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Application of Hybrid Metaheuristics in Solving Magic Type Labeling of Graphs

Kafaei Kashefi Moghaddam, Peyman | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44143 (01)
  4. University: Sharif University of Technology
  5. Department: Industrial Engineering
  6. Advisor(s): Eshghi, Koorosh
  7. Abstract:
  8. Graph Labeling is one of the most active initiatives in graph theory which was introduced in the early 1960’s. One of the most prominent kind of labeling in literature is magic-type labeling inspired by defining magic numbers and magic squares. It also encompasses various types. Total edge magic labeling of Graph G, is a bijection f from V(G)∪E(G) on the set of {1,2,…,|V(G) |+|E(G) |}, on this condition that the summation of each edge label and its vertices’ labels is constant for all edges. Since introducing total edge magic labeling, numerous researches is done that mostly are dedicated to prove mathematical theorems and depicting a whether a distinct graph is magic or not. Therefore, it is proper to propose an algorithm on the procedure of magic labeling of graphs. Before this, only one algorithm based on mathematical modeling has been developed. In this research a hybrid algorithm composed of ant colony optimization and simulated annealing is proposed and parameters are deduced by design of experiments technique and response surface method. The feasible solution created by this algorithm is an edge magic total labeling of desired graph. Results of applying this algorithm on various types of graphs are compared with the ones of the algorithm based on mathematical modeling. It is showed that for many types of graphs, the proposed algorithm has a better performance
  9. Keywords:
  10. Graph Labeling ; Hybrid Meta Heuristic Algorithm ; Ant Colony Optimization (ACO) ; Simulated Annealing Method ; Magic Labeling ; Edge Magic Total Labeling

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