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

机译：多目标水资源分配优化模型排序问题的最小二乘支持向量机

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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.
机译：为了解决水资源分配的多目标优化问题，使用多目标进化算法（MOEA）的趋势正在增加。但是，通常结果是一组帕累托最优解，它们构成了目标函数之间的权衡面。为了让决策者从一组Pareto最优解中选择满意的替代方案，本文提出了一种基于最小二乘支持向量机（LSSVM）和k均值聚类的新方法，用于对最优解进行多目标分配。水资源。首先，采用k-均值聚类方法将大量解减少为几个代表性解。然后，为了捕获和表示决策者的偏好以及选择最理想的替代方案，应用了LSSVM方法来获得每个代表性解决方案的效用值。根据效用值的大小，确定了代表性解决方案的最终优先级顺序。最后，将该方法应用于对河北省南水北调工程受水区水资源分配多目标优化问题获得的帕累托最优解集进行排序。此外，还将该方法与信息熵方法和人工神经网络模型进行了比较。比较结果表明，该方法具有对多目标运行优化模型的非主导解进行排序的能力，可用于流域水量分配与管理决策。

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