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合成全局优化


大规模集成水网的综合通常表示为非凸混合整数二次约束规划 （MIQCP） 或 QCP 问题。由于在对污染物质量流和表示存在单位或流的二进制变量进行建模时，双线性项带来了复杂性，因此存在许多局部最优值，因此带来了重大的优化挑战。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分区变量选择相结合的同步分区策略。此外，引入了几种自适应绑定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。该算法的有效性和稳健性通过大型测试集得到证明，与商业求解器相比，特别是在 MIQCP 问题上表现出卓越的性能。