An Evolutionary Algorithm Based on CMSA for Rooted Max Tree Coverage

doi:10.1109/TEVC.2024.3522012

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An Evolutionary Algorithm Based on CMSA for Rooted Max Tree Coverage

2024-12-23

PRE

Jiang Zhou

Peng Zhang

DOI：10.1109/TEVC.2024.3522012

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Abstract

En 中文

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.

Keywords:

Construct

merge

solve

and adapt (CMSA)

combinatorial optimization

evolutionary algorithm

heuristic algorithm

max tree cover