An Effective Algorithm for Globally Solving Sum of Linear Ratios Problems. (4th June 2017)

• Record Type: Journal Article
• Authors: Jiao, Hongwei; Cai, Lei; Hou, Zhisong; Bai, Chunyang
• Other Names: Du Haibo Academic Editor.
• Is Part Of: Journal of control science and engineering. Volume 2017(2017)
• Publication Date: 2017-06-04
• Subjects: Control theory -- Periodicals; 629.831205
• DOI: 10.1155/2017/8138975
• Languages: English
• ISSNs: 1687-5249

Abstract

Abstract : In this study, we propose an effective algorithm for globally solving the sum of linear ratios problems. Firstly, by introducing new variables, we transform the initial problem into an equivalent nonconvex programming problem. Secondly, by utilizing direct relaxation, the linear relaxation programming problem of the equivalent problem can be constructed. Thirdly, in order to improve the computational efficiency of the algorithm, an out space pruning technique is derived, which offers a possibility of pruning a large part of the out space region which does not contain the optimal solution of the equivalent problem. Fourthly, based on out space partition, by combining bounding technique and pruning technique, a new out space branch-and-bound algorithm for globally solving the sum of linear ratios problems (SLRP) is designed. Finally, numerical experimental results are presented to demonstrate both computational efficiency and solution quality of the proposed algorithm.