A Global Optimization Algorithm for Solving the Minimum Multiple Ratio Spanning Tree Problem∗

This paper studies the sum-of-ratios version of the classical minimum spanning tree (MST) problem. We develop a branch-and-bound algorithm for solving the general version of the problem based on its image space representation. The suggested approach specifically addresses the difficulties arising in the case when the number of ratios exceeds two. The efficacy of our approach is demonstrated on randomly generated complete and sparse graph instances. Key words: fractional programming, sum-of-ratios, multiple-ratio minimum spanning tree 1