A local multi-energy system (LMES) is a decentralized energy system producing energy under multiple forms to satisfy the energy demand of a set of buildings located in its neighborhood. We study the problem of optimally designing an LMES over a multi-phase horizon. This problem is formulated as a large-size mixed-integer linear program with a block-decomposable structure involving mixed-integer sub-problems. We propose a new way to adapt a recently published framework for generalized Benders decomposition to our problem. This is done by exploiting the fact that the constraint matrix appearing in front of the first-stage variables in the coupling constraints is non-negative. The obtained generalized Benders decomposition algorithm relies on the use of a new type of non-convex Benders cuts involving indicator functions. We first prove that, under the assumption that all first-stage decision variables are integer and bounded, the finite and optimal convergence of our algorithm is guaranteed in theory. We then investigate how to obtain a good numerical performance in practice. Finally, we report the results of a computational study carried out on a real-life case study. These results show that the proposed algorithm clearly outperforms both a mathematical programming solver directly solving the problem as a whole and a state-of-the art hierarchical decomposition algorithm.

中文翻译：

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局部多能源系统优化设计的广义 Benders 分解方法


本地多能源系统（LMES）是一种分散的能源系统，以多种形式生产能源，以满足其附近一组建筑物的能源需求。我们研究在多相范围内优化设计 LMES 的问题。该问题被表述为具有涉及混合整数子问题的块可分解结构的大型混合整数线性程序。我们提出了一种新的方法来适应最近发布的广义 Benders 分解框架来解决我们的问题。这是通过利用耦合约束中出现在第一阶段变量前面的约束矩阵是非负的这一事实来完成的。所获得的广义 Benders 分解算法依赖于使用涉及指示函数的新型非凸 Benders 割。我们首先证明，在所有第一阶段决策变量均为整数且有界的假设下，理论上保证了算法的有限最优收敛。然后我们研究如何在实践中获得良好的数值性能。最后，我们报告了对现实案例研究进行的计算研究的结果。这些结果表明，所提出的算法明显优于直接解决整个问题的数学规划求解器和最先进的分层分解算法。