{'fraction_non_alphanumeric': 0.02771618625277162, 'fraction_numerical': 0.0, 'mean_word_length': 5.359154929577465, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
An Effective Algorithm for Globally Solving a Class of Linear Fractional Programming Problem

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 R^p , rather than in R^n , 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.