An Effective Genetic Algorithm for Solving the Clustered Shortest-Path Tree Problem

The clustered shortest-path tree problem (CluSPTP) is an extension of the classical single-source problem, in which, given a graph with set nodes partitioned into predefined, mutually exclusive and exhaustive clusters, we are looking for spanning from source to all other graph, property that each cluster should induce connected subtree. CluSPTP belongs class generalized combinatorial optimization problems, and, general, proved be non-deterministic polynomial time hard (NP-hard) problem. In this paper, propose novel genetic algorithm (GA), which designed fit challenges investigated main features our GA are: use innovative representation scheme allows us define meaningful operators hybrid initial population. Extensive computational results reported discussed two sets instances: euclidean non-euclidean. performance proposed was evaluated on six types benchmark instances available literature non-euclidean obtained corresponding ones. show improvement respect existing methods literature, both terms quality achieved solutions computation times necessary obtain them. They demonstrate outperforms providing optimal 30 independent trials.