RT Journal Article
T1 Solving the multi-objective Hamiltonian cycle problem using a Branch-and-Fix based algorithm
A1 Murua, M.
A1 Galar, D.
A1 Santana, R.
AB 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.
SN 1877-7503
YR 2022
FD 2022-04
LA eng
NO Murua , M , Galar , D & Santana , R 2022 , ' Solving the multi-objective Hamiltonian cycle problem using a Branch-and-Fix based algorithm ' , Journal of Computational Science , vol. 60 , 101578 , pp. 101578 . https://doi.org/10.1016/j.jocs.2022.101578
NO Publisher Copyright: © 2022 Elsevier B.V.
DS TECNALIA Publications
RD 1 jul 2024