A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem (Journal of Computational Mathematics, 2024)
The mixed-integer quadratically constrained quadratic fractional programming (MIQCQFP) problem often appears in various fields such as engineering practice, managementscience and network communication. However, most of the solutions to such problemsare often designed for their unique circumstances. This paper puts forward a new globaloptimization algorithm for solving the problem MIQCQFP. We first convert the MIQCQFP into an equivalent generalized bilinear fractional programming (EIGBFP) problemwith integer variables. Secondly, we linearly underestimate and linearly overestimate thequadratic functions in the numerator and the denominator respectively, and then givea 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 solvingMIQCQFP globally is proposed. Finally, a series of test problems are given to illustratethe effectiveness, feasibility and other performance of this algorithm.