Applied Intelligence

, Volume 49, Issue 7, pp 2546–2566 | Cite as

Generalized vertex cover using chemical reaction optimization

  • Md. Rafiqul IslamEmail author
  • Imran Hossain Arif
  • Rifat Hasan Shuvo


The generalized vertex cover problem (GVC) is a new variant of classic vertex cover problem which considers both vertex and weight of the edge into the objective function. The GVC is a renowned NP-hard optimization problem that finds the vertex subset where the sum of vertices and edge weight are minimized. In the mathematical field of electrical, networking and telecommunication GVC is used to solve the vertex cover problem. Finding the minimum vertex cover using GVC has a great impact on graph theory. Some exact algorithms were proposed to solve this problem, but they failed to solve it for real-world instances. Some approximation and metaheuristic algorithms also were proposed to solve this problem. Chemical Reaction Optimization (CRO) is an established population-based metaheuristic for optimization and comparing with other existing optimization algorithms it gives better results in most of the cases. The CRO algorithm helps to explore the search space locally and globally over the large population area. In this paper, we are proposing an algorithm by redesigning the basic four operators of CRO to solve GVC problem and an additional operator named repair function is used to generate optimal or near-optimal solutions. We named the proposed algorithm as GVC_CRO. Our proposed GVC_CRO algorithm is compared with the hybrid metaheuristic algorithm (MAGVCP), the local search with tabu strategy and perturbation mechanism (LSTP) and Genetic Algorithm (GA), which are state of the arts. The experimental results show that our proposed method gives better results than other existing algorithms to solve the GVC problem with less execution time in maximum cases. Statistical test has been performed to demonstrate the superiority of the proposed algorithm over the compared algorithm.


Chemical reaction optimization (CRO) Generalized vertex cover problem Decomposition Synthesis Metaheuristic 


Compliance with Ethical Standards

Conflict of interests

The authors have no conflict of interest.


  1. 1.
    Cai S, Su K, Chen Q (2010) Ewls: A new local search for minimum vertex cover. In: AAAIGoogle Scholar
  2. 2.
    Guo J, Niedermeier R, Wernicke S (2007) Parameterized complexity of vertex cover variants. Theory Comput Syst 41(3):501–520MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Hassin R, Levin A (2003) The minimum generalized vertex cover problem. In: European symposium on algorithms, pp 289-300. SpringerGoogle Scholar
  4. 4.
    Hu S, Li R, Zhao P, Yin M (2018) A hybrid metaheuristic algorithm for generalized vertex cover problem. Memetic Computing 10(2):165–176CrossRefGoogle Scholar
  5. 5.
    Islam MR, Saifullah CMK, Asha ZT, Ahmet R (2018) Chemical reaction optimization for solving longest common subsequence problem for multiple string. Soft Comput 1–25.
  6. 6.
    James JQ, Lam AYS (2011) Victor OK Li. Evolutionary artificial neural network based on chemical reaction optimization. In: IEEE congress on evolutionary computation (CEC), pp 2083-2090, IEEE, pp 2011Google Scholar
  7. 7.
    Kabir R, Islam R (2018) Chemical reaction optimization for rna structure prediction. Appl Intell 1–24.
  8. 8.
    Karakostas G (2009) A better approximation ratio for the vertex cover problem. ACM Trans Algorithms (TALG) 5(4):41MathSciNetzbMATHGoogle Scholar
  9. 9.
    Karp RM (1972) Reducibility among combinatorial problems, pp 85-103. In: Miller RE, Thatcher JW (eds) Complexity of computer computationsGoogle Scholar
  10. 10.
    Kochenberger G, Lewis M, Glover F, Wang H (2015) Exact solutions to generalized vertex covering problems: a comparison of two models. Optim Lett 9(7):1331–1339MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lam AYS, Li VOK (2012) Chemical reaction optimization: a tutorial. Memetic Computing 4(1):3–17CrossRefGoogle Scholar
  12. 12.
    Li R, Hu S, Wang Y, Yin M (2017) A local search algorithm with tabu strategy and perturbation mechanism for generalized vertex cover problem. Neural Comput & Applic 28(7):1775– 1785CrossRefGoogle Scholar
  13. 13.
    Milanovi M (2012) Solving the generalized vertex cover problem by genetic algorithm. Commun Inf 29 (6+):1251–1265Google Scholar
  14. 14.
    Saifullah KCM, Islam MR (2016) Chemical reaction optimization for solving shortest common supersequence problem. Comput Biol Chem 64:82–93CrossRefGoogle Scholar
  15. 15.
    Truong TK, Li K, Xu Y (2013) Chemical reaction optimization with greedy strategy for the 0-1 knapsack problem. Appl Soft Comput 13(4):1774–1780CrossRefGoogle Scholar
  16. 16.
    Xu J, Lam AYS, Li VOK (2010) Parallel chemical reaction optimization for the quadratic assignment problem. In: World Congress in Computer Science, Computer engineering, and applied computing, Worldcomp 2010Google Scholar
  17. 17.
    Xu J, Lam AYS, Li VOK (2011) Chemical reaction optimization for task scheduling in grid computing. IEEE Trans Parallel Distrib Syst 22(10):1624–1631CrossRefGoogle Scholar
  18. 18.
    Pooja P, Punnen AP (2018) The generalized vertex cover problem and some variations. Discrete OptimizationGoogle Scholar
  19. 19.
    Bugra C et al (2014) On partial vertex cover and budgeted maximum coverage problems in bipartite graphs. In: IFIP international conference on theoretical computer science. Springer, BerlinGoogle Scholar
  20. 20.
    Reuven B-Y, Hermelin D, Rawitz D (2010) An extension of the Nemhauser-Trotter theorem to generalized vertex cover with applications. SIAM J Discret Math 24.1:287–300MathSciNetzbMATHGoogle Scholar
  21. 21.
    Oliveto PS, He J, Yao X (2007) Evolutionary algorithms and the vertex cover problem. In: IEEE congress on evolutionary computation, 2007. CEC 2007. IEEEGoogle Scholar
  22. 22.
    Jochen K, Parekh O, Segev D (2006) A unified approach to approximating partial covering problems.European symposium on algorithms. Springer, BerlinzbMATHGoogle Scholar
  23. 23.
    Mitchell M (2003) Genetic algorithms. pp 747-748Google Scholar

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Md. Rafiqul Islam
    • 1
    Email author
  • Imran Hossain Arif
    • 1
  • Rifat Hasan Shuvo
    • 1
  1. 1.Computer Science & Engineering DisciplineKhulna UniversityKhulnaBangladesh

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