A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem
Year: 2024
Author: Bo Zhang, Yuelin Gao, Xia Liu, Xiaoli Huang
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 3 : pp. 784–813
Abstract
The mixed-integer quadratically constrained quadratic fractional programming (MIQCQFP) problem often appears in various fields such as engineering practice, management science and network communication. However, most of the solutions to such problems are often designed for their unique circumstances. This paper puts forward a new global optimization algorithm for solving the problem MIQCQFP. We first convert the MIQCQFP into an equivalent generalized bilinear fractional programming (EIGBFP) problem with integer variables. Secondly, we linearly underestimate and linearly overestimate the quadratic functions in the numerator and the denominator respectively, and then give a linear fractional relaxation technique for EIGBFP on the basis of non-negative numerator. After that, combining rectangular adjustment-segmentation technique and midpoint-sampling strategy with the branch-and-bound procedure, an efficient algorithm for solving MIQCQFP globally is proposed. Finally, a series of test problems are given to illustrate the effectiveness, feasibility and other performance of this algorithm.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2210-m2021-0067
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 3 : pp. 784–813
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 30
Keywords: Global optimization Branch and bound Quadratic fractional programming Mixed integer programming.