Coupled Self-Adaptive Multiobjective Differential Evolution and Network Flow Algorithm Approach for Optimal Reservoir Operation
Publication: Journal of Water Resources Planning and Management
Volume 141, Issue 10
Abstract
This paper presents a coupled self-adaptive multiobjective differential evolution and network flow algorithm for the optimal operation of complex multipurpose reservoir systems. The developed algorithm (i.e., self-adaptive multiobjective differential evolution) is compared to nondominated sorting genetic algorithm II using a set of common test problems and a real-world case study. An out-of-kilter method for minimal-cost flow problems is used to optimize the water resource system from self-adaptive multiobjective differential evolution inputs driven by the evolutionary process. Self-adaptive multiobjective differential evolution is then used to evaluate objective functions based on the outputs from out-of-kilter algorithm and the process continues until the stop criterion is met. The advantages of the proposed approach include (1) flexible evolutionary algorithms for solving highly complex objective function, and (2) efficient network flow method for dealing with large and highly constrained problems. The case study includes one part of a complex water supply system located in southwestern Brazil that provides water for almost 20 million people in Sao Paulo metropolitan area. The objectives of the case study include minimization of demand shortage (the difference between demand for water and available water supply), maximization of water quality (or minimization of the deviation from the water quality standards), and minimization of pumping cost. The coupled model is applied to the case study using one inflow scenario representing a drought period with inflows below historical average. Multiobjective analyses are performed by comparing two pairs of objective functions, as follows: (1) minimization of demand shortage versus minimization of pumping cost, and (2) minimization of demand shortage versus minimization of the deviation from the water quality standards. The problem constraints include reservoir capacity, capacity of tunnels, channel flow limitations, and minimum downstream release for all reservoirs within the system. The proposed coupled model (self-adaptive multiobjective differential evolution and out-of-kilter) is outperforming both pure self-adaptive multiobjective differential evolution and nondominated sorting genetic algorithm II, as it requires significantly smaller number of generations to derive the Pareto front. In addition, the proposed approach is capable of handling larger problems without major computational burden. The coupled model and self-adaptive multiobjective differential evolution also converge closer to, and provide better coverage of the true Pareto front than, nondominated sorting genetic algorithm II.
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Acknowledgments
The research in this paper was supported by the National Council for Research and Development (CNPq, Brazil), Scholarship Numbers 200827/2012-0, and the Natural Sciences and Engineering Research Council of Canada grant. Data for case study is provided by Companhia de Abastecimento Basico do Estado de Sao Paulo (SABESP), Sao Paulo State, Brazil.
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Journal of Water Resources Planning and Management
Volume 141 • Issue 10 • October 2015
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© 2015 American Society of Civil Engineers.
History
Received: Oct 8, 2013
Accepted: Jan 26, 2015
Published online: Mar 11, 2015
Discussion open until: Aug 11, 2015
Published in print: Oct 1, 2015
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