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Water 2017, 9(5), 322; doi:10.3390/w9050322

A Multi-Objective Chance-Constrained Programming Approach for Uncertainty-Based Optimal Nutrients Load Reduction at the Watershed Scale

1
College of Environment Science and Engineering, Tongji University, Shanghai 20092, China
2
College of Environmental Science and Engineering, Key Laboratory of Water and Sediment Sciences (MOE), Peking University, Beijing 100871, China
3
Yunnan Key Laboratory of Pollution Process and Management of Plateau Lake-Watershed, Kunming 650034, China
*
Author to whom correspondence should be addressed.
Academic Editor: Gordon Huang
Received: 1 March 2017 / Revised: 8 April 2017 / Accepted: 27 April 2017 / Published: 3 May 2017
(This article belongs to the Special Issue Modeling of Water Systems)
View Full-Text   |   Download PDF [2770 KB, uploaded 3 May 2017]   |  

Abstract

A multi-objective chance-constrained programming integrated with Genetic Algorithm and robustness evaluation methods was proposed to weigh the conflict between system investment against risk for watershed load reduction, which was firstly applied to nutrient load reduction in the Lake Qilu watershed of the Yunnan Plateau, China. Eight sets of Pareto solutions were acceptable for both system investment and probability of constraint satisfaction, which were selected from 23 sets of Pareto solutions out of 120 solution sets. Decision-makers can select optimal decisions from the solutions above in accordance with the actual conditions of different sub-watersheds under various engineering measures. The relationship between system investment and risk demonstrated that system investment increased rapidly when the probability level of constraint satisfaction was higher than 0.9, but it reduced significantly if appropriate risk was permitted. Evaluation of robustness of the optimal scheme indicated that the Pareto solution obtained from the model provided the ideal option, since the solutions were always on the Pareto frontier under various distributions and mean values of the random parameters. The application of the multi-objective chance-constrained programming to optimize the reduction of watershed nutrient loads in Lake Qilu indicated that it is also applicable to other environmental problems or study areas that contain uncertainties. View Full-Text
Keywords: multi-objective chance-constrained programming; genetic algorithm; robustness evaluation; watershed load reduction; Lake Qilu multi-objective chance-constrained programming; genetic algorithm; robustness evaluation; watershed load reduction; Lake Qilu
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Liu, X.; Zhang, M.; Su, H.; Dong, F.; Ji, Y.; Liu, Y. A Multi-Objective Chance-Constrained Programming Approach for Uncertainty-Based Optimal Nutrients Load Reduction at the Watershed Scale. Water 2017, 9, 322.

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