On the Structure of Decision Diagram–Representable Mixed-Integer Programs with Application to Unit Commitment
研究了哪些混合整数规划问题可以用决策图表示，提出了矩形化框架，并应用于能源系统的随机机组组合问题，计算实验表明该方法显著优于现有求解器和算法。
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.