A Novel and Efficient Mathematical Programming Approach for the Optimal Design of Rainwater Drainage Networks

Abstract

Urban sanitation, especially in developing nations, relies on pipe networks, but determining flow in these networks is challenging. Rainwater Drainage Networks (RDNs) face high flow unpredictability due to extreme events and climate change. Optimization studies focused on RDNs frequently employ stochastic techniques due to these systems’ inherent complexities. This study aims to optimize RDNs design, reducing costs while adhering to standards, by selecting appropriate pipes, diameters, and inclinations using a deterministic method. Two mathematical models were developed and evaluated on three case studies exhibiting varying levels of complexity. A Rigorous Model provides a detailed and comprehensive approach to modeling the geometric dimensions of circular sections. However, its inherent non-linear and non-convex properties limit the model’s suitability to smaller-scale problems. The complex characteristics exhibited by larger-scale network surpass the capacities of the Rigorous Model. A Sequential Model is presented as a novel and effective formulation that replaces certain hydraulic equations with constraints, thus guaranteeing feasibility and an optimal network design without compromising the rigor. The model is formulated as a convex Mixed-Integer Quadratic Constrained Programming (MIQCP), solvable by advanced global optimum solvers. The Sequential Model, effectively and quickly, found optimal designs for all case studies, including a network with 160 nodes, offering a practical tool for engineers and urban planners in designing cost-effective RDNs.This work was supported by the National Council for Scientific and Technological Development – Processes 141165/2023-5, 309026/2022-9 and 406544/2023-9– CNPq (Brazil), the Coordination for the Improvement of Higher Education Personnel – Process 88881.892679/2023-01 – CAPES (Brazil), and the Spanish Ministry of Science and Innovation under the project – PID2021-124139NB-C21. SUS4Energy