A Clustering-Enhanced Memetic Algorithm for the Quadratic Minimum Spanning Tree Problem

Abstract

The quadratic minimum spanning tree problem (QMSTP) is a spanning tree optimization problem that considers the interaction cost between pairs of edges arising from a number of practical scenarios. This problem is NP-hard, and therefore there is not a known polynomial time approach to solve it. To find a close-to-optimal solution to the problem in a reasonable time, we present for the first time a clustering-enhanced memetic algorithm (CMA) that combines four components, i.e., (i) population initialization with clustering mechanism, (ii) a tabu-based nearby exploration phase to search nearby local optima in a restricted area, (iii) a three-parent combination operator to generate promising offspring solutions, and (iv) a mutation operator using Lévy distribution to prevent the population from premature. Computational experiments are carried on 36 benchmark instances from 3 standard sets, and the results show that the proposed algorithm is competitive with the state-of-the-art approaches. In particular, it reports improved upper bounds for the 25 most challenging instances with unproven optimal solutions, while matching the best-known results for all but 2 of the remaining instances. Additional analysis highlights the contribution of the clustering mechanism and combination operator to the performance of the algorithm.

Keywords

• quadratic minimum spanning tree problem
• memetic algorithm
• combinatorial optimization
• agglomerative clustering