- Tytuł:
- A genetic algorithm for the maximum 2-packing set problem
- Autorzy:
-
Trejo-Sánchez, Joel Antonio
Fajardo-Delgado, Daniel
Gutierrez-Garcia, J. Octavio - Powiązania:
- https://bibliotekanauki.pl/articles/330154.pdf
- Data publikacji:
- 2020
- Wydawca:
- Uniwersytet Zielonogórski. Oficyna Wydawnicza
- Tematy:
-
maximum 2-packing set
genetic algorithms
graph algorithms
algorytm genetyczny
algorytm grafowy - Opis:
- Given an undirected connected graph G = (V, E), a subset of vertices S is a maximum 2-packing set if the number of edges in the shortest path between any pair of vertices in S is at least 3 and S has the maximum cardinality. In this paper, we present a genetic algorithm for the maximum 2-packing set problem on arbitrary graphs, which is an NP-hard problem. To the best of our knowledge, this work is a pioneering effort to tackle this problem for arbitrary graphs. For comparison, we extended and outperformed a well-known genetic algorithm originally designed for the maximum independent set problem. We also compared our genetic algorithm with a polynomial-time one for the maximum 2-packing set problem on cactus graphs. Empirical results show that our genetic algorithm is capable of finding 2-packing sets with a cardinality relatively close (or equal) to that of the maximum 2-packing sets. Moreover, the cardinality of the 2-packing sets found by our genetic algorithm increases linearly with the number of vertices and with a larger population and a larger number of generations. Furthermore, we provide a theoretical proof demonstrating that our genetic algorithm increases the fitness for each candidate solution when certain conditions are met.
- Źródło:
-
International Journal of Applied Mathematics and Computer Science; 2020, 30, 1; 173-184
1641-876X
2083-8492 - Pojawia się w:
- International Journal of Applied Mathematics and Computer Science
- Dostawca treści:
- Biblioteka Nauki
Artykuł