Combinatorial Optimization through Bayesian Optimization for Parameterization and Decomposition-Based Methods

Abstract

Real-world decision-making problems are increasingly complex due to combinatorial structures, un- certain environments, and conflicting multi-objective goals. Operations research (OR) provides a power- ful set of mathematical tools to structure and solve such problems, but traditional OR approaches often rely on expert-driven formulations, fixed parameters, and predefined search strategies. In large-scale combinatorial optimization (CO) problems, where the solution space is vast and uncertainty is inherent, computational complexity quickly becomes prohibitive, making conventional methods impractical for many real-world applications. Recent advances in machine learning (ML) offer promising directions for addressing these challenges. ML can learn complex problem structures directly from data, approximate expensive computations, and adapt to different problem distributions through simulation and experience. By learning policies tailored to specific problem instances, ML enables scalable and adaptive decision- making in dynamic environments. This thesis proposes an integrated methodological framework that combines ML-based modules with mathematical optimization to robustly and effectively solve various CO problems arising in real- world industrial contexts. The proposed framework links quantitative forecasting, qualitative evaluation, and structured optimization models into a cohesive system, designed to be domain-agnostic and broadly applicable without requiring intensive expert intervention. In particular, the framework leverages the efficiency of exact solvers from the OR domain and the flexibility of ML techniques to address large- scale decision-making problems through gradient-free optimization. This thesis is structured as follows: Chapter 1 introduces the motivation and background for integrating machine learning (ML) tech- niques with operations research (OR) to address complex combinatorial optimization (CO) problems in real-world decision-making. It discusses the background and necessity of the research, highlighting the increasing complexity of decision problems due to structural constraints and uncertainty. The chapter also presents the potential of ML to complement traditional OR methods by learning from data and adapting to changing environments. It further emphasizes the need for a unified ML-OR framework that combines the strengths of both fields. The overarching goal of this thesis is to develop and evaluate new integrated methods that address the limitations of conventional approaches and enable scalable, adaptive solutions to large-scale CO problems without relying heavily on domain-specific expertise. Chapter 2 describes the theoretical background and related literature on integrating ML with OR for solving large-scale CO problems. The chapter reviews key developments in BO, hyperparameter tuning, solver configuration, and learning-based algorithm design. The challenges and limitations of traditional OR methods for dealing with real-world CO problems are discussed, highlighting their dependence on expert knowledge, manual parameter calibration, and limited adaptability to dynamic problem distribu- tions. These limitations emphasize the need for new data-driven approaches that can effectively handle the complexity and variability of decision-making in uncertain environments. Overall, the goal of this thesis is to advance the integration of ML and OR by proposing scalable, adaptive, and generalizable optimization frameworks that are applicable across diverse industrial domains. Chapter 3 focuses primarily on the problem of industrial steam procurement, where decision-makers must balance cost efficiency, supplier quality, and carbon emissions. A key challenge in this case study lies in handling the discontinuities and uncertainties introduced by block-rate pricing policies applied to steam usage. This study provides a novel integrated decision-making method using a BO-based ensem- ble forecasting model and a hybrid multi-criteria decision-making framework. A multi-objective linear programming model is then developed to optimize trade-offs among cost, qualitative supplier perfor- mance, and environmental impact. The proposed framework is validated through a case study of a major manufacturing firm in Ulsan, Republic of Korea. Chapter 4 addresses the location-allocation problem of EV charging stations (EVCSs) on directed highway networks, considering path-based demands and flexible station capacities. The proposed model jointly determines the locations of EVCSs and the number of chargers at each site, relaxing the common assumption of fixed charger quantities. Since the number of feasible configurations grows exponen- tially with the number of candidate sites and charger options per site, this study adopts a modified BO algorithm using the expected improvement criterion to guide the search efficiently. The BO approach balances demand coverage with model uncertainty to focus on promising combinations. Case studies on the Pennsylvania and South Dakota highway networks demonstrate that flexible capacity planning outperforms uniform allocation strategies in terms of cost, coverage, and computational efficiency. Chapter 5 presents a multi-period optimization framework for the urban-scale deployment of electric vehicle charging stations (EVCSs) under demand uncertainty and budget constraints. To estimate charg- ing needs in areas without existing infrastructure, the study introduces the latent charging demand rate (LCDR) and latent charging demand (LCD) using a survival analysis approach. A large-scale mixed- integer programming model is formulated to determine annual installation and expansion decisions over a multi-year horizon. To efficiently solve this high-dimensional problem, a hybrid metaheuristic com- bining large neighborhood search (LNS) and BO is developed. A five-year case study in Seoul, Republic of Korea, demonstrates the effectiveness of phased investment strategies that adapt to spatiotemporal demand patterns. Chapter 6 presents a summary of the key findings and conclusions of this study. The major con- tributions are highlighted, and the implications of the results for future research are discussed. It is demonstrated that the proposed ML-OR integrated framework can effectively solve large-scale combina- torial optimization problems under uncertainty, offering practical value for real-world decision-making. Possible extensions include online decision-making, reinforcement learning integration, and real-time infrastructure planning in dynamic environments.