An Evolutionary Algorithm Based on CMSA for Rooted Max Tree Coverage

Abstract

The rooted max tree coverage (MTC) problem has wide applications in areas, such as network design and vehicle routing. Given a graph with non-negative costs defined on edges, a vertex used as the root, and a budget, the rooted MTC problem asks to find a tree containing the root and having total cost at most the budget, so that the number of vertices spanned by the tree is maximized. Rooted MTC is NP-hard and has constant factor approximation algorithms. However, the existing approximation algorithms for rooted MTC are very complicated and hard to be implemented practically. In this article, we formulate a polynomial size mixed integer linear program (MILP) for rooted MTC for the first time. Based on this, we develop a simple evolutionary algorithm for rooted MTC (called CMSA-MTC) using the CMSA meta-heuristic, where construct, merge, solve, and adapt (CMSA) is a meta-heuristic proposed recently. Experimental results show that CMSA-MTC has very good practical performance. For the small size instances of the problem, CMSA-MTC almost always finds the optimal solutions. For the large size instances, CMSA-MTC finds solutions better than that of CPLEX within the same running time and two additional greedy algorithms.