A branch-and-bound algorithm to globally solve the sum of several linear ratios

In this paper we propose a branch-and-bound algorithm to globally solve the sum of several linear fractional functions over a polytope. For minimizing problem a linear lower bounding function (LLBF) of the objective function is constructed, then a linear programming is obtained which is solved by a simplex algorithm and provides the lower bounding of the optimal value. The proposed branch-and-bound algorithm is convergent to the global minimum through the successive refinement of the solutions of a series of linear programming problems. The numerical experiment is reported to show the effectiveness and feasibility of the proposed algorithm. Also, this method is extended to solve the maximizing problems. (c) 2004 Elsevier Inc. All rights reserved.