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 - <p style="text-align: justify;">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.</p>