A Two-Level Hybrid Based Genetic Algorithm to Solve the Clustered Shortest-Path Tree Problem Using the Prüfer Code.

The clustered shortest-path tree (CluSPT) problem is a generalization of the popular shortest path problem, in which, given a graph with the set of vertices divided into a given set of clusters, we look for a shortest-path spanning tree from a predefined source vertex to all the other vertices of the graph, with the property that every cluster should generate a connected subgraph. In this paper, we describe a two-level hybrid algorithm to solve the CluSPT problem, in which a framework with a macro-level genetic algorithm (GA) used to generate trees connecting the clusters using Prufer code, is combined with a micro-level algorithm based on dynamic programming (DP) that determines the best corresponding feasible solution of the CluSPT problem associated to a given tree spanning the clusters. Finally, some preliminary computational results are stated on a set of 40 standard benchmark non-euclidean instances from the literature to illustrate the performance of our developed two-level hybrid algorithm. The obtained computational results demonstrate that our novel hybrid algorithm is highly competitive against the existing algorithms.