Full metadata record
| DC Field | Value | Language |
|---|---|---|
| dc.contributor | Department of Logistics and Maritime Studies | en_US |
| dc.contributor.advisor | Pan, Kai (LMS) | en_US |
| dc.creator | Jiang, Shiyi | - |
| dc.identifier.uri | https://theses.lib.polyu.edu.hk/handle/200/14461 | - |
| dc.language | English | en_US |
| dc.publisher | Hong Kong Polytechnic University | en_US |
| dc.rights | All rights reserved | en_US |
| dc.title | Computationally efficient approaches for modern optimization problems | en_US |
| dcterms.abstract | Optimization problems lie at the core of decision-making processes across multiple disciplines, including supply chain management, industrial engineering, and energy systems. With the exponential growth of data volume and increasing complexity of industrial applications, these optimization problems have grown substantially in both scale (characterized by the number of decision variables and constraints) and complexity (reflected in non-convex, stochastic, or robust formulations). Conventional solution approaches often prove inadequate when addressing such challenges, frequently encountering computational bottlenecks due to either time or memory constraints. This growing computational challenge has created an urgent need for developing more efficient solution approaches capable of handling modern large-scale and complex optimization problems. In this thesis, we present three recent studies on computationally efficient approaches for modern optimization problems. | en_US |
| dcterms.abstract | In this first study, we investigate moment-based distributionally robust optimization (DRO), where the underlying joint distribution of random parameters runs in a distributional ambiguity set constructed by moment information. Although most moment-based DRO problems can be reformulated as semidefinite programming (SDP) problems that can be solved in polynomial time, solving high-dimensional SDPs is still time-consuming. Unlike existing approximation approaches that first reduce the dimensionality of random parameters and then solve the approximated SDPs, we propose an optimized dimensionality reduction (ODR) approach by integrating the dimensionality reduction of random parameters with the subsequent optimization problems. Such integration enables two outer and one inner approximations of the original problem, all of which are low-dimensional SDPs that can be solved efficiently, providing two lower bounds and one upper bound correspondingly. More importantly, these approximations can theoretically achieve the optimal value of the original high-dimensional SDPs. As these approximations are nonconvex SDPs, we develop modified Alternating Direction Method of Multipliers (ADMM) algorithms to solve them efficiently. We demonstrate the effectiveness of our proposed ODR approach and algorithm in solving multiproduct newsvendor and production-transportation problems. Numerical results show significant advantages of our approach regarding computational time and solution quality over the three best possible benchmark approaches. Our approach can obtain an optimal or near-optimal (mostly within 0.1%) solution and reduce the computational time by up to three orders of magnitude. | en_US |
| dcterms.abstract | In the second study, we consider non-convex quadratically constrained programs (QCPs), which are generally NP-hard and challenging problems. We propose two novel mixed-integer linear programming (MILP) approximations for a non-convex QCP. Our method begins by utilizing an eigenvalue-based decomposition to express the non-convex quadratic function as the difference of two convex functions. We then introduce an additional variable to partition each non-convex constraint into a second-order cone (SOC) constraint and the complement of an SOC constraint. We employ two polyhedral approximation approaches to approximate the SOC constraint. The complement of an SOC constraint is approximated using a combination of linear and complementarity constraints. As a result, we approximate the non-convex QCP with two linear programs with complementarity constraints (LPCCs). More importantly, we prove that the optimal values of the LPCCs asymptotically converge to that of the original non-convex QCP. By proving the boundedness of the LPCCs, we further reformulate the LPCCs as MILPs. We demonstrate the effectiveness of our approaches via numerical experiments by applying our proposed approximations to randomly generated instances and two application problems: the joint decision and estimation problem and the two-trust-region subproblem. The numerical results show significant advantages of our approaches in terms of solution quality and computational time compared to existing benchmark approaches. | en_US |
| dcterms.abstract | In the third study, we focus on the planning of distributed energy resources in distribution systems. This problem has been challenged by the significant uncertainties and complexities of distribution systems. To ensure system reliability, one often employs chance-constrained programs to seek a highly likely feasible solution while minimizing certain costs. The traditional sample average approximation (SAA) is commonly used to represent uncertainties and reformulate a chance-constrained program into a deterministic optimization problem. However, the SAA introduces additional binary variables to indicate whether a scenario sample is satisfied and thus brings great computational complexity to the already challenging distributed energy resource planning problems. In this study, we introduce a new paradigm, i.e., the partial sample average approximation (PSAA) using real data, to improve computational tractability. The innovation is that we sample only a part of the random parameters and introduce only continuous variables corresponding to the samples in the reformulation, which is a mixed-integer convex quadratic program. Our extensive experiments on the IEEE 33-Bus and 123-Bus systems show that the PSAA approach performs better than the SAA because the former provides better solutions in a shorter time in in-sample tests and provides better guaranteed probability for system reliability in out-of-sample tests. | en_US |
| dcterms.extent | xiv, 226 pages : color illustrations | en_US |
| dcterms.isPartOf | PolyU Electronic Theses | en_US |
| dcterms.issued | 2026 | en_US |
| dcterms.educationalLevel | Ph.D. | en_US |
| dcterms.educationalLevel | All Doctorate | en_US |
| dcterms.accessRights | open access | en_US |
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