Classic Optimization Techniques Applied to Stormwater and Nonpoint Source Pollution Management at the Watershed Scale James F. Limbrunner, M.ASCE 1 ; Richard M. Vogel, M.ASCE 2 ; Steven C. Chapra, F.ASCE 3 ; and Paul H. Kirshen, M.ASCE 4 Abstract: Linear and dynamic programming formulations are introduced for optimizing the placement of distributed best management practices (BMPs) at the watershed scale. The results of linear programming optimization of infiltration-based stormwater management BMPs are compared with the results of genetic algorithm (GA)optimization using a nonlinear distributed model. Additionally, linear and dynamic programming optimization of sediment-trapping BMPs are compared with GA optimization using a nonlinear distributed model. The results indicate that the solution to stormwater peak-flow reduction is influenced primarily by distributed-flow arrival time, and a linear programming analog to a nonlinear optimization model can efficiently reproduce much of the same solution structure. Linear and dynamic programming solutions to the storm sediment-management problem indicate natural sediment trapping is an important consideration, and a solution to the sediment-management-optimization problem can be efficiently found using a dynamic programming formulation. DOI: 10.1061/(ASCE) WR.1943-5452.0000361. © 2013 American Society of Civil Engineers. CE Database subject headings: Watersheds; Nonpoint pollution; Best management practice; Stormwater management; Sediment loads; Optimization. Author keywords: Watershed management; Nonpoint source pollution; Best management practices; Stormwater; Sediment load; Linear programming; Dynamic programming. Introduction Simulation models are widely used for studying watershed best management practice (BMP) system behavior, and it is likely that their use will continue in developing total maximum daily loads (TMDLs) and in designing solutions to nonpoint source pollution problems (National Research Council 2001). Stormwater and nonpoint load generation mechanisms are complex, as are the models used to simulate them. Using complex simulation models for management alternative scenario testing is a popular approach to designing stormwater and nonpoint source pollution manage- ment systems, whereby various management options are tested in a simulation model, and the resulting stormwater and nonpoint source loads are compared for selection of a management alterna- tive. Where design choices may be limited by other factors, such as available locations for construction, testing a few practical alternatives using a simulation model is often a satisfactory approach. But there may be other cases where flexibility in construction sites, technology selection, and budget make many combinations of alternatives possible. For these less-constrained design situations, testing a few scenarios may not be adequate to find a near-optimal solution. Contemporary optimization tech- niques, such as GAs and other evolutionary algorithms, have been employed to perform more comprehensive searches of large decision spaces and have become popular for analyzing nonpoint source pollution management designs. While contemporary optimi- zation techniques expand the horizons for evaluation of nonpoint source pollution management alternatives, the computational time needed by the algorithms to perform many runs of a complex simulation model can be burdensome. Long waits for results may limit the practicality of using evolutionary algorithms in typical forums for collaborative decision making, such as stakeholder workshops and brainstorming sessions, which lie at the heart of navigating the often contentious process of making decisions regarding natural resources. Since convening large groups of stakeholders is expensive, real-time responses to questions and suggestions are desirable to make the most of workshops and to move a decision process forward. The many runs of computationally intensive simulation models, which are required for genetic algorithm optimization, when com- bined with the need for real-time stakeholder involvement, present a conundrum regarding the selection of tools for natural resource decision-making processes. Simulation models are needed to adequately describe many of a watershed’ s physical processes, and at the same time, fast analyses and optimizations are needed to facilitate collaborative processes for negotiating complex deci- sions among groups of stakeholders. An approach that combines rapid screening of ideas during a stakeholder workshop, followed 1 Senior Water Systems Analyst, HydroLogics, Venture Development Center, Univ. of Massachusetts Boston, Boston, MA 02125 (corresponding author). E-mail: jlimbrunner@hydrologics.net 2 Professor, Dept. of Civil and Environmental Engineering, Tufts Univ., Medford, MA 02155. 3 Professor and Berger Chair, Dept. of Civil and Environmental Engineering, Tufts Univ., Medford, MA 02155. 4 Research Professor, Environmental Research Group, Civil Engineering Dept. and Institute for the Study of Earth, Oceans, and Space, Univ. of New Hampshire, Durham, NH 03824. Note. This manuscript was submitted on October 17, 2011; approved on February 14, 2013; published online on August 15, 2013. Discussion period open until February 1, 2014; separate discussions must be submitted for individual papers. This paper is part of the Journal of Water Resources Planning and Management, Vol. 139, No. 5, September 1, 2013. © ASCE, ISSN 0733-9496/2013/5-486-491/$25.00. 486 / JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT © ASCE / SEPTEMBER/OCTOBER 2013 J. Water Resour. Plann. Manage. 2013.139:486-491. Downloaded from ascelibrary.org by TUFTS UNIVERSITY on 08/19/13. Copyright ASCE. For personal use only; all rights reserved.