Solve Constrained Minimum Spanning Tree By cross-entropy (CE) method

Abstract

Given an undirected graph and nonnegative numbers as weights for each edge, we consider the problem of finding a spanning tree that has lowest total cost with respect to cost weight and has constrained budget with respect to constrains weight [1]. Different from the traditional Lagrangean relaxation method, we proposed a new randomized method for solving the constrained spanning tree problem in this paper. For this newly proposed method every solution found is in the original problem’s feasible region, there is no need to do the hard work to close the gap between the Lagrangean relaxation and the original problem. And the proposed algorithm is very easy to parallelize, can take full advantage of multi-core processors to improve problem solving efficiency. For most optimization algorithms, properly selecting the super parameters have big impact on the algorithm’s practical performance. Through computer numerical simulation, we can see that our algorithm is robust to super parameters.