给水管网中阀门和加氯器优化配置与控制的松弛-收紧-循环算法
Relax-Tighten-Round Algorithm for Optimal Placement and Control of Valves and Chlorine Boosters in Water Networks
摘要：
本文提出了一种新的混合整数非线性规划公式，用于给水管网中减压阀和加氯站的优化布置和运行。目标是最小化平均区域压力，同时惩罚偏离目标氯浓度的偏差。我们提出了一个松弛-收紧-轮算法的基础上收紧多面体松弛和舍入计划来计算可行解，其最优性差距的界限。这是因为现成的全局优化求解器无法计算所考虑的非凸混合整数非线性规划的可行解。实施的算法进行评估，使用三个基准水网络，他们表现出优于现成的求解器，这些案例研究。所提出的启发式算法，使计算质量好的可行解在大多数情况下，与业务水网络模型中观察到的不确定性顺序的最优性差距的界限。
英文摘要：
In this paper, a new mixed integer nonlinear programming formulation is proposed for optimally placing and operating pressure reducing valves and chlorine booster stations in water distribution networks. The objective is the minimization of average zone pressure, while penalizing deviations from a target chlorine concentration. We propose a relax-tighten-round algorithm based on tightened polyhedral relaxations and a rounding scheme to compute feasible solutions, with bounds on their optimality gaps. This is because off-the-shelf global optimization solvers failed to compute feasible solutions for the considered non-convex mixed integer nonlinear program. The implemented algorithm is evaluated using three benchmarking water networks, and they are shown to outperform off-the-shelf solvers, for these case studies. The proposed heuristic has enabled the computation of good quality feasible solutions in most instances, with bounds on the optimality gaps that are comparable to the order of uncertainty observed in operational water network models.
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