Optimal Computing Budget Allocation Research Articles

Bat algorithm assisted by ordinal optimization for solving discrete probabilistic bicriteria optimization problems

The discrete probabilistic bicriteria optimization problem (DPBOP) is a discrete optimization problem with probabilistic criteria which should be optimized simultaneously. The DPBOP belongs to a class of NP-hard problems because the computing time increases much faster when the size of the solution space increases. To solve the DPBOP efficiently, an algorithm that used bat algorithm (BA) assisted by ordinal optimization (OO), abbreviated as BAOO, is proposed to determine an outstanding solution within an acceptable time. The BAOO algorithm comprises three parts, surrogate model, exploration and exploitation. In surrogate model, the support vector regression is utilized as a fitness evaluation of a solution. In exploration, an amended bat algorithm is adopted to select N superior solutions from the whole solution space. In exploitation, an intensified optimal computing budget allocation scheme is adopted to decide an outstanding solution from the N superior solutions. The above three parts substantially decrease the required computing overhead of DPBOP. Finally, the BAOO algorithm is applied to a facility-sizing optimization problem in factory, which is formulated as a DPBOP. Three different size problems are considered as test examples. The BAOO algorithm is compared with three general optimization methods, particle swarm optimization, genetic algorithm and evolutionary strategy. Experimental results illustrate that the BAOO algorithm yields an outstanding solution with a higher quality and efficiency than three general optimization methods.

Operational decision making for a referral coordination alliance- When should patients be referred and where should they be referred to?

In China, due to lack of clear regulation on care pathway of patients, it is commonly observed that the system experiences substantial utilization imbalance. One way to address this challenge is through creating healthcare alliances. Among the alliance, patients can be referred from high utilized hospitals to low utilized ones for services that can be provided in both types of hospitals with similar service qualities. Such an alliance system, usually includes one upper level high utilized hospital (ULH) (e.g. a Comprehensive Hospital) and several lower level hospital (LLH) that are low utilized (e.g. Community Hospitals). The alliance hopes to reduce waiting time of the system, especially the waiting time in the high utilized hospital. As a result, the utilization of the low utilized hospitals will be improved. Nevertheless, it remains unclear how to control the referral decision process. In this paper, we investigate when patients at the ULH will need to be referred to the LLH and to which LLH they should be referred to. Firstly, we focus our attention on an easy-to-implement threshold policy for the ULH for making the decision whether to referral patients. Then, we analyze five different selection strategies (Random Transfer, Maximum Number of Beds Available, Minimum Number of Beds Available, Maximum Available Beds Rate Status, and Minimum Available Beds Rate Status) to determine the LLH to which the patient is referred to. Simulation experiments are performed to make these analyses. Opposite to the intuition that it is best to send patients to the LLH with the most available beds, the results show that sending patients to the LLH with the lowest available bed rate (Minimum Available Beds Rate Status) is the best strategy. This is because that the ULH's waiting time is more important in the objective, sending patients to an LLH that its current available resources are more likely to be occupied by its own normal patients later, will help improve the overall probability that the ULH successfully refer patients out in the long run. Secondly, we also developed a PSO-OCBA method which integrates the idea from Optimal Computing Budget Allocation (OCBA) into the searching Particle Swarm Optimization (PSO) algorithm for generating best control threshold. We find that if we can adaptively achieve the optimal K with the different selection strategies, the difference of the performance between the five strategies will be highly reduced. Our research is the first work that applies system engineering to the real-time referral decision problem between one ULH and several LLHs. It provides a novel perspective of patient referral control studies in the coordination alliance operation literature.

TD-OCBA: Optimal computing budget allocation and time dilation for simulation optimization of manufacturing systems

Discrete event simulation has been widely applied to study the behavior of stochastic manufacturing systems. This is due to the fact that manufacturing systems are usually too complex to obtain a closed-form analytical model that can accurately predict their performance. This becomes particularly critical when the optimization of these systems is of concern. In fact, Simulation optimization techniques are employed to identify the manufacturing system configuration which can maximize the expected system performance when this can only be estimated by running a simulator. In this article, we look into simulation-based optimization when a finite number of solutions are available and we have to identify the best. In particular, we propose, for the first time, the integration of Optimal Computing Budget Allocation (OCBA), which is based on independent measures from each simulation experiment, and Time Dilation (TD), which is a single-run simulation optimization algorithm. As a result, the optimization problem is solved when only one experiment of the system is performed by changing the “speed” of the simulation at each configuration in order to control the computational effort. The challenge is how to iteratively select such a speed. We solve this problem by proposing TD-OCBA, which integrates TD and OCBA while relying on standardized time series variance estimators. Numerical experiments have been conducted to study the performance of the algorithm when the response is generated from a time series. This provides the possibility to test the robustness of TD-OCBA. Comparison between TD-OCBA and the original TD method was performed by simulating a job shop system reported in the literature. Finally, an application involving semiconductors remote diagnostics is used to compare the TD-OCBA method and what is known as the equal allocation method.

Optimisation for quay crane scheduling problem under uncertainty using PSO and OCBA

This paper addresses the quay crane scheduling problem (QCSP) under uncertain conditions at container terminals. Variations in container volume, arrival time, equipment functionality and weather conditions create significant uncertainties when scheduling loading and unloading tasks. In order to maintain the service level of the port under various conditions, port operator urgently need to execute a robust schedule. In this paper, a stochastic programming model is formulated to minimise the makespan of quay crane service, using a particle swarm optimisation (PSO) algorithm integrated with optimal computing budget allocation (OCBA) to improve computational efficiency. Numerical experiments show that the applied algorithm performs well under uncertainty.

Top-κ selection with pairwise comparisons

In this work, we consider active, pairwise top-κ selection, the problem of identifying the highest quality subset of given size from a set of alternatives, based on the information collected from noisy, sequentially chosen pairwise comparisons. We adapt two well known Bayesian sequential sampling techniques, the Knowledge Gradient policy and the Optimal Computing Budget Allocation framework for the pairwise setting and compare their performance on a range of empirical tests. We demonstrate that these methods are able to match or outperform the current state of the art racing algorithm approach.

The Local Time Method for Targeting and Selection

We propose a framework for targeting and selection (T&S), a new problem class in simulation optimization where the objective is to select a simulation alternative whose mean performance matches a prespecified target as closely as possible. T&S resembles the more well-known problem of ranking and selection but presents unexpected challenges: for example, a one-step look-ahead method may produce statistically inconsistent estimates of the values, even under very standard normality assumptions. We create a new and fundamentally different approach, based on a Brownian local time model, that exhibits characteristics of two widely studied methodologies, namely expected value of information and optimal computing budget allocation. We characterize the asymptotic sampling rates of this method and relate them to the convergence rates of metrics of interest. The local time method outperforms benchmarks in experiments, including problems where the modeling assumptions of T&S are violated. The online appendix is available at https://doi.org/10.1287/opre.2018.1731 .

Optimal Computing Budget Allocation to Select the Nondominated Systems—A Large Deviations Perspective

We consider the optimal computing budget allocation problem to select the nondominated systems on finite sets under a stochastic multi-objective ranking and selection setting. This problem has been addressed in the settings of correct selection guarantee when all the systems have normally distributed objectives with no correlation within and between solutions. We revisit this problem from a large deviation perspective and present a mathematically robust formulation that maximizes the lower bound of the rate function of the probability of false selection ( $P(\text{FS})$ ) defined as the probability of not identifying the true Pareto set. The proposed formulation allows general distributions and explicitly characterizes the sampling correlations across performance measures. Three budget allocation strategies are proposed. One of the approaches is guaranteed to attain the global optimum of the lower bound of the rate function but has high computational cost. Therefore, a heuristic to approximate the global optimal strategy is proposed to save computational resources. Finally, for the case of normally distributed objectives, a computationally efficient procedure is proposed, which adopts an iterative algorithm to find the optimal budget allocation. Numerical experiments illustrate the significant improvements of the proposed strategies over others in the existing literature in terms of the rate function of $P(\text{FS})$ .

Gradient-Based Myopic Allocation Policy: An Efficient Sampling Procedure in a Low-Confidence Scenario

In this note, we study a simulation optimization problem of selecting the alternative with the best performance from a finite set, or a so-called ranking and selection problem, in a special low-confidence scenario. The most popular sampling allocation procedures in ranking and selection do not perform well in this scenario, because they all ignore certain induced correlations that significantly affect the probability of correct selection in this scenario. We propose a gradient-based myopic allocation policy that takes the induced correlations into account, reflecting a tradeoff between the induced correlation and the two factors (mean-variance) found in the optimal computing budget allocation formula. Numerical experiments substantiate the efficiency of the new procedure in the low-confidence scenario.

A novel optimal replication allocation strategy for particle swarm optimization algorithms applied to simulation optimization problem

This study proposes a simulation optimization algorithm, called optimal replication allocation strategy (ORAS), for particle swarm optimization (PSO) algorithms in simulation models with high computing cost in large design spaces. In this study, the PSO is employed to explore and exploit near-optimal or optimal solution in the design space. Given the uncertainties in real-word applications, a simulation model is constructed to evaluate the performance of each design alternative. Optimal computing budget allocation (OCBA), a state-of-the-art resampling method, is combined with metaheuristic principles to improve the accuracy of estimating best solutions and enhancing efficiency by intelligently allocating the number of replications. However, the solution space is nonlinear or multimodal; that is, various local or global solutions exist. In OCBA, the probability of correct selection (P(CS)) in the currect best solution serves as an important measurement. P(CS) refers to the probability that the “best” of k populations is selected according to some specified criteria of best. OCBA can halt allocation when P(CS) reaches higher than the desired value, i.e., P(CS)*. The multimodal solution space features a high probability of reaching a low P(CS) as many solutions perform closely to the current best of each generation. This situation indicates that P(CS) cannot achieve P(CS)*; OCBA cannot stop allocation, and additional computational cost may be wasted. In this study, we redefine and modify P(CS). The new version is P(CSE), which considers calculation of global best, called the super individual, instead of current best solution within a confidence level. The proposed ORAS can provide an asymptotically optimal allocation rule for combining with population metaheuristics based on P(CSE). We apply ORAS using an original particle swarm optimization (PSO) and two variants of PSO to address stochastic buffer allocation problem and stochastic function optimization problem compared with several state-of-the-art technologies from literature. The resulting ORAS with three PSOs is an effective procedure as it intelligently utilizes limited computing resources. Numerical tests indicate that ORAS increases P(CSE) in each generation and subsequently enhances the efficiency of PSO algorithms.

A new strategy for selecting good enough designs using optimal computing budget allocation

In this paper, we consider the problem of selecting a subset of good designs from a finite set of simulated designs. Instead of selecting exactly the top r(r > 1) designs from k alternatives, our approach seeks to select r good enough designs which are defined as designs from the set of top g designs (r ≤ g < k) . By doing so, the selection efficiency could be improved significantly, and the performances of the selected designs remain in an acceptable range. Using the optimal computing budget allocation framework, we formulate the problem as that of maximizing the probability of correctly selecting r good enough designs subject to a simulation budget constraint. Based on two different approximate measures of the probability of correct selection, we derive two asymptotically optimal selection procedures for selecting a good enough subset. Some computational experiments are conducted to compare the performance of the proposed allocation rules with other methods in the literature.

Simulation-based optimization approach for simultaneous scheduling of vehicles and machines with processing time uncertainty in FMS

Many stochastic factors, such as vehicle congestion, deadlock or conflict, or stochastic processing time have significant effects on performance in scheduling problem in flexible manufacturing system (FMS). This paper proposed a simulation-based optimization, L-GAOCBA, to address the simultaneous scheduling of vehicles and machines in FMS. The simulation model is constructed to evaluate the performance of scheduling decision, and includes stochastic elements, such as vehicle congestion, deadlock, and uncertain processing time. Genetic algorithm (GA) combined with local search, L-GA, plays important role in exploring the good design alternative based on simulation output. Optimal computing budget allocation (OCBA) embedded with L-GA is used to allocate the number of replications for reducing simulation replications. The design of experiments is used to analyze and set the parameters of L-GA and OCBA. This study shows that L-GAOCBA is superior for enhancing solution quality and search efficiency.

Integrating operational decisions into the planning of one-way vehicle-sharing systems under uncertainty

This study proposes a systematic approach for planning and operating a one-way vehicle-sharing system (VSS) under demand uncertainty. It investigates the distribution of parking spaces and vehicles considering stochastic demand and interactions with the major operational decisions, namely vehicle redistribution activities. An optimization model is formulated that aims to determine the best deployment strategy for minimizing overall cost while achieving a certain level of service (LoS). Then, a simulation-based solution approach based on a discrete-event simulator (DES), Particle Swarm Optimization (PSO), and Optimal Computing Budget Allocation (OCBA) is devised to solve the mathematical model. The methodology is then applied to a car-sharing system in Singapore. Results demonstrate that considering rebalancing activities is imperative in making deployment strategies. The case study also provides managerial insights regarding designing and operating one-way VSS.

A Combined Statistical Selection Procedure Measured by the Expected Opportunity Cost

Selecting one of the best systems among finite but huge stochastic alternative systems is very important area of research since it has many applications in real life such as manufacturing systems, supply chain management and communication networks. Simulation is the main approach to estimate the performance values of these alternative systems. We propose a selection procedure which consists of two phases. In phase one, the ordinal optimization ( $${\textit{OO}}$$ ) technique is used to select a set K of k systems randomly. The probability that this set contains the actual best system can be measured using order statistics. In the second step of this phase, the optimal computing budget allocation ( $${\textit{OCBA}}_m$$ ) is used to select a smaller set of m systems from the set K. It is assumed that the computational budget is limited, the aim of $${\textit{OCBA}}_m$$ is to allocate these computational budget on the different systems to maximize the probability of correct selection P(CS). It gives the alternatives that have more influence on the solution, more computational budget; these two procedures are performed repeatedly until the available budget is consumed. In the second phase, the ranking and selection ( $$ R \& S$$ ) approach is applied on the smaller subset in order to select the best system. The algorithm is implemented on a generic example, and the expected opportunity cost is utilized to measure the potentially of incorrect selection. The numerical results show that the algorithm indeed selects a good enough system.

Embedding Advanced Harmony Search in Ordinal Optimization to Maximize Throughput Rate of Flow Line

Flow line systems are production systems in which successive operations are performed on a product in a manner so that it moves through the factory in a certain direction. This work firstly formulates a flow line system as an integer-ordered inequality-constrained simulation–optimization problem and present a stochastic simulation procedure to estimate the throughput rate. The mathematical formulation and simulated procedure can be used for any distribution of processing rate and can be applied to high-dimensional problems. An approach that embeds advanced harmony search (AHS) in ordinal optimization (OO), abbreviated as AHSOO, is developed to find a near-optimal design of the flow line system to maximize the throughput rate. The proposed approach comprises three levels, which are meta-modeling, diversification and intensification. A radial basis function network is a meta-model to approximate the performance of a design. The proposed approach integrates the AHS approach for diversification with improved optimal computing budget allocation (IOCBA) for intensification. AHS favorably explores the solution space initially and moves toward exploiting good solutions close to the end. The IOCBA maximized the overall simulation efficiency for finding an optimal solution. The proposed AHSOO is tested on three examples. In the moderately sized example, simulation results reveal that the average best-so-far performances that were determined using PSO, GA and ES were 6.12, 9.65 and 8.53% less than that obtained using AHSOO—even after the former took more than 50 times the CPU time that was consumed by AHSOO upon completion. Analytical results reveal that the proposed method yields designs of much higher quality with a much higher computing efficiency than the seven competing methods.

Optimal computing budget allocation to the differential evolution algorithm for large-scale portfolio optimization

Differential evolution (DE) is one of the popular techniques in large-scale portfolio optimization, which is noticed for its applications in the problems that are non-convex, non-continuous, non-differentiable, and so on. This technique suffers specific short-comings, for example, unstable convergence in the final solution, trapped in local optimum, and demand for high number of replications. Optimal Computing Budget Allocation (OCBA) technique gives an efficient way to reach the global optimum by optimally assigning computing resource among designs. The integration of DE and OCBA gives better performance than DE alone in terms of convergence rate and the attained global optimum. The ordering of the integration also plays a vital role, that is, the strategy of first applying DE before OCBA outperforms the reversely ordered one. Both integration strategies are essentially the improved DE algorithms for large-scale portfolio optimization. In addition to numerical tests, empirical analysis of 100 stocks in S&P500 over a 10-year period confirms the conclusions.

On parallel policies for ranking and selection problems

ABSTRACTIn this paper we develop and test experimental methodologies for selection of the best alternative among a discrete number of available treatments. We consider a scenario where a researcher sequentially decides which treatments are assigned to experimental units. This problem is particularly challenging if a single measurement of the response to a treatment is time-consuming and there is a limited time for experimentation. This time can be decreased if it is possible to perform measurements in parallel. In this work we propose and discuss asynchronous extensions of two well-known Ranking & Selection policies, namely, Optimal Computing Budget Allocation (OCBA) and Knowledge Gradient (KG) policy. Our extensions (Asynchronous Optimal Computing Budget Allocation (AOCBA) and Asynchronous Knowledge Gradient (AKG), respectively) allow for parallel asynchronous allocation of measurements. Additionally, since the standard KG method is sequential (it can only allocate one experiment at a time) we propose a parallel synchronous extension of KG policy – Synchronous Knowledge Gradient (SKG). Computer simulations of our algorithms indicate that our parallel KG-based policies (AKG, SKG) outperform the standard OCBA method as well as AOCBA, if the number of evaluated alternatives is small or the computing/experimental budget is limited. For experimentations with large budgets and big sets of alternatives, both the OCBA and AOCBA policies are more efficient.

Merging crow search into ordinal optimization for solving equality constrained simulation optimization problems

Equality-constrained simulation optimization problems (ECSOP) involve the finding of optimal solutions by simulation within a well-defined search space under deterministic equality constraints. ECSOPs belong to the class of NP-hard problems. The large search space makes them difficult to solve in a short period using conventional optimization techniques. An approach that merges the crow search (CS) into ordinal optimization (OO), abbreviated as CSOO, is developed to find a near-optimal solution to the ECSOP within a reasonable time. The proposed approach has three phases, which are surrogate model, exploration and exploitation. First, a surrogate model, based on the multivariate adaptive regression splines, is used to evaluate the fitness of a solution. Next, an enhanced crow search algorithm is used to find N excellent solutions in the search space. Finally, an intensified optimal computing budget allocation is used to find a near-optimal solution among the N excellent solutions. The proposed CSOO approach is applied to a three-stage ten-node network-type production line, and the formulated problem is an ECSOP with a large search space. The developed formulation can be used for network-type production lines with any distribution of arrivals and production times. Simulation results that are obtained using the CSOO are compared with those obtained using four competing methods Test results reveal that the proposed approach yields a near-optimal solution of much higher quality than obtained using four competing methods, and with a much higher computing efficiency.

Real options and flexibility analysis in design and management of one-way mobility on-demand systems using decision rules

This study explores the concepts of real options and flexibility analysis asan approach to address uncertain demand growth in mobility on-demand (MoD) vehicle-sharing systems, with the goal of improving expected lifecycle performance. As MoD systems are gaining popularity worldwide, they inevitably face significant uncertainty in terms of needs and customer demands. Designing, planning capacity deployment, and operating such system can be challenging, and require significant capital investments for companies and cities. Two distinct real options analysis (ROA) models are developed to evaluate and optimize flexible strategies for these systems, relying on a novel methodological approach to value flexibility based on decision rules. The decision-rule-based approach differs from standard ROA approaches used to quantify the value of flexibility in irreversible investment projects, typically based on dynamic programming. It emulates the decision-making process by capturing mathematically a triggering mechanism that determines when it is best to exercise the flexibilities embedded in the system design. Two prevalent types of MoD systems are studied in this paper as demonstration of the methodological framework: a station-based system where customers must pick up and return the vehicle at specific locations, and a free-floating system, where customers may pick up and drop the car anywhere within a certain area. A simulation-based approach is used to analyze the station-based system, which models the rebalancing operations from a micro-level perspective. The approach consists of a discrete event simulator for performance estimation, and an optimization algorithm for design space exploration that integrates a population-based search algorithm with Optimal Computing Budget Allocation (OCBA). For the free-floating system, an analytical model is developed where the decision rule is formulated into and solved using stochastic mixed integer programming (MIP). The study provides guidance to system operators on potential strategies for deploying MoD systems, considering explicitly uncertainty and flexibility as a value enhancing mechanism.

Capacity planning for mega container terminals with multi-objective and multi-fidelity simulation optimization

ABSTRACTContainer terminals play a significant role as representative logistics facilities for contemporary trades by handling outbound, inbound, and transshipment containers to and from the sea (shipping liners) and the hinterland (consignees). Capacity planning is a fundamental decision process when constructing, expanding, or renovating a container terminal to meet demand, and the outcome of this planning is typically represented in terms of configurations of resources (e.g., the numbers of quay cranes, yard cranes, and vehicles), which enables the container flows to satisfy a high service level for vessels (e.g., berth-on-arrivals). This study presents a decision-making process that optimizes the capacity planning of large-scale container terminals. Advanced simulation-based optimization algorithms, such as Multi-Objective Multi-Fidelity Optimization with Ordinal Transformation and Optimal Sampling (MO-MO2TOS), Multi-Objective Optimal Computing Budget Allocation (MOCBA), and Multi-Objective Convergent Optimization via Most-Promising-Area Stochastic Search (MO-COMPASS), were employed to formulate and optimally solve the large-scale multi-objective problem with multi-fidelity simulation models. Various simulation results are compared with one another in terms of the capacities over different resource configurations to understand the effect of various parameter settings on optimal capacity across the algorithms.

Approximately Optimal Computing Budget Allocation for Selection of the Best and Worst Designs

Ordinal optimization is an efficient technique to choose and rank various engineering designs that require time-consuming discrete-event simulations. Optimal computing budget allocation (OCBA) has been an important tool to enhance its efficiency such that the best design is selected in a timely fashion. It, however, fails to address the issue of selecting the best and worst designs efficiently. The need to select both rapidly given a fixed computing budget has arisen from many applications. This work develops a new OCBA-based approach for selecting both best and worst designs at the same time. Its theoretical foundation is laid. Our numerical results show that it can well outperform all the existing methods in terms of probability of correct selection and computational efficiency.