Advanced Methods to Solve Stochastically Constrained Simulation Optimization: Theory and Applications


Student thesis: Doctoral Thesis

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Awarding Institution
  • Siyang GAO (Supervisor)
  • Kwok Leung TSUI (Co-supervisor)
Award date24 Aug 2020


Operations research (OR) serves as a catalyst in every walk of life to improve production efficiency and make wise decisions. Especially, the development of Industrial 4.0 and big data promotes the bloom of OR techniques to optimize more complex systems such as airport operations, multi-level health services, port dispatch. This kind of systems always involves complex service processes, closely related activities, and hard-to-measure uncertainties. Compared to traditional OR methods like mathematical modeling, simulation optimization techniques show great success in modeling large-scale systems and addressing complicated issues as computing power and memory increasing.

Operational managers always formulate a specific simulation optimization problem according to the characteristic factors such as the type of solutions, the size of issues, and the number of performance measures. When optimizing a practical complex system, we should consider multiple measures to enhance the overall performance. Take a hospital as an example. The medical budgets, resource utilization, and patient service levels are highly related to hospital operations. In such a case, OR scholars always formulate a stochastically constrained simulation optimization problem where the primary performance is optimized subject to secondary performance constraints. There are some challenges to tackle the problem. 1) The objective and constraints have no analytical forms and need to be evaluated via simulation. 2) We should make a tradeoff between exploiting around the best solution and exploring more unknown regions. 3) Both the objective value and feasibility determine the quality of a solution. Motivated by these issues, we concentrate on the hot topic–stochastically constrained simulation optimization, study the advanced algorithms, and explore the performance in solving practical problems.

We divide stochastically constrained simulation optimization to stochastically constrained discrete optimization via simulation (DOvS) and stochastically constrained discrete optimization via simulation (COvS) according to the form of solutions. The thesis first reviews the state-of-art techniques to handle these two types of problems and then yields the detailed descriptions of two progressive methods in Chapter 2 and Chapter 3. In particular, Chapter 2 reports a random search method, called adaptive Gaussian process-based search (AGPS), to get a globally optimal solution from the discrete candidate set. AGPS constructs the kriging model for each performance and builds a new sampling distribution based on observations. The advantage of AGPS lies in the ability to balance exploration and exploitation, considering the objective and stochastic constraints. Chapter 3 presents constrained Bayesian optimization based on the knowledge gradient method. Bayesian optimization emerges as an essential tool to address black-box optimization problems, one of which simulation optimization problems can be regarded. We introduce a new acquisition function called constrained knowledge gradient (c − KG) and apply stochastic approximation to maximize it with an unbiased estimator of the gradient of c − KG.

In addition to the theoretical study, we showcase the applications of stochastically constrained simulation optimization in real problems. Chapter 4 discusses a medical staff allocation issue for an emergency department in Hong Kong. The hospital authority aims to guarantee high service levels for different categories of patients. We formulate a DOvS with stochastic constraints problem that minimizes the proportion of critical patients whose waiting time exceeds the threshold subject to other category patients’ waiting time targets. In Chapter 5, we employ the AGPS method to tackle an engineering problem: an (s, S) inventory problem. To demonstrate the potential of AGPS and its suitability for the application, we investigate preliminary experiments from the perspectives of accuracy, efficiency, robustness, and performance. Several noteworthy findings are shown in the (s, S) inventory problem, adding substantially to users’ understanding of operational management in industrial engineering.