A Multilevel Genetic Algorithm for the Traveling Salesman Problem

In this paper, we introduce a multilevel genetic algorithm for the traveling salesman problem. The resulting new algorithm starts by coarsening the original problem into a sequence of smaller problems using a coarsening scheme. Thereafter an initial feasible population is generated at the smallest problem and this population is projected back to the original problem by going through a refinement phase at each intermediate level using a simple genetic algorithm. Experimental results indicate that the combination of the genetic algorithm with the multilevel paradigm produces tours of better quality than those produced by the standard genetic algorithm.