An Efficient Algorithm for Quadratic Sum-of-Ratios Fractional Programs Problem

ABSTRACT

The quadratic sum-of-ratios fractional program problem has a broad range of applications in practical problems. This article will present an efficient branch-and-bound algorithm for globally solving the quadratic sum-of-ratios fractional program problem. In this algorithm, lower bounds are computed by solving a series of parametric relaxation linear programming problems, which are established by utilizing new parametric linearizing technique. To enhance the computational speed of the proposed algorithm, a rectangle reducing tactic is used to reject a part of the investigated rectangle or the whole rectangle where there does not contain any global optimal solution of the quadratic sum-of-ratios fractional program problem. Compared with the known approaches, the proposed algorithm does not need to introduce new variables and constraints. Therefore, the proposed algorithm is more suitable for application in engineering.

KEYWORDS:

• Branch-and-bound
• fractional programs
• global optimization
• parametric linearizing technique
• quadratic sum-of-ratios

MATHEMATICS SUBJECT CLASSIFICATION:

• 90C30
• 90C32
• 65K05

Acknowledgment

The authors are grateful to the responsible editor and the anonymous referees for their valuable comments and suggestions, which have greatly improved the earlier version of this paper.