Otimização do traçado de redes coletoras de esgoto utilizando estratégias de caminhos mínimos em árvores de busca em largura

Abstract

The layout of sewer collection networks is one of the most challenging phases in the planning of sanitation systems, with a significant influence on implementation costs and the hydraulic performance of the network. In urban areas with irregular terrain and high population density, conventional methods, based on the manual interpretation of contour lines and the designer's experience, tend to result in suboptimal solutions, culminating in inverted sections, overloading of manholes, and the need for deep excavations. These limitations reinforce the importance of automated approaches capable of integrating topographic and hydraulic criteria in the layout definition process. Given this scenario, this work proposes the development of an algorithm for the automatic generation of sewer collection network layouts, using shortest path strategies applied to breadth-first search trees. The methodology considers aspects related to Graph Theory, with nodes representing manholes and edges corresponding to pipe sections, and applies routines to identify and correct terminal nodes and nodes with multiple outlets. Criteria such as relative slope, accumulated length, and penalties for sections running against the gravitational flow were used to select hydraulically more favorable and economically viable trajectories. The model was validated in three real-world case studies: the Alto da Expectativa and Belchior neighborhoods in the municipality of Sobral, Ceará, and a large-scale network in Villa Hermosa, Dominican Republic. The results demonstrated the algorithm's effectiveness in reducing the number of inverted sections and reorganizing sub-basins to balance contributing areas, even in scenarios with 3.157 sections, 2.206 nodes, and 219 terminal nodes, as in the case of the Villa Hermosa network. Furthermore, economic efficiency was observed in the Belchior neighborhood case study, where the optimized layout resulted in cost reductions for piping and excavation of approximately R$ 90.302,74. Computational time ranged from three seconds in smaller networks to four minutes for the Villa Hermosa network. The proposed algorithm stood out for its ability to explore all possible paths in the graph, select the most efficient route, and offer a robust and applicable solution for urban planning in the area of basic sanitation projects.