Siyang Gao

An Optimal Sample Allocation Strategy for Partition-Based Random Search

Partition-based random search (PRS) provides a class of effective algorithms for global optimization. In each iteration of a PRS algorithm, the solution space is partitioned into subsets which are randomly sampled and evaluated. One subset is then determined to be the promising subset for further partitioning. In this paper, we propose the problem of allocating samples to each subset so that the samples are utilized most efficiently. Two types of sample allocation problems are discussed, with objectives of maximizing the probability of correctly selecting the promising subset (P{CSPS}) given a sample budget and minimizing the required sample size to achieve a satisfied level of P{CSPS}, respectively. An extreme value-based prospectiveness criterion is introduced and an asymptotically optimal solution to the two types of sample allocation problems is developed. The resulting optimal sample allocation strategy (OSAS) is an effective procedure for the existing PRS algorithms by intelligently utilizing the limited computing resources. Numerical tests confirm that OSAS is capable of increasing the P{CSPS} in each iteration and subsequently improving the performance of PRS algorithms.

Efficient subset selection for the expected opportunity cost

A lot of problems in automatic control aim at seeking top designs for discrete-event systems. In many cases, these problems are most suitable to be modeled as simulation optimization problems, and a key question for solving these problems is how to efficiently and accurately select the top designs given a limited simulation budget. This paper considers the generalized problem of selecting the top m designs from a finite set of design alternatives based on simulated outputs, subject to a constraint on the total number of samples available. The quality of the selection is measured by the expected opportunity cost, which penalizes particularly bad choices more than the slightly incorrect selections and is preferred by risk-neutral practitioners and decision makers. An efficient simulation budget allocation procedure, called E O C - m , is developed for this problem. The efficiency of the proposed method is illustrated through numerical testing.

A surrogate-based metaheuristic global search method for beam angle selection in radiation treatment planning.

An important element of radiation treatment planning for cancer therapy is the selection of beam angles (out of all possible coplanar and non-coplanar angles in relation to the patient) in order to maximize the delivery of radiation to the tumor site and minimize radiation damage to nearby organs-at-risk. This category of combinatorial optimization problem is particularly difficult because direct evaluation of the quality of treatment corresponding to any proposed selection of beams requires the solution of a large-scale dose optimization problem involving many thousands of variables that represent doses delivered to volume elements (voxels) in the patient. However, if the quality of angle sets can be accurately estimated without expensive computation, a large number of angle sets can be considered, increasing the likelihood of identifying a very high quality set. Using a computationally efficient surrogate beam set evaluation procedure based on single-beam data extracted from plans employing equallyspaced beams (eplans), we have developed a global search metaheuristic process based on the nested partitions framework for this combinatorial optimization problem. The surrogate scoring mechanism allows us to assess thousands of beam set samples within a clinically acceptable time frame. Tests on difficult clinical cases demonstrate that the beam sets obtained via our method are of superior quality.

Selecting the Best Simulated Design With the Expected Opportunity Cost Bound

In many applications, we wish to select the best simulated design among a set of design alternatives. While most work in the literature evaluates the quality of a selection procedure by the probability of correct selection of the best design, the expected opportunity cost of a potentially incorrect selection is also an important and useful measure, especially when the design performance reflects economic value. In this technical note, we consider the selection problem with an expected opportunity cost constraint. Based on some approximations, we derive for the selection problem an asymptotic closed-form allocation rule, which is easy to compute and implement. The numerical testing shows that the proposed selection procedure can enhance the simulation efficiency significantly.

A Partition-based Random Search for Stochastic Constrained Optimization via Simulation

We consider the global optimization problem over finite solution space with a deterministic objective function and stochastic constraints, where noise-corrupted observations of the constraint measures are evaluated via simulation. This problem is challenging in that the solution space often lacks rich structure that can be utilized in identifying the optimal solution, and the feasibility of a solution cannot be known for certain, due to the noisy measurements of the constraints. To tackle these two issues, we adopt a partitioning scheme to explore the solution space and develop a feasibility detection procedure to detect the feasibility of the sampled solutions. A new random search method, called partition-based random search with multi-constraint feasibility detection (PRS-MFD), is proposed. It is shown that PRS-MFD converges to the set of global optima with probability one. The significantly higher efficiency of it is demonstrated by numerical experiments.

Efficient Feasibility Determination With Multiple Performance Measure Constraints

Feasibility determination has emerged as a widely applied problem in simulation optimization. It seeks to provide all the feasible designs from a finite set of design alternatives based on which the final decision can be chosen by the decision maker. In this paper, we consider the feasibility determination problem in presence of multiple performance measure constraints. The optimal solution to maximize the probability of correct feasibility determination is derived under asymptotic approximation. A corresponding sequential selection procedure is designed for implementation. The numerical testing shows that our approach can enhance the simulation efficiency significantly.

A New Budget Allocation Framework for the Expected Opportunity Cost

In this paper, we present a new budget allocation framework for the problem of selecting the best simulated design from a finite set of alternatives. The new framework is developed on the basis of general underlying distributions and a finite simulation budget. It adopts the expected opportunity cost (EOC) quality measure, which, compared to the traditional probability of correct selection (PCS) measure, penalizes a particularly bad choice more than a slightly incorrect selection, and is thus preferred by risk-neutral practitioners and decision makers. To this end, we establish a closed-form approximation of EOC to formulate the budget allocation problem and derive the corresponding optimality conditions. A sequential budget allocation algorithm is then developed for implementation. The efficiency of the proposed method is illustrated via numerical experiments. We also link the EOC and PCS-based budget allocation problems by showing that the two are asymptotically equivalent. This result explains, to some...

A new budget allocation framework for selecting top simulated designs

ABSTRACT In this article, the problem of selecting an optimal subset from a finite set of simulated designs is considered. Given the total simulation budget constraint, the selection problem aims to maximize the Probability of Correct Selection (PCS) of the top m designs. To simplify the complexity of the PCS, an approximated probability measure is developed and an asymptotically optimal solution of the resulting problem is derived. A subset selection procedure, which is easy to implement in practice, is then designed. More important, we provide some useful insights on characterizing an efficient subset selection rule and how it can be achieved by adjusting the simulation budgets allocated to all of the designs.

A Sequential Budget Allocation Framework for Simulation Optimization

Many problems in automation and manufacturing are most suitable to be modeled as simulation optimization problems. Solving these problems typically involves two efforts: one is to explore the solution space, and the other is to exploit the performance values of the sampled solutions. When the amount of computing budget is limited, we need to know how to balance these two efforts in order to obtain the best result. In this study, we derive two measures to quantify the marginal contribution of exploring the search space and exploiting the performance values. A sequential budget allocation framework is designed by keeping the two measures approximately the same at each iteration. Numerical experiments on both continuous and discrete simulation optimization problems demonstrate that our new approach can significantly enhance the computing efficiency.

Optimal computing budget allocation with input uncertainty

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.