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

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...

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Veröffentlicht in:Journal of computational science Jg. 60; S. 101578
Hauptverfasser: Murua, M., Galar, D., Santana, R.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier B.V 01.04.2022
Schlagworte:
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
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Beschreibung
Zusammenfassung: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.
ISSN:1877-7503
1877-7511
1877-7511
DOI:10.1016/j.jocs.2022.101578