%0 Journal Article %A Murua, M. %A Galar, D. %A Santana, R. %T Solving the multi-objective Hamiltonian cycle problem using a Branch-and-Fix based algorithm %D 2022 * Elsevier %X The Hamiltonian cycle problem consists of finding a cycle in a given graph that passes through every single vertex exactly once, or determining that this cannot be achieved. In this investigation, a graph is considered with an associated set of matrices. The entries of each of the matrix correspond to a different weight of an arc. A multi-objective Hamiltonian cycle problem is addressed here by computing a Pareto set of solutions that minimize the sum of the weights of the arcs for each objective. Our heuristic approach extends the Branch-and-Fix algorithm, an exact method that embeds the problem in a stochastic process. To measure the efficiency of the proposed algorithm, we compare it with a multi-objective genetic algorithm in graphs of a different number of vertices and density. The results show that the density of the graphs is critical when solving the problem. The multi-objective genetic algorithm performs better (quality of the Pareto sets) than the proposed approach in random graphs with high density; however, in these graphs it is easier to find Hamiltonian cycles, and they are closer to the multi-objective traveling salesman problem. The results reveal that, in a challenging benchmark of Hamiltonian graphs with low density, the proposed approach significantly outperforms the multi-objective genetic algorithm. %@ 1877-7503 %K Graph theory %K Multi-objective optimization %K Discrete optimization problems %K Hamiltonian cycle problem %K Branching algorithm doi 10.1016/j.jocs.2022.101578 %U http://hdl.handle.net/11556/1271 %~ GOEDOC, SUB GOETTINGEN