基于PSO算法的权的最小平方法
The Least Square Method of Weight Based on PSO Algorithm
摘要: 基于互反判断矩阵的决策中,权的最小平方法是确定决策变量权重的一种重要方法,通常借用拉格朗日函数去求解该模型的最优解。本文主要采用粒子群优化算法(PSO)去求解权的最小平方模型,并通过实例与拉格朗日函数法进行对比分析,说明了该算法的可行性。
Abstract: In the decision making based on reciprocal judgment matrix, the least square method of weights is an important method to determine the weight of decision variables, and Lagrange function is often used to solve the optimal solution of the model. In this paper, particle swarm optimization (PSO) is mainly used to solve the least-square model of weights, and the feasibility of the algorithm is illustrated by the comparison and analysis between an example and Lagrange function method.
文章引用:刘祖林, 吴志远, 李甲聪. 基于PSO算法的权的最小平方法[J]. 运筹与模糊学, 2020, 10(3): 263-267. https://doi.org/10.12677/ORF.2020.103027

参考文献

[1] Satty, T.L. and Alexander, J.M. (1989) Conflict Resolution: The Analytic Hierarchy Approach. Praeger, New York.
[2] Crawford, G. and Williams, C. (1985) A Note on the Analysis of Subjective Judgment Matrices. Journal of Mathematical Psychology, 29, 387-405. [Google Scholar] [CrossRef
[3] Chu, A.T.W., Kalaba, R.E. and Spingarn, K. (1979) A Comparison of Two Methods for Determining the Weights of Belonging to Fuzzy Sets. Journal of Optimization Theory and Applications, 27, 531-538. [Google Scholar] [CrossRef
[4] 徐泽水. 互补判断矩阵的两种排序方法——权的最小平方法及特征向量法[J]. 系统工程理论与实践, 2002(7): 71-75.
[5] Satty, T.L. (1980) The Analytic Hierarchy Process. Vol. 41, McGraw-Hill, New York, 19-28.
[6] Kennedy, J. and Eberhart, R. (1995) Particle Swarm Optimization. IEEE Inter-national Conference on Neural Networks, Perth, 2002, 1942-1948.