A Novel Branch‐And‐Bound Algorithm for Minimizing a Class of Generalized Sum of Linear Ratio Programming Problems

ABSTRACT This paper proposes an efficient algorithm for solving generalized sum of linear ratio programming problems (GSLRP) to obtain global optimal solutions. To establish this algorithm, we employ convex separation techniques to construct a linear relaxation problem that is computationally tractable and provides a rigorous lower bound for the original problem. Based on a branch‐and‐bound framework and the previously proposed linear programming relaxation problem, a corresponding branch‐and‐bound algorithm is proposed in this paper, and the convergence of the algorithm is analyzed. Finally, numerical experiments demonstrate the feasibility and effectiveness of this algorithm.