1. On the Structure of Decision Diagram–Representable Mixed-Integer Programs with Application to Unit Commitment.
- Author
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Salemi, Hosseinali and Davarnia, Danial
- Subjects
OPERATIONS research ,COMBINATORIAL optimization ,ELECTRICITY markets ,INTEGER programming ,INTEGERS - Abstract
Despite the successful applications of decision diagrams (DDs) to solve various classes of integer programs in the literature, the question of which mixed-integer structures admit a DD representation remains open. The present work addresses this question by developing both necessary and sufficient conditions for a mixed-integer program to be DD-representable through identification of certain rectangular formations in the underlying sets. This so-called rectangularization framework is applicable to all bounded mixed-integer linear programs, providing a notable extension of the DD domain to continuous problems. As an application, the paper uses the developed methods to solve stochastic unit commitment problems in energy systems. Computational experiments conducted on benchmark instances show that the DD approach uniformly and significantly outperforms the existing solution methods and modern solvers. The proposed methodology opens new pathways to solving challenging mixed-integer programs in energy systems more efficiently. Over the past decade, decision diagrams (DDs) have been used to model and solve integer programming and combinatorial optimization problems. Despite successful performance of DDs in solving various discrete optimization problems, their extension to model mixed-integer programs (MIPs), such as those appearing in energy applications, is lacking. More broadly, the question of which problem structures admit a DD representation is still open in the DD community. In this paper, we address this question by introducing a geometric decomposition framework based on rectangular formations that provides both necessary and sufficient conditions for a general MIP to be representable by DDs. As a special case, we show that any bounded mixed-integer linear program admits a DD representation through a specialized Benders decomposition technique. The resulting DD encodes both integer and continuous variables and, therefore, is amenable to the addition of feasibility and optimality cuts through refinement procedures. As an application for this framework, we develop a novel solution methodology for the unit commitment problem (UCP) in the wholesale electricity market. Computational experiments conducted on a stochastic variant of the UCP show a significant improvement of the solution time for the proposed method when compared with the outcome of modern solvers. History: This paper has been accepted for the Operations Research Special Issue on Computational Advances in Short-Term Power System Operations. Funding: This work was supported by the Iowa Economic Development Authority [Grant 20IEC005]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2353. [ABSTRACT FROM AUTHOR]
- Published
- 2023
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