A new deterministic global computing algorithm for solving a kind of linear fractional programming

This paper investigates a class of linear fractional programming (LFP) problem, which minimizes the sum of a finite number of linear fractional functions over a polyhedral region. Firstly, the equivalence problem (EP) of the LFP problem is given by a new two-stage transformation method. Secondly, considering the characteristics that the branch-and-bound algorithm can guarantee the global optimality of the solution to an optimization problem, and then based on the EP, we discuss the bounding operation, branching operation, pruning operation and rectangle-region reduction technique of this algorithm. After that, the convergence of the algorithm is proved and its computational complexity is deduced from the worst case. Finally, some experiments are reported to verify the effectiveness, feasibility and other performance of the proposed algorithm.

Automated summary

This paper investigates linear fractional programming (LFP) problem and provides an equivalence problem using a new two-stage transformation method. The characteristics of the branch-and-bound algorithm are considered to discuss the operations and complexity of the algorithm. The effectiveness, feasibility, and other performance of the proposed algorithm are verified through experiments.