An Efficient Branch-and-Bound Algorithm for Globally Solving Minimax Linear Fractional Programming Problem. (27th November 2021)

• Record Type: Journal Article
• Authors: Jia, Pujun; Jiao, Hongwei; Shi, Dongwei; Yin, Jingben
• Other Names: Skouri Konstantina Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2021(2021)
• Publication Date: 2021-11-27
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2021/3584494
• Languages: English
• ISSNs: 1024-123X

Abstract

Abstract : This paper presents an efficient outer space branch-and-bound algorithm for globally solving a minimax linear fractional programming problem (MLFP), which has a wide range of applications in data envelopment analysis, engineering optimization, management optimization, and so on. In this algorithm, by introducing auxiliary variables, we first equivalently transform the problem (MLFP) into the problem (EP). By using a new linear relaxation technique, the problem (EP) is reduced to a sequence of linear relaxation problems over the outer space rectangle, which provides the valid lower bound for the optimal value of the problem (EP). Based on the outer space branch-and-bound search and the linear relaxation problem, an outer space branch-and-bound algorithm is constructed for globally solving the problem (MLFP). In addition, the convergence and complexity of the presented algorithm are given. Finally, numerical experimental results demonstrate the feasibility and efficiency of the proposed algorithm.