A Record-to-Record Travel Approach for solving the Capacitated Minimum Spanning Tree Problem

A Capacitated Minimum Spanning Tree (CMST) is a minimal cost spanning tree of a graph that has a designated root node r and satisfies the capacity constraint k. The CMST problem is proved to be NP-complete and has wide theoretical and practical applications. In this paper a novel approach based on the Record-to-Record Travel (RRT) method, which is a deterministic variant of the Simulated Annealing (SA), is presented for solving the CMST problem. First the demand nodes are partitioned into a number of clusters in the form of subgraphs connected to the root node. After that the capacity constraints have been satisfied, the minimum spanning tree of each partition is determined. Finally, the costs of all MSTs are integrated to yield the CMST of the whole graph. Experimental results showed the success of the proposed approach in solving CMST problem instances