Department of Civil Engineering, Faculty of Civil Engineering and Transportation, University of Isfahan, Isfahan, Iran.
School of Civil Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran.
Water Environ Res. 2019 Apr;91(4):300-321. doi: 10.1002/wer.1027. Epub 2019 Jan 31.
The ant colony optimization algorithm (ACOA) is hybridized with nonlinear programming (NLP) for the optimal design of sewer networks. The resulting problem is a highly constrained mixed integer nonlinear problem (MINLP) presenting a challenge even to the modern heuristic search methods. In the proposed hybrid method, The ACOA is used to determine pipe diameters while the NLP is used to determine the pipe slopes of the network by proposing two different formulations. In the first formulation, named ACOA-NLP1, a penalty method is used to satisfy the problem constraints while in the second one, named ACOA-NLP2, the velocity and flow depth constraints are expressed in terms of the slope constraints which are easily satisfied as box constraint of the NLP solver leading to a considerable reduction of the search space size. In addition, the assumption of minimum cover depth at the network inlets is used to calculate the nodal cover depths and the pump and drop heights at the network nodes, if required, leading to a complete solution. The total cost of the constructed solution is used as the objective function of the ACOA, guiding the ant toward minimum cost solutions. Proposed hybrid methods are used to solve three test examples, and the results are presented and compared with those produced by a conventional application of ACOA. The results indicate the effectiveness and efficiency of the proposed formulations and in particular the ACOA-NLP2 to optimally solve the sewer network design optimization problems. PRACTITIONER POINTS: ACOA is hybridized with NLP for the effective optimal design of sewer networks. Here, ACOA is used to determine pipe diameters and NLP is used to determine the network pipe slopes with predefined pipe diameters. In ACOA-NLP1, a penalty method is used to enforce the problem constraints. In ACOA-NLP2, velocity and flow depth constrains are expressed in terms of slope constraint.
蚁群优化算法（ACOA）与非线性规划（NLP）相结合，用于优化污水管网的设计。由此产生的问题是一个高度约束的混合整数非线性问题（MINLP），即使是现代启发式搜索方法也难以解决。在提出的混合方法中，ACOA 用于确定管道直径，而 NLP 用于通过提出两种不同的公式来确定管网的管道坡度。在第一种公式中，称为 ACOA-NLP1，使用惩罚方法来满足问题约束，而在第二种公式中，称为 ACOA-NLP2，将速度和流量深度约束表示为坡度约束，这很容易满足，因为 NLP 求解器的箱式约束会导致搜索空间大小的显著减少。此外，假设管网入口处的最小覆盖深度用于计算管网节点的覆盖深度以及管网节点处的泵和下降高度，如果需要，则可以得到完整的解决方案。所构建解决方案的总成本用作 ACOA 的目标函数，引导蚂蚁寻找最低成本的解决方案。提出的混合方法用于解决三个测试示例，并给出了结果并与常规 ACOA 应用产生的结果进行了比较。结果表明了所提出的公式的有效性和效率，特别是 ACOA-NLP2 能够有效地解决污水管网设计优化问题。
ACOA 与 NLP 相结合，用于有效地优化污水管网的设计。在这里，ACOA 用于确定管道直径，而 NLP 用于确定具有预定义管道直径的管网管道坡度。在 ACOA-NLP1 中，使用惩罚方法来执行问题约束。在 ACOA-NLP2 中，速度和流量深度约束表示为坡度约束。
