2024-06-21T16:17:10Zhttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_oaipmhoai:ipsj.ixsq.nii.ac.jp:000773452024-03-29T05:26:34Z01164:02735:06337:06524
An Improvement of the Stochastic Algorithm for Solving the Sum-of-Ratios ProblemAn Improvement of the Stochastic Algorithm for Solving the Sum-of-Ratios Problemenghttp://id.nii.ac.jp/1001/00077345/Technical Reporthttps://ipsj.ixsq.nii.ac.jp/ej/?action=repository_action_common_download&item_id=77345&item_no=1&attribute_id=1&file_no=1Copyright (c) 2011 by the Information Processing Society of JapanCollege of Information and Electronic Engineering, Muroran Institute of Technology, Mruoran, JapanCollege of Information and Electronic Engineering, Muroran Institute of Technology, Mruoran, JapanCollege of Information and Electronic Engineering, Muroran Institute of Technology, Mruoran, JapanCollege of Information and Electronic Engineering, Muroran Institute of Technology, Mruoran, JapanYangyang, HuShinya, WatanabeYongkang, JiJianming, ShiThere are many applications of Sum-of-Ratios (SOR) problem in the fields of engineering and economy. Theoretically, the SOR problem is NP-hard. Most existing deterministic algorithms are of branch-and-bound. When the number of terms of ratios is greater than 30, the SOR problem can not be solved by these algorithms within a reasonable time. On the other hand, recently, the stochastic algorithm has been well developed to find an ε-optimal solution to the SOR problem. We first improve such an algorithm by using line search method, give some theoretical results for the convergence of the proposed algorithm, and we apply the modified algorithm to solving the SOR problem. The results of computational experiments we conducted show that the modified algorithm is quite efficient than its ancestor.There are many applications of Sum-of-Ratios (SOR) problem in the fields of engineering and economy. Theoretically, the SOR problem is NP-hard. Most existing deterministic algorithms are of branch-and-bound. When the number of terms of ratios is greater than 30, the SOR problem can not be solved by these algorithms within a reasonable time. On the other hand, recently, the stochastic algorithm has been well developed to find an ε-optimal solution to the SOR problem. We first improve such an algorithm by using line search method, give some theoretical results for the convergence of the proposed algorithm, and we apply the modified algorithm to solving the SOR problem. The results of computational experiments we conducted show that the modified algorithm is quite efficient than its ancestor.AN10505667研究報告数理モデル化と問題解決（MPS）2011-MPS-855162011-09-082011-09-02