Bi-criteria evolution strategy in estimating weights from the AHP ratio-scale matrices
Bi-criteria evolution strategy in estimating weights from the AHP ratio-scale matrices
复制标题
DOI：
10.1016/j.amc.2011.06.006
复制
发表时间：
2011-10
期刊：
影响因子：
--
通讯作者：
B. Srdjevic;Z. Srdjevic
中科院分区：
文献类型：
--
作者：
B. Srdjevic;Z. Srdjevic
在层次分析法（AHP）中，从比率尺度矩阵中获取权重的问题一直是国内外学者研究的热点。有各种方法来解决这个问题，通常分为简单的矩阵和优化方法。所有的方法都收到了批评，关于派生权重的准确性，不同的标准是在使用比较从不同的方法获得的权重。由于Pareto非支配解集（权值）是未知的，并且对于不一致矩阵是不确定的，因此提出了一种双准则优化方法来处理此类矩阵。具体问题的进化策略算法（ESA）实现了一个强大的随机搜索可行的不定解空间。适应度函数被定义为一个标量向量函数，由共同的误差度量，即欧几里得距离和一个最小违规误差组成，该最小违规误差不违反秩序。调整搜索引擎的编码方案和其他组件以保持与权重的所需归一化值相关的所施加的约束。所提出的方法产生的解决方案进行了比较，从文献中采取的三个判断矩阵的五个著名的优先级排序技术获得的解决方案。在这些和其他测试应用程序中，优先级排序方法，使用题为权重估计的进化策略算法（WEESA）似乎是上级其他方法，如果只有两个，最常用的方法，应用：欧几里德距离和最小违规排除标准。
The problem of deriving weights from ratio-scale matrices in an analytic hierarchy process (AHP) is addressed by researchers worldwide. There are various ways to solve the problem that are generally grouped into simple matrix and optimization methods. All methods have received criticism regarding the accuracy of derived weights, and different criteria are in use to compare the weights obtained from different methods. Because the set of Pareto non-dominated solutions (weights) is unknown and for inconsistent matrices is indefinite, a bi-criterion optimization approach is proposed for manipulating such matrices. The problem-specific evolution strategy algorithm (ESA) is implemented for a robust stochastic search over a feasible indefinite solution space. The fitness function is defined as a scalar vector function composed of the common error measure, i.e. the Euclidean distance and a minimum violation error that accounts for no violation of the rank ordering. The encoding scheme and other components of the search engine are adjusted to preserve the imposed constraints related to the required normalized values of the weights. The solutions generated by the proposed approach are compared with solutions obtained by five well-known prioritization techniques for three judgment matrices taken from the literature. In these and other test applications, the prioritization method that uses the entitled weights estimation by evolution strategy algorithm (WEESA) appears to be superior to other methods if only two, the most commonly used methods, are applied: the Euclidean distance and minimum violation exclusion criteria.