In this paper, the incremental solution building capability of Ant Colony Optimization Algorithm (ACOA) is exploited using a Tree Growing Algorithm (TGA) augmented with the efficiency of Nonlinear Programming (NLP) methods leading to a hybrid ACOA-TGA-NLP algorithm for the effective layout and pipe size optimization of pumped/gravitational sewer networks. Solution of layout and pipe size optimization of sewer network requires the determination of pipe locations, pipe diameters, average pipe cover depths, drop and pump heights minimizing the total cost of the sewer network subject to operational constraints. The resulting problem is a highly constrained Mixed-Integer Nonlinear Programming (MINLP) problem presenting a challenge even to the modern heuristic search methods. In the proposed method, the TGA is used to construct feasible tree-like layouts out of the base layout defined for the sewer network, the ACOA is used to optimally determine the pipe diameters of the constructed layout, and finally NLP is used to determine the pipe slopes from which the remaining characteristics of the network such as pump/drop locations and heights are determined. In the NLP stage of the model, the velocity and flow depth constraints are expressed in terms of the slope constraints which are easily enforced as box constraint of the NLP solver leading to a considerable reduction of the search space size. The proposed hybrid ACOA-TGA-NLP has two significant advantages over other available methods. First, this method can be used for both pumped and gravitational sewer networks. Second, the computational effort is significantly reduced compared to alternative methods. Another method is also proposed here in which the layout of the network is determined by an ad-hoc method based on engineering judgment while the component design of the network is carried out by ACOA-NLP method as defined above. Proposed hybrid methods are used to solve a benchmark example from the literature and a hypothetical test example and the results are presented and compared with those produced by the existing methods such as SPST-DDDP, SDM-DDDP and GA-DDDP. The results indicate the efficiency and effectiveness of the proposed methods and in particular the ACOA-TGA-NLP method. In fact, the optimal solution of ACOA-TGA-NLP is 149, 64.1, 22.2 and 13.6% cheaper than those of ACOA-NLP, SPST-DDDP, SDM-DDDP and GA-DDDP methods, respectively, for the benchmark text example. Furthermore, ACOA-TGA-NLP yields a solution 80% cheaper than that of ACOA-NLP method for hypothetical test example.

中文翻译：

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混合蚁群优化算法在下水道网络布局和尺寸优化中的扩展

在本文中，蚁群优化算法 (ACOA) 的增量解决方案构建能力是利用树生长算法 (TGA) 来开发的，该算法增强了非线性规划 (NLP) 方法的效率，从而导致混合 ACOA-TGA-NLP 算法用于抽水/重力下水道网络的有效布局和管道尺寸优化。下水道网络布局和管道尺寸优化的解决方案需要确定管道位置、管道直径、平均管道覆盖深度、落差和泵高度，以最大限度地减少受运营限制的下水道网络的总成本。由此产生的问题是一个高度约束的混合整数非线性规划 (MINLP) 问题，甚至对现代启发式搜索方法提出了挑战。在提出的方法中，TGA 用于在为下水道网络定义的基本布局之外构建可行的树状布局，ACOA 用于优化确定所构建布局的管道直径，最后 NLP 用于确定管道坡度，从确定网络的其余特性，例如泵/滴位置和高度。在模型的 NLP 阶段，速度和流动深度约束以斜率约束表示，这些约束很容易作为 NLP 求解器的框约束强制执行，从而大大减少了搜索空间的大小。所提出的混合 ACOA-TGA-NLP 与其他可用方法相比具有两个显着优势。首先，这种方法可用于抽水和重力下水道网络。第二，与替代方法相比，计算工作量显着减少。这里还提出了另一种方法，其中网络的布局通过基于工程判断的 ad-hoc 方法确定，而网络的组件设计则通过上述定义的 ACOA-NLP 方法进行。提出的混合方法用于解决文献中的基准示例和假设测试示例，并展示结果并与现有方法（如 SPST-DDDP、SDM-DDDP 和 GA-DDDP）产生的结果进行比较。结果表明了所提出方法的效率和有效性，特别是 ACOA-TGA-NLP 方法。事实上，ACOA-TGA-NLP 的最优解比 ACOA-NLP、SPST-DDDP、SDM-DDDP 和 GA-DDDP 方法分别便宜 149、64.1、22.2 和 13.6%，对于基准文本示例。此外，对于假设测试示例，ACOA-TGA-NLP 产生的解决方案比 ACOA-NLP 方法的解决方案便宜 80%。