To improve the inconsistency in the analytic hierarchy process(AHP), a new method based on marginal optimization theory is proposed. During the improving process, this paper regards the reduction of consistency ratio(...To improve the inconsistency in the analytic hierarchy process(AHP), a new method based on marginal optimization theory is proposed. During the improving process, this paper regards the reduction of consistency ratio(CR) as benefit, and the maximum modification compared to the original pairwise comparison matrix(PCM) as cost, then the improvement of consistency is transformed to a benefit/cost analysis problem. According to the maximal marginal effect principle, the elements of PCM are modified by a fixed increment(or decrement) step by step till the consistency ratio becomes acceptable, which can ensure minimum adjustment to the original PCM so that the decision makers’ judgment is preserved as much as possible. The correctness of the proposed method is proved mathematically by theorem. Firstly, the marginal benefit/cost ratio is calculated for each single element of the PCM when it has been modified by a fixed increment(or decrement).Then, modification to the element with the maximum marginal benefit/cost ratio is accepted. Next, the marginal benefit/cost ratio is calculated again upon the revised matrix, and followed by choosing the modification to the element with the maximum marginal benefit/cost ratio. The process of calculating marginal effect and choosing the best modified element is repeated for each revised matrix till acceptable consistency is reached, i.e., CR<0.1. Finally,illustrative examples show the proposed method is more effective and better in preserving the original comparison information than existing methods.展开更多
针对干旱区水资源分配不合理的问题,以新疆开都河流域水资源为研究对象,以流域水-能源-生态综合收益最高为目标,建立水资源多目标优化配置模型,采用基于参考点的非支配排序进化算法(reference-point based many-objective,NSGA-Ⅲ)对模...针对干旱区水资源分配不合理的问题,以新疆开都河流域水资源为研究对象,以流域水-能源-生态综合收益最高为目标,建立水资源多目标优化配置模型,采用基于参考点的非支配排序进化算法(reference-point based many-objective,NSGA-Ⅲ)对模型进行求解。针对优化方案选择问题,以经济效益、社会效益和生态效益为准则层构建流域水资源最适配置方案评价指标体系,采用层次分析法对优化结果进行评价分析。结果表明:最适配置方案相较于传统配置方案,水库发电量增加5.83%,农业经济效益减少2.34%,生态效益提高40.08%;当地种植结构需进行适当调整,应增加玉米和西红柿的种植面积,减少小麦、棉花和辣椒的种植面积;博斯腾湖大湖和小湖水位均达到最适生态水位。研究成果可为当地制定水资源配置方案提供决策参考,有重要的理论意义和应用价值。展开更多
基金supported by the National Natural Science Foundation of China(6160150161502521)
文摘To improve the inconsistency in the analytic hierarchy process(AHP), a new method based on marginal optimization theory is proposed. During the improving process, this paper regards the reduction of consistency ratio(CR) as benefit, and the maximum modification compared to the original pairwise comparison matrix(PCM) as cost, then the improvement of consistency is transformed to a benefit/cost analysis problem. According to the maximal marginal effect principle, the elements of PCM are modified by a fixed increment(or decrement) step by step till the consistency ratio becomes acceptable, which can ensure minimum adjustment to the original PCM so that the decision makers’ judgment is preserved as much as possible. The correctness of the proposed method is proved mathematically by theorem. Firstly, the marginal benefit/cost ratio is calculated for each single element of the PCM when it has been modified by a fixed increment(or decrement).Then, modification to the element with the maximum marginal benefit/cost ratio is accepted. Next, the marginal benefit/cost ratio is calculated again upon the revised matrix, and followed by choosing the modification to the element with the maximum marginal benefit/cost ratio. The process of calculating marginal effect and choosing the best modified element is repeated for each revised matrix till acceptable consistency is reached, i.e., CR<0.1. Finally,illustrative examples show the proposed method is more effective and better in preserving the original comparison information than existing methods.
文摘针对干旱区水资源分配不合理的问题,以新疆开都河流域水资源为研究对象,以流域水-能源-生态综合收益最高为目标,建立水资源多目标优化配置模型,采用基于参考点的非支配排序进化算法(reference-point based many-objective,NSGA-Ⅲ)对模型进行求解。针对优化方案选择问题,以经济效益、社会效益和生态效益为准则层构建流域水资源最适配置方案评价指标体系,采用层次分析法对优化结果进行评价分析。结果表明:最适配置方案相较于传统配置方案,水库发电量增加5.83%,农业经济效益减少2.34%,生态效益提高40.08%;当地种植结构需进行适当调整,应增加玉米和西红柿的种植面积,减少小麦、棉花和辣椒的种植面积;博斯腾湖大湖和小湖水位均达到最适生态水位。研究成果可为当地制定水资源配置方案提供决策参考,有重要的理论意义和应用价值。
