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Volume 42, Issue 3
A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem

Bo Zhang, Yuelin Gao, Xia Liu & Xiaoli Huang

J. Comp. Math., 42 (2024), pp. 784-813.

Published online: 2024-04

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  • 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.

  • AMS Subject Headings

90C57, 90C26

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-42-784, author = {Zhang , BoGao , YuelinLiu , Xia and Huang , Xiaoli}, title = {A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem}, journal = {Journal of Computational Mathematics}, year = {2024}, volume = {42}, number = {3}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2210-m2021-0067}, url = {http://global-sci.org/intro/article_detail/jcm/23036.html} }
TY - JOUR T1 - A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem AU - Zhang , Bo AU - Gao , Yuelin AU - Liu , Xia AU - Huang , Xiaoli JO - Journal of Computational Mathematics VL - 3 SP - 784 EP - 813 PY - 2024 DA - 2024/04 SN - 42 DO - http://doi.org/10.4208/jcm.2210-m2021-0067 UR - https://global-sci.org/intro/article_detail/jcm/23036.html KW - Global optimization, Branch and bound, Quadratic fractional programming, Mixed integer programming. AB -

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.

Bo Zhang, Yuelin Gao, Xia Liu & Xiaoli Huang. (2024). A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem. Journal of Computational Mathematics. 42 (3). 784-813. doi:10.4208/jcm.2210-m2021-0067
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