An Effective Algorithm for Globally Solving Sum of Linear Ratios Problems

Author:

Jiao Hongwei1ORCID,Cai Lei2ORCID,Hou Zhisong2,Bai Chunyang1ORCID

Affiliation:

1. School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China

2. School of Information Engineering, Henan Institute of Science and Technology, Xinxiang 453003, China

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.

Funder

Cultivation Plan of Young Key Teachers in Colleges and Universities of Henan Province

Publisher

Hindawi Limited

Subject

Electrical and Electronic Engineering,Computer Science Applications,Modelling and Simulation

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