving the optimization problem of the RGPO jamming strategy.

Convergence rate analysis for optimal computing budget allocation algorithms

Ordinal optimization (OO) is a widely-studied technique for optimizing discrete-event dynamic systems (DEDS). It evaluates the performance of the system designs in a finite set by sampling and aims to correctly make ordinal comparison of the designs. A well-known method in OO is the optimal computing budget allocation (OCBA). It builds the optimality conditions for the number of samples allocated to each design, and the sample allocation that satisfies the optimality conditions is shown to asymptotically maximize the probability of correct selection for the best design. In this paper, we investigate two popular OCBA algorithms. With known variances for samples of each design, we characterize their convergence rates with respect to different performance measures. We first demonstrate that the two OCBA algorithms achieve the optimal convergence rate under measures of probability of correct selection and expected opportunity cost. It fills the void of convergence analysis for OCBA algorithms. Next, we extend our analysis to the measure of cumulative regret, a main measure studied in the field of machine learning. We show that with minor modification, the two OCBA algorithms can reach the optimal convergence rate under cumulative regret. It indicates the potential of broader use of algorithms designed based on the OCBA optimality conditions.

Two-Stage Genetic Algorithm for Scheduling Stochastic Unrelated Parallel Machines in a Just-in-Time Manufacturing Context

This paper considers a stochastic parallel machine scheduling problem in a just-in-time manufacturing context, in which its processing time can be described by a gamma or log-normal distribution. In order to obtain a high-performance schedule in a reasonable time, this work proposes a two-stage genetic algorithm with optimal computing budget allocation (OCBA) and improved Monte-Carlo Policy Evaluation (MCPE). In it, a genetic algorithm is selected as a main optimizer. An OCBA-based approach is developed to improve search efficiency, which is designed for two scenarios in a just-in-time manufacturing context. Different from most prior OCBA studies, this work considers that the stochastic processing time of jobs does not obey normal distribution. It extends the application area of OCBA by laying a theoretical foundation. A parameter control scheme based on MCPE is proposed, which aims to balance the global and local search in GA. To further enhance the efficiency and effectiveness of the proposed method, a two-stage framework is constructed. In the first stage, the performance is estimated roughly aiming at locating satisfactory solution regions. In the second stage, OCBA is incorporated to provide the reliable evaluation of excellent individuals. The theoretic interpretation of the proposed OCBA, and the convergence analysis results of the proposed method are presented. Various simulation results with benchmark and randomly generated cases validate that the proposed algorithm is more efficient and effective than several existing optimization algorithms. Note to Practitioners—A parallel machine scheduling problem under stochastic processing time is usually solved via meta-heuristic algorithms. However, their computational efficiency requires substantial improvement, especially for a stochastic optimization case that requires Monte Carlo sampling to estimate the actual objective function values in a precise manner. Most of them are parameter-sensitive, and choosing their proper parameters is highly challenging. For the first thorny issue, we develop an OCBA-based approach for determining the optimal numbers of simulations according to both prior knowledge and simulation results. In order to select proper control parameters of the proposed algorithm iteratively, we introduce a parameter control scheme based on MCPE. The combination of a meta-heuristic algorithm, OCBA and MCPE makes it possible to find high-quality solutions for the concerned scheduling problems in a short time. Theoretic analysis and numerical simulation results suggest that the proposed framework is valid and efficient. Hence, it can be readily applicable to practical systems, e.g., semiconductor manufacturing.

A comparison between the OCBA and the KN selection procedures for maximizing the probability of correct selection

Selecting a system or a subset of systems that have the best performance among many alternative systems is an important area of research. All efforts are paid to do this selection with a high probability of correct selection [Formula: see text]. In this paper, we compare the performance of two popular procedures used to select the best systems, namely, the method of Kim and Nelson [Formula: see text] which is considered as a ranking and selection procedure, and the Optimal Computing Budget Allocation [Formula: see text] procedure. Both of these procedures determine the number of samples for each system that are needed to achieve the maximum [Formula: see text]. Recently, the [Formula: see text] has been developed in order to be able to approximate the value of [Formula: see text], so both procedures approximate the value of [Formula: see text]. To do the comparison, we implement the two methods on two examples; one is a generic example and the other one involves a management of inventory model. The two examples assure that the [Formula: see text] method always outperforms the [Formula: see text] method.

Ranking and selection for pairwise comparison

AbstractIn many real‐world applications, designs can only be evaluated pairwise, relative to each other. Nevertheless, in the simulation literature, almost all the ranking and selection procedures are developed based on the individual performances of each design. This research considers the statistical ranking and selection problem when the design performance can only be simulated pairwise. We formulate this new problem using the optimal computing budget allocation approach and derive the asymptotic optimality condition based on some approximations. The numerical study indicates that our approach can reduce the number of simulations required to confidently identify the best design.

Optimizing resource allocation in service systems via simulation: A Bayesian formulation

The service sector has become increasingly important in today's economy. To meet the rising expectation of high‐quality services, efficiently allocating resources is vital for service systems to balance service qualities with costs. In particular, this paper focuses on a class of resource allocation problems where the service‐level objective and constraints are in the form of probabilistic measures. Further, process complexity and system dynamics in service systems often render their performance evaluation and optimization challenging and relying on simulation models. To this end, we propose a generalized resource allocation model with probabilistic measures, and subsequently, develop an optimal computing budget allocation (OCBA) formulation to select the optimal solution subject to random noises in simulation. The OCBA formulation minimizes the expected opportunity cost that penalizes based on the quality of the selected solution. Further, the formulation takes a Bayesian approach to consider the prior knowledge and potential performance correlations on candidate solutions. Then, the asymptotic optimality conditions of the formulation are derived, and an iterative algorithm is developed accordingly. Numerical experiments and a case study inspired by a real‐world problem in a hospital emergency department demonstrate the effectiveness of the proposed algorithm for solving the resource allocation problem via simulation.

Learning-Based Grey Wolf Optimizer for Stochastic Flexible Job Shop Scheduling

This work considers a stochastic flexible job shop scheduling with limited extra resources and machine-dependent setup time in a semiconductor manufacturing environment, which is an NP-hard problem. In order to obtain its reliable and high-performance schedule in a reasonable time, a learning-based grey wolf optimizer is proposed. In it, an optimal computing budget allocation-based approach, which is designed for two scenarios from real manufacturing environments, is proposed to intelligently allocate computing budget and improve search efficiency. It extends the application area of optimal computing budget allocation by laying a theoretic foundation. Besides, to obtain proper control parameters iteratively, a reinforcement learning algorithm with a newly designed delay update strategy is used to build a parameter tuning scheme of a grey wolf optimizer. The scheme acts as a guide for balancing global and local search, thereby enhancing effectiveness of the proposed algorithm. The theoretic interpretation of the developed optimal computing budget allocation-based approach and the convergence analysis results of the proposed algorithm are presented. Various experiments with benchmarks and randomly generated cases are performed to compare it with several updated algorithms. The results shows its superiority over them. Note to Practitioners—Meta-heuristic are often deployed to solve semiconductor manufacturing scheduling problems. However, they face to two thorny issues when they face stochastic manufacturing environments. 1) their computational efficiency is quite low, thus requiring substantial improvement, since a stochastic optimization problem requires Monte Carlo sampling to estimate the actual objective function values in a precise manner; and 2) most of them are parameter-sensitive, and choosing their proper parameters is highly challenging in such environments. To address the first issue, we develop an optimal computing budget allocation-based method for deciding the optimal numbers of sampling times based on both prior knowledge and simulation results. To address the second one, we propose a reinforcement learning algorithm to self-adjust the parameters of our proposed method called Learning-based Grey Wolf Optimizer. In addition, we design a delay update strategy to enhance its robustness, and thus, a feasible and high-quality schedule can be founded in a short time for real-time scheduling problems. Theoretic proofs and experimental results show that the proposed method is effective and efficient. Consequently, it can be readily applicable to practical semiconductor manufacturing systems.

Managing hospital inpatient beds under clustered overflow configuration

Inpatient beds represent one of the most critical resources in hospitals, of which the availability has been under increasing pressure in China. Such beds are usually to be either used exclusively (“dedicated”) by each department or shared (“pooled”) among departments. This paper considers a generalized bed configuration known as the clustered overflow configuration. The departments are partitioned and managed as clusters. Each department has its dedicated beds and can also admit patients to overflowed beds shared among the departments in the same cluster. A mixed-integer stochastic programming model is developed to optimize the partition and bed-allocation decisions. The objective is to minimize the weighted total cost of rejecting patients, holding patients waiting, nursing cost, and partitioning cost. A simulation-based metaheuristic approach (SMA) is proposed to solve the problem. A niching genetic algorithm (NGA) framework is first proposed to optimize the partitions, and then each partition is evaluated by optimizing the underlying bed-allocation plan through adaptive hyperbox algorithm-based local search (AHA-LS). In AHA-LS, two speeding mechanisms are proposed to effectively identify promising partitions and discard the worst ones. One is an original sequential simulation budget allocation (SSBA) mechanism to sequentially allocate the simulation iteration to evaluate the bed allocation decisions for a given partition; the other is optimal computing budget allocation (OCBA) to allocate the simulation budget to evaluate the bed-allocation plans. The elite clusters form a cluster pool, based on which a set covering model is proposed and solved to obtain a better solution. Case studies are conducted based on real data collected from a public hospital in Shanghai, China. The numerical results collectively demonstrate the applicability and efficiency of the proposed method. Sensitivity analyses are also performed to gain managerial insights.

A four‐stage yield optimization technique for analog integrated circuits using optimal computing budget allocation and evolutionary algorithms

A four‐stage yield optimization technique for analog integrated circuits using optimal computing budget allocation and evolutionary algorithms

An Efficient Simulation-Based Policy Improvement with Optimal Computing Budget Allocation Based on Accumulated Samples

Markov decision processes (MDPs) are widely used to model stochastic systems to deduce optimal decision-making policies. As the transition probabilities are usually unknown in MDPs, simulation-based policy improvement (SBPI) using a base policy to derive optimal policies when the state transition probabilities are unknown is suggested. However, estimating the Q-value of each action to determine the best action in each state requires many simulations, which results in efficiency problems for SBPI. In this study, we propose a method to improve the overall efficiency of SBPI using optimal computing budget allocation (OCBA) based on accumulated samples. Previous works have mainly focused on improving SBPI efficiency for a single state and without using the previous simulation samples. In contrast, the proposed method improves the overall efficiency until an optimal policy can be found in consideration of the state traversal property of the SBPI. The proposed method accumulates simulation samples across states to estimate the unknown transition probabilities. These probabilities are then used to estimate the mean and variance of the Q-value for each action, which allows the OCBA to allocate the simulation budget efficiently to find the best action in each state. As the SBPI traverses the state, the accumulated samples allow appropriate allocation of OCBA; thus, the optimal policy can be obtained with a lower budget. The experimental results demonstrate the improved efficiency of the proposed method compared to previous works.

A Simulation-Based Metaheuristic Approach to Integrated Scheduling of Seedling Production

Seedling production is important to modern agriculture for its economic value in land utilization and yield promotion. Three crucial decisions for seedling production are new order acceptance, backlogged order fulfillment, and growth rate control. The first decision is made in an on-line fashion whenever a new order arrives, whereas the subsequent two decisions are made periodically. Given the interplay between the three operations and requirements on the heterogeneous frequency of the decisions, many analytical methods lack sufficient flexibility to deal with the problem and difficult to apply in practice. In this letter, we propose a simulation-based metaheuristic optimization approach to identify the appropriate policy for the above decisions, including a fine-grained simulation model for a representative seedling production process, heuristic decision rules on each of the decisions, and a particle swarm optimization algorithm embeds an optimal computing budget allocation scheme to explore the rules combination space efficiently. Through numerical experiments, we justify the viability of our metaheuristic algorithm; show the superiority of our backlog order fulfillment rules over two benchmark sequential dispatching rules; also demonstrate the economic benefit to periodically regulate the production rate rather than keep in invariant rate. Our work presents a novel application of simulation optimization to smart seedling production operations management.

Dynamic Intra-Cell Repositioning in Free-Floating Bike-Sharing Systems Using Approximate Dynamic Programming

In bike-sharing systems, the spatiotemporal imbalance of bike flows leads to shortages of bikes at some locations and overages at some others, depending on the time of the day, resulting in user dissatisfaction. Repositioning needs to be performed timely to deal with the spatiotemporal imbalance and to meet user demand in time. In this paper, we study the dynamic intra-cell repositioning of bikes by a single mover in free-floating bike-sharing systems. Considering that users can drop off bikes almost anywhere in free-floating systems, we study the simultaneous reposition of bikes among gathering points and collection of bikes scattered along the paths between gathering points under stochastic demands at both the gathering points and along the paths. We formulate the problem as a Markov decision process (MDP), design a policy function approximation (PFA) algorithm, and apply the optimal computing budget allocation method (OCBA) to search for the optimal policy parameters. We perform a comprehensive numerical study using test instances constructed based on the real data set of a major free-floating bike-sharing company in China, which demonstrates the outperformance of the proposed PFA policy against the benchmark policies and the practical implications on the value of repositioning and the impact of bike scatteredness.