Solving the multi-objective Hamiltonian cycle problem using a Branch-and-Fix based algorithm

• Published in: Journal of computational science Vol. 60; p. 101578
• Main Authors: Murua, M., Galar, D., Santana, R.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2022
• Subjects: Branching algorithm; Discrete optimization problems; Drift och underhållsteknik; Graph theory; Hamiltonian cycle problem; Multi-objective optimization; Operation and Maintenance; Branching algorithm; Graph theory; Multi-objective optimization; Hamiltonian cycle problem; Discrete optimization problems
• ISSN: 1877-7503; 1877-7511; 1877-7511
• DOI: 10.1016/j.jocs.2022.101578

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. •An algorithm for solving the multi-objective Hamiltonian cycle problem.•It is an heuristic approach that can apply for both directed and undirected graphs.•Compared to multi-objective genetic algorithm in different benchmarks.•Outstanding results for large-sized graphs up to 3000 nodes.