¹School of Mathematical Sciences, Henan Institute of Science and Technology, Xinxiang 453003, China
²Henan Mechanical and Electrical Engineering College, Xinxiang 453002, China
³Department of Mathematics, Henan University, Xinxiang 453000, China

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Abstract—This article presents a branch-and-bound algorithm for globally solving the general linear sum of ratios problem (GFP). By utilizing equivalent transformation and linearization technique, a linear relaxation programming (LRP) of original problem is constructed. The algorithm economizes the required computations by conducting the branch-and-bound search in Rp , rather than in Rn , where p is the number of ratios in the objective function of problem (P) and n is the number of decision variables in problem (P). To implement the algorithm, the main computations involve solving a sequence of linear programming problems for which simplex algorithm are available. Numerical experiments are given to demonstrate that the proposed algorithm can systematically solve problem (GFP) to find the global optimum.

Index Terms—Global optimization, linear relaxation, branch and bound, fractional programming, sum-of-ratios.

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Cite: Baolin Ma, Lei Geng, Jingben Yin, Liping Fan, "An Effective Algorithm for Globally Solving a Class of Linear Fractional Programming Problem," Journal of Software vol. 8, no. 1, pp. 118-125, 2013.