Establishing an Optimization Model for Sewer System Layout with Applied Genetic Algorithm

Abstract

In this study, a genetic algorithm (GA) is first used to establish a combinatorial optimization model, called the Sewer System Optimization Model for Layout & Hydraulics (GA/SSOM/LH), to find an optimal design for a real urban sewer system. The problems of "network layout" and "hydraulic design" optimization are considered simultaneously. The modeling concept is to combine the fundamental principles of the GA, to the generation of possible network layouts as well as to develop a "hydraulic design" optimization module, the Sewerage System Optimization model (SSOM), which can find the best sewer system layout by checking the overall least-cost hydraulic design of several possible alternate network layouts. SSOM is a 0-1 Mixed Integer Programming (MIP) in which a traditional algorithm, the Bounded Implicit Enumeration (BIE) is applied to determine the optimal size and slope for each. Unlike the BIE algorithm, 'one chromosome' in the GA evolution is coded to represent 'one system layout' parameter. Specific coding strings on 'parameters' are operated directly and are more robust when combined with the SSOM module. Hence the GA can evolve quickly generating an optimized system layout and ensuring a solution closer to the global optimum in a 'fast' manner. Finally, a case study was conducted on a 73-node project to verify the optimal system layout as generated by the GA/SSOM/LH model.

Keywords: Bounded Implicit Enumeration, Genetic Algorithm, hydraulic design, N-P Complete problem, system layout, 0-1 Mixed Integer Programming