标题： 多面体研究：集成最小开/关时间和爬坡多胞体 显示英文标题

标题： A Polyhedral Study of the Integrated Minimum-Up/-Down Time and Ramping Polytope

摘要： 本文研究了一种集成最小开机/关机时间和爬坡多面体的几何结构，该多面体在多个行业中具有广泛的应用。 我们研究的多面体包括最小开机/关机时间、发电爬坡率、逻辑约束以及发电上下限约束。 通过探索其特殊结构，我们推导出强有效不等式，并开发了一种新的证明技术来证明这些不等式在不同参数设置下足以描述两种和三种时间段多面体的凸包。 对于多时段情况，我们推导了广义强有效不等式（分别包含一个、两个和三个连续变量），并在温和条件下进一步证明这些不等式是面定义的。 此外，我们发现了这些不等式的高效多项式时间分离算法，以提高计算效率。 最后，通过测试这些不等式在自调度和网络约束机组组合问题中的应用，进行了广泛的计算实验，验证了所提出的强有效不等式的有效性，我们的方法显著优于默认的CPLEX。 显示英文摘要

摘要： In this paper, we study the polyhedral structure of an integrated minimum-up/-down time and ramping polytope, which has broad applications in variant industries. The polytope we studied includes minimum-up/-down time, generation ramp-up/-down rate, logical, and generation upper/lower bound constraints. By exploring its specialized structures, we derive strong valid inequalities and explore a new proof technique to prove these inequalities are sufficient to provide convex hull descriptions for variant two-period and three-period polytopes, under different parameter settings. For multi-period cases, we derive generalized strong valid inequalities (including one, two, and three continuous variables, respectively) and further prove that these inequalities are facet-defining under mild conditions. Moreover, we discover efficient polynomial time separation algorithms for these inequalities to improve the computational efficiency. Finally, extensive computational experiments are conducted to verify the effectiveness of our proposed strong valid inequalities by testing the applications of these inequalities to solve both self-scheduling and network-constrained unit commitment problems, for which our derived approach outperforms the default CPLEX significantly.