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This article presents global optimization algorithm for globally solving the nonlinear sum of ratios problem (NRS) on nonconvex feasible region. Two folds are presented. Firstly, a problem (P1) is derived which is equivalent to problem (NRS). Second, by utilizing the parametric linearization relaxation method, initial non-convex nonlinear problem (NRS) is reduce to a sequence of linear programming problems through the successive refinement of a linear relaxation of feasible region and of the objective function. 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. A numerical example is given to illustrate the feasibility of the present algorithm.