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

Xujun Liu,Mengjiao Zhang,Yao Ji,Han Su,Feifei Dong,Yong Liu

doi:10.3390/w9050322

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.

Highlights

Lake eutrophication is one of the greatest environmental challenges, which hampers and destroys ecological functions of water bodies, and leads to deterioration of water quality [1,2]
We developed an optimal model that used the Lake Qilu watershed as the management objective
(c) The ideal solutions obtained from the model can provide a reasonable and reliable planning basis for decision-makers, which are screened under robustness estimates for all the optimal schemes that were obtained from multi-objective, chance-constrained, programming by using Genetic Algorithm (GA), even when multi-objective tradeoffs and random uncertainty exist simultaneously

Summary

Introduction

Lake eutrophication is one of the greatest environmental challenges, which hampers and destroys ecological functions of water bodies, and leads to deterioration of water quality [1,2]. Many irreversible effects on aquatic ecosystems and drinking water supplies have resulted from degeneration of water quality, and this issue has become the principal bottleneck to the sustainable development of watersheds and the protection of human health [3,4,5]. Watershed planning and management of water quality is imperative. Load reduction of watershed nutrients (mainly Nitrogen and Phosphorus) is an effective approach to water quality improvement. Load reduction is an important approach to balancing watershed development and protection of water quality, because nutrient loads to water bodies are mainly due to human production and activities, and they are a primary cause of water quality impairment [6,7]. Optimization models are applied widely to provide effective load reduction

Methods

Results

Discussion

Conclusion