A hybrid genetic algorithm for the Hamiltonian p-median problem

The Hamiltonian p-median problem consists of finding p($p$ is given) non-intersecting Hamiltonian cycles in a complete edge-weighted graph such that each cycle visits at least three vertices and each vertex belongs to exactly one cycle, while minimizing the total cost of pcycles. In this work, we present an effective and scalable hybrid genetic algorithm to solve this computationally challenging problem. The algorithm combines an edge-assembly crossover to generate promising offspring solutions from high-quality parents, and a multiple neighborhood local search to improve each offspring solution. To promote population diversity, the algorithm applies a mutation operator to the offspring solutions and a quality-and-distance update strategy to manage the population. We compare the method to the best reference algorithms in the literature based on three sets of 145 popular benchmark instances (with up to 318 vertices), and report improved best upper bounds for eight instances. To evaluate the scalability of the method, we perform experiments on a new set of 70 large instances (with up to 1060 vertices). We examine the contributions of key components of the algorithm.