A Deterministic Method for Solving the Sum of Linear Ratios Problem. (28th September 2020)

• Record Type: Journal Article
• Authors: Wang, Zhenping; Zhang, Yonghong
• Other Names: Manfredi Paolo Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2020(2020)
• Publication Date: 2020-09-28
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2020/6174352
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : Since the sum of linear ratios problem (SLRP) has many applications in real life, for globally solving it, an efficient branch and bound algorithm is presented in this paper. By utilizing the characteristic of the problem (SLRP), we propose a convex separation technique and a two-part linearization technique, which can be used to generate a sequence of linear programming relaxation of the initial nonconvex programming problem. For improving the convergence speed of this algorithm, a deleting rule is presented. The convergence of this algorithm is established, and some experiments are reported to show the feasibility and efficiency of the proposed algorithm.