Improving nonlinear optimization algorithms for BMP implementation in a combined sewer system

Implementing best management practices (BMP) on watersheds could help mitigate the effects of urbanization and climate change on the hydrological cycle. Techniques such as retention ponds, rain gardens, infiltration trenches, and green roofs vary in technical performance, space requirements, and cost. The trade-offs between these present a challenge toward BMP selection and placement, therefore requiring optimization. Three optimization methods were applied for BMP implementation on a combined sewer: linear programming (LP); genetic algorithm (GA); and simulated annealing (SA). LP served as a reference point. The SA solution was only marginally better, 4.7% cheaper, whereas GA's solution was 17.9% more expensive after computations froze at a local minimum; both methods required approximately 18 h of computational time. A second round of optimization used the solution from LP as a starting point. This modification significantly increased the performance of GA, providing a new solution that was 14% cheaper than LP, with reduced computational times for both GA and SA. SA's solution, though still cheaper than that of LP, was 3.9% more expensive than the one previously obtained with SA.