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Water 2017, 9(4), 257; doi:10.3390/w9040257

Least Squares Support Vector Machine for Ranking Solutions of Multi-Objective Water Resources Allocation Optimization Models

1
Nanchang Institute of Technology, Jiangxi Engineering Research Center of Water Engineering Safety and Resources Efficient Utilization, Nanchang 330099, Jiangxi, China
2
School of Civil Engineering, Hefei University of Technology, Hefei 230009, Anhui, China
*
Author to whom correspondence should be addressed.
Academic Editor: Ashok K. Chapagain
Received: 23 January 2017 / Revised: 22 March 2017 / Accepted: 31 March 2017 / Published: 5 April 2017
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Abstract

There is an increasing trend in the use of multi-objective evolutionary algorithms (MOEAs) to solve multi-objective optimization problems of the allocation of water resources. However, typically the outcome is a set of Pareto optimal solutions which make up a trade-off surface between the objective functions. For decision makers to choose a satisfactory alternative from a set of Pareto-optimal solutions, this paper suggests a new method based on least squares support vector machine (LSSVM) and k-means clustering for ranking the optimal solutions for the multi-objective allocation of water resources. First, the k-means clustering method was adopted to reduce the large set of solutions to a few representative solutions. Then, to capture and represent the decision maker's preferences as well as to select the most desirable alternative, the LSSVM method was applied to obtain the utility value for each representative solution. According to the magnitude of the utility values, the final priority orders of the representative solutions were determined. Finally, this methodology was applied to rank the Pareto optimal solution set obtained from the multi-objective optimization problems of water resources allocation for the water-receiving areas of the South-to-North Water Transfer Project in Hebei Province, China. Moreover, the comparisons of the proposed method with the information entropy method and the artificial neural network (ANN) model were given. The results of the comparison indicate that the proposed method has the ability to rank the non-dominated solutions of the multi-objective operation optimization model and that it can be employed for decision-making on water allocation and management in a river basin. View Full-Text
Keywords: least squares support vector machine (LSSVM); k-means clustering; artificial neural network (ANN); water resources allocation least squares support vector machine (LSSVM); k-means clustering; artificial neural network (ANN); water resources allocation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Liu, W.; Liu, L.; Tong, F. Least Squares Support Vector Machine for Ranking Solutions of Multi-Objective Water Resources Allocation Optimization Models. Water 2017, 9, 257.

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