On the Convergence Rates of Expected Improvement Methods

We consider the optimal computing budget allocation (OCBA) problem where the simulated designs are correlated. The exact optimal allocation is presented for two designs, and an approximation proposed for more than two designs. Numerical experiments for several examples compare the approximation with some other allocation procedures. Results on convergence rates and the non-Gaussian setting are also discussed.

Convergence rate analysis for optimal computing budget allocation algorithms

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.

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.

This chapter reviews the problem of selecting the best of a finite set of alternatives, where best is defined with respect to the highest mean performance, and where the performance is uncertain but may be estimated with simulation. This problem has been explored from several perspectives, including statistical ranking and selection, multiple comparisons, and stochastic optimization. Approaches taken in the literature include frequentist statistics, Bayesian statistics, related heuristics, and asymptotic convergence in probability. This chapter presents algorithms that are derived from Bayesian and related conceptual frameworks to provide empirically effective performance for the ranking and selection problem. In particular, we motivate the optimal computing budget allocation (OCBA) algorithm and expected value of information (EVI) approaches, give example algorithms, and provide pointers to the literature for detailed derivations and extensions of these approaches.KeywordsAllocation RuleCorrect SelectionMultiple AlternativeLinear LossEqual AllocationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Particle Swarm Optimization (PSO) is a population-based algorithm designed to find good solutions to optimization problems. Its characteristics have encouraged its adoption to tackle a variety of problems in different fields. However, when such problems are subject to noise, the performance of PSO suffers an immediate deterioration which demands the incorporation of noise handling mechanisms. One such mechanism comprises resampling methods, which re-evaluate the solutions multiple times in order to estimate their true objective values. The state-of-the-art integration with which the best results have been obtained utilizes the resampling method named Optimal Computing Budget Allocation (OCBA). This resampling method starts by estimating the objective values of all the solutions via Equal Resampling (ER), and then sequentially allocating further re-evaluations to the estimated best solutions. However, after having a first estimate via ER, we question the importance of the additional efforts to correctly select the true best solutions when a good-enough and accurate one can be selected. In this paper, we propose a new PSO algorithm based on ER in which the additional evaluations are allocated at once to the estimated best solutions, thus skipping the complexity of using OCBA. Experiments on 20 large-scale benchmark functions subject to different levels of noise show that the proposed algorithm produces similar results to PSO with OCBA in most cases.

The dynamics of many systems nowadays follow not only physical laws but also man-made rules. These systems are known as discrete event dynamic systems and their performances can be accurately evaluated only through simulations. Existing studies on simulation-based optimization (SBO) usually assume deterministic simulation time for each replication. However, in many applications such as evacuation, smoke detection, and territory exploration, the simulation time is stochastic due to the randomness in the system behavior. We consider the computing budget allocation for SBO's with stochastic simulation time in this paper, which has not been addressed in existing literatures to the author's best knowledge. We make the following major contribution. The relationship between simulation time and performance estimation accuracy is quantified. It is shown that when the asymptotic performance is of interest only the mean value of individual simulation time matters. Then based on the existing optimal computing budget allocation (OCBA) method for deterministic simulation time we develop OCBA for stochastic simulation time (OCBAS), and show that OCBAS is asymptotically optimal. Numerical experiments are used to discuss the impact of the variance of simulation time, the impact of correlated simulation time and performance estimation, and to demonstrate the performance of OCBAS on a smoke detection problem in wireless sensor network. The numerical results also show that OCBA for deterministic simulation time is robust even when the simulation time is stochastic.

Stochastic point location (SPL) is to search for a target point on the line in stochastic environment. An SPL solver can be described as a Learning Machine (LM) attempting to locate a target point on a line. By using the prompts from stochastic environment, possibly erroneous, the LM moves along the line yielding updated estimates to approximate the target point. This paper proposes an SPL algorithm based on Optimal Computing Budget Allocation (OCBA), named as SPL-OCBA, which employs OCBA and the historical sample information to guide to the location of a target point in stationary and stochastic environment. The proposed algorithm partitions or combines the subintervals of the target line adaptively. Then, OCBA considers such subintervals as its designs and allocates the sample budget for them based on the historical data, thereby resulting in a new method. Extensive experiments show that the newly proposed algorithm is significantly more efficient than the existing ones.

In this paper, a simulation-based optimization approach, named NHOCBA, for a typical resource allocation problem is presented. The hybrid algorithm based on neighborhood algorithm is applied to explore toward optimal direction in design space. For increasing efficiency, an optimal computing budget allocation (OCBA) is adopted to compute the optimal number of replications and to provide reliable evaluation of variance. In addition, we deal with the resource allocation problem which exist multiple global optima in design space. Therefore, a trim procedure which prevents to allocate extra numbers of replication to local optima has been proposed to enhance efficiency. Then, we use confidence interval at the end of algorithm procedure to find an optimal set instead of an optimal solution from design space. Finally, we compare the NHOCBA with different algorithms by experimentation study which shows that NHOCBA approach can perform better than the other algorithms under certain conditions.

Evolutionary algorithm assisted by surrogate model in the framework of ordinal optimization and optimal computing budget allocation

Real-time planning and scheduling in a shop floor are not easy to accomplish due to the concurrent flow of various parts as well as sharing of different types of resources. Multi-pass scheduling is a well-known method for solving the aforementioned problem. Its success depends largely on selecting the best decision-making rule fast and effectively. Although many efforts have been made in the past, a way to minimize the computational load of rule evaluation and selection has yet to appear. The objective of the paper is to apply a nested partitioning (NP) method and an optimal computing budget allocation (OCBA) method to reduce the computational load without the loss of the performance of multi-pass scheduling. The experimental design and analysis was performed to validate that NP and OCBA can be successfully applied to multi-pass scheduling in order to enhance the performance of multi-pass scheduling.

A hybrid differential evolution(DE) algorithm,namely OHTDE,is proposed to solve the stochastic flow shop scheduling problem(FSSP) with limited buffers between consecutive machines.Two different criteria are considered.The first is to minimize a general earliness/tardiness cost function and the second is to minimize the total completion time.The proposed algorithm is a hybrid of DE and two techniques:the optimal computing budget allocation(OCBA) technique and hypothesis test(HT) .DE is used to execute both global and local search.OCBA is utilized to reasonably allocate a limited sampling budget for every solution,assigning more for better individuals to improve the confidence level of getting good solutions under noise environment.HT is adopted to perform a statistical comparison on solutions performances so that the repeated search on the similar region of the solution space can be avoided to some extent.Moreover,a special crossover,which is performed on some good solutions identified by OCBA and HT,is designed to enhance the capability of local search.Furthermore,the stochastic convergence property of OHTDE is analyzed by using the theory of finite Markov chain.Experimental results and comparison show the effectiveness and robustness of the proposed OHTDE.

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.

Simulation models of emergency departments (EDs) are often built based on incomplete data, for example, missing arrival times or service-time durations. The difficulty in collecting reliable and complete data can subsequently lead to invalid simulation results. To tackle this problem, we propose a simulation and optimisation method to characterise the unavailable durations of service times. Since many services in an ED are sequential and dependent on each other, this paper considers these multiple process steps cooperatively. We first use lognormal distributions to characterise the key service durations. Then we propose a new meta-heuristic approach, which combines an Improved Adaptive Genetic Algorithm (AGA) and Simulated Annealing (SA), IAGASA, to search for the optimal set of service-time distribution parameters. To address the difficulties of applying IAGASA when noise is involved in the performance measures and improve the simulation efficiency, we jointly apply IAGASA and Optimal Computing Budget Allocation (OCBA) technology. OCBA minimises the total simulation cost for achieving a desired level of probability of correctly selecting the best set of distribution parameters, which improves the search efficiency significantly. The experimental results indicate that our proposed method can find accurate estimates of service-time distribution parameters within a relatively short time.

The automated material handling system (AMHS) in semiconductor industry plays a vital role in reducing wafer cycle times and enhancing fabrication plant productivity. Vehicle allocation for the AMHS is a challenging task because of the complexity of the manufacturing process and the stochasticity introduced by the inherent variability of processing times. This situation is observed especially in 300 mm wafer fabrication plants where the AMHS comprises both interbay and intrabay systems that perform the timely deliveries. To address this issue, we use the optimal computing budget allocation (OCBA) and extend it by adding genetic algorithm (GA). Under this combined approached, the number of iterations of each alternative is determined by OCBA, and then the optimal solution in the domain of feasible solutions is found through GA. This research provides a useful reference for both scholars and practitioners seeking optimal allocation of lithographical resources and number of iterations using random parameters.