A Modified Binary Crow Search Algorithm for Solving the Graph Coloring Problem

The graph coloring problem (GCP) is a well-known classical combinatorial optimization problem in graph theory. It is known to be an NP-Hard problem, so many heuristic algorithms have been employed to solve this problem. This article proposes a modified binary crow search algorithm (MBCSA) to solve t...

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Published in:International journal of applied evolutionary computation Vol. 11; no. 2; pp. 28 - 46
Main Authors: Mahseur, Mohammed, Meraihi, Yassine, Acheli, Dalila
Format: Journal Article
Language:English
Published: Hershey IGI Global 01.04.2020
Subjects:
Algorithms
Combinatorial analysis
Graph coloring
Graph theory
Heuristic methods
Normal distribution
Random variables
Search algorithms
Statistical analysis
Transfer functions
ISSN:1942-3594, 1942-3608
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Abstract The graph coloring problem (GCP) is a well-known classical combinatorial optimization problem in graph theory. It is known to be an NP-Hard problem, so many heuristic algorithms have been employed to solve this problem. This article proposes a modified binary crow search algorithm (MBCSA) to solve the graph coloring problem. First, the binary crow search algorithm is obtained from the original crow search algorithm using the V-shaped transfer function and the discretization method. Second, we use chaotic maps to choose the right values of the flight length (FL) and the awareness probability (AP). Third, we adopt the Gaussian distribution method to replace the random variables used for updating the position of the crows. The aim of these contributions is to avoid the premature convergence to local optima and ensure the diversity of the solutions. To evaluate the performance of our algorithm, we use the well-known DIMACS benchmark graph coloring instances. The simulation results reveal the efficiency of our proposed algorithm in comparison with other existing algorithms in the literature.
AbstractList The graph coloring problem (GCP) is a well-known classical combinatorial optimization problem in graph theory. It is known to be an NP-Hard problem, so many heuristic algorithms have been employed to solve this problem. This article proposes a modified binary crow search algorithm (MBCSA) to solve the graph coloring problem. First, the binary crow search algorithm is obtained from the original crow search algorithm using the V-shaped transfer function and the discretization method. Second, we use chaotic maps to choose the right values of the flight length (FL) and the awareness probability (AP). Third, we adopt the Gaussian distribution method to replace the random variables used for updating the position of the crows. The aim of these contributions is to avoid the premature convergence to local optima and ensure the diversity of the solutions. To evaluate the performance of our algorithm, we use the well-known DIMACS benchmark graph coloring instances. The simulation results reveal the efficiency of our proposed algorithm in comparison with other existing algorithms in the literature.
Author Mahseur, Mohammed
Meraihi, Yassine
Acheli, Dalila
AuthorAffiliation University of Sciences and Technology Houari Boumediene, Bab Ezzouar, Algeria
University of M'Hamed Bougara, Boumerdes, Algeria
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  surname: Meraihi
  fullname: Meraihi, Yassine
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  givenname: Dalila
  surname: Acheli
  fullname: Acheli, Dalila
  organization: University of M'Hamed Bougara, Boumerdes, Algeria
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SubjectTerms Algorithms
Combinatorial analysis
Graph coloring
Graph theory
Heuristic methods
Normal distribution
Random variables
Search algorithms
Statistical analysis
Transfer functions
Title A Modified Binary Crow Search Algorithm for Solving the Graph Coloring Problem
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