Abstract
Stochastic simulation optimization is a powerful modeling tool for analyzing modern complex systems, such as manufacturing, supply chain, transportation, healthcare, call center and finance systems. Since conducting simulation experiments can be both economically expensive and time-consuming, a number of procedures have been developed to enhance the simulation efficiency of finding the design (solution) that possesses the optimality. This problem setting falls under the well-established branch of statics known as Ranking and Selection (R&S). Among the various R&S procedures, the procedures for subset selection problem and the stochastic constrained problem are the most commonly used in practical applications. Although the advance of computer technology has dramatically increased computational power, the selection efficiency is still a big concern especially when the total number of designs is large. In this thesis, we aim to further improve the efficiency of subset selection and stochastic constrained problems, respectively.In Chapter 2, we first consider the problem of selecting a subset of $m$ designs from a finite set of t alternative designs. We introduce a new idea to further improve the efficiency for subset selection. Instead of selecting exactly the top m (m>1) designs from t alternatives, we seek to select m good enough designs which are defined as designs from the set of top g designs (m≤g<t). 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 (OCBA) framework, we formulate the problem as that of maximizing the probability of correctly selecting m 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.
In Chapter 3, we consider the problem of selecting exactly the optimal subset (the top-m designs) from a finite set of t alternative designs. We seek to explore the potential of further improving the subset selection efficiency by incorporating the information from across the domain into quadratic regression metamodels. Under some common assumptions in most regression based approaches, we first propose an approximately optimal rule that determines the designs need to be simulated and the number of simulation replications allocated to the selected designs across the solution space. In addition, to better fulfill the assumptions used in regression based approaches and extend our proposed approach to more general cases, we divided the solution space into adjacent partitions. The underlying function can be approximately quadratic with homogeneous noise within each partition. We then propose another approximately optimal rule determining the number of simulation replications allocated to each design for both between and within each partition.
In Chapter 4, we propose an efficient procedure that addresses the R&S problem subject to stochastic constraints (the stochastic constrained problem). In order to further improve the selection efficiency, we incorporate the information from across the domain into quadratic regression metamodels for both the main objective and stochastic constraints. Similar to the setting in chapter 3, the solution space is divided into adjacent partitions to better fulfill the assumptions used for the regression metamodels. Based on the large deviations theory, we characterize the asymptotically optimal allocation rule by maximizing the rate at which the probability of false selection tends to zero.
In Chapter 5, we use both the abstract and the practical problems to test our proposed R&S procedures. The results show that our proposed approaches can dramatically improve the simulation efficiency on the typical selection examples compared to the existing approaches.
In Chapter 6, we conclude this thesis and discuss the future work and the potential of the procedures proposed in this thesis.
| Date of Award | 24 Aug 2018 |
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| Original language | English |
| Awarding Institution |
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| Supervisor | Siyang GAO (Supervisor) |