The synthesis of large-scale integrated water networks is typically formulated as nonconvex mixed-integer quadratic constrained programming (MIQCP) or QCP problems. With the complexity arising from bilinear terms in modeling mass flows of contaminants and binary variables representing the presence of units or streams, numerous local optima exist, thus presenting a significant optimization challenge. This study introduces a deterministic global optimization algorithm based on mixed-integer programming (MIP) to tackle such problems. The approach involves dynamically strengthening the relaxed problems to converge towards the original problems. A simultaneous partition strategy is proposed combining locally uniform division with dynamic partitioned variables choosing. Furthermore, several adaptive bound contraction schemes are introduced to efficiently manage the size of the relaxed problems, assisting in accelerating the solution process. The algorithm's effectiveness and robustness are demonstrated with a large test set, showing superior performance compared to commercial solvers specifically on MIQCP problems.

中文翻译：

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基于动态分区和自适应边界紧缩的大规模水网络综合全局优化


大规模综合供水网络的综合通常被表述为非凸混合整数二次约束规划 (MIQCP) 或 QCP 问题。由于对污染物质量流和表示单元或流存在的二元变量进行建模时双线性项产生的复杂性，存在许多局部最优值，从而提出了重大的优化挑战。本研究引入了一种基于混合整数规划（MIP）的确定性全局优化算法来解决此类问题。该方法涉及动态强化松弛的问题以收敛到原始问题。提出了一种将局部均匀划分与动态划分变量选择相结合的同时划分策略。此外，引入了几种自适应边界收缩方案来有效管理松弛问题的大小，有助于加速求解过程。该算法的有效性和鲁棒性通过大型测试集得到了证明，与专门针对 MIQCP 问题的商业求解器相比，显示出了卓越的性能。