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A hybrid algorithm based on modified chemical reaction optimization and best-first search algorithm for solving minimum vertex cover problem

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Abstract

The minimum vertex cover problem (MVCP) is one of the well-known NP-complete problems that can be used to formulate numerous real-life applications. The MVCP has been solved using different approaches, exact, heuristic, and metaheuristic. Chemical reaction optimization (CRO) is a population-based metaheuristic algorithm that simulates what happens in chemical reactions to solve many problems. In this paper, the MVCP is solved using hybridization of a modified version of the CRO algorithm and the best-first search (BFS) algorithm. This hybridization is symbolized by MCROA-BFS. The BFS algorithm is exploited to generate initial populations with high-quality initial solutions in comparison with the random bit-vector (RBV) approach as a traditional approach for generating initial populations for several population-based metaheuristic algorithms. At first, the MCROA is evaluated analytically in terms of run time complexity. Then the performance of the MCROA is evaluated experimentally to show the effectiveness of exploiting the BFS in terms of quality of gained solutions and run time. The most valuable player algorithm (MVPA), genetic algorithm (GA), and hybrid CRO algorithm (HCROA) are metaheuristic algorithms that used the RBV approach to generate the initial population. MCROA-BFS is compared, under the selected performance metrics, with these metaheuristic algorithms in addition to MCROA with the RBV approach (MCROA-RBV). The conducted experiments were carried out using 18 instances of DIMACS and BHOSLIB benchmarks. The experimental results revealed the superiority of MCROA-BFS over MVPA, GA, and MCROA-RBV in terms of both performance metrics. Although HCROA has the smallest run time, it failed to obtain high-quality solutions in comparison with MCROA.

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References

  1. Cormen T, Leiserson C, Rivest R, Stein C (2001) Introduction to algorithms. MIT press Cambridge, London

    MATH  Google Scholar 

  2. Kavalci V, Ural A, Dagdeviren O (2014) Distributed vertex cover algorithms for wireless sensor networks. Int J Comput Netw Commun 6(1):95–110. https://doi.org/10.5121/ijcnc.2014.6107

    Article  Google Scholar 

  3. Barah M, Mazaheri E (2012) Matching theory. In: Farahani R, Miandoabchi E (eds) Graph theory for operations research and management: applications in industrial engineering. Book News, Portland, pp 127–141

    Google Scholar 

  4. Sperschneider V (2008) Bioinformatics: problem solving paradigms. Springer, Berlin

    MATH  Google Scholar 

  5. Islam M, Arif I, Shuvo R (2019) Generalized vertex cover using chemical reaction optimization. Appl Intell 49:2546–2566. https://doi.org/10.1007/s10489-018-1391-z

    Article  Google Scholar 

  6. Khattab H, Sharieh A, Mahafzah B (2019) Most valuable player algorithm for solving minimum vertex cover problem. Int J Adv Comput Sci Appl 10(8):159–167

    Google Scholar 

  7. Eshtey M, Sliet A, Sharieh A (2016) NMVSA greedy solution for vertex cover problem. Int J Adv Comput Sci Appl 7(3):60–64

    Google Scholar 

  8. Guangyong Z, Yuimg X, Kenli L, Shibin S (2016) Hybrid chemical reaction optimization algorithm for minimum vertex cover problem. Electr Tech Info Sci 33(9):2669–2672

    Google Scholar 

  9. Li R, Hu S, Wang Y, Yin M (2016) A local search algorithm with tabu strategy and perturbation mechanism for generalized vertex cover problem. Neural Comput & Applic 28:1775–1785. https://doi.org/10.1007/s00521-015-2172-9

    Article  Google Scholar 

  10. Zhou Y, Wang Y, Gao J, Luo N, Wang J (2016) An efficient local search for partial vertex cover problem. Neural Comput & Applic 30:2245–2256. https://doi.org/10.1007/s00521-016-2800-z

    Article  Google Scholar 

  11. 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):1331–1339. https://doi.org/10.1007/s11590-015-0851-1

    Article  MathSciNet  MATH  Google Scholar 

  12. Khan I, Khan S (2014) Experimental comparison of five approximation algorithms for minimum vertex cover. Int J u-and e-Service 7(6):69–84

    Google Scholar 

  13. Cai S, Su K, Sattar A (2011) Local Search with edge weighting and configuration checking heuristics for minimum vertex cover. Artif Intell 175:1672–1696. https://doi.org/10.1016/j.artint.2011.03.003

    Article  MathSciNet  MATH  Google Scholar 

  14. Jovanovic R, Tuba M (2011) An ant colony optimization algorithm with improved pheromone correction strategy for the minimum weight vertex cover problem. Appl Soft Comput 11(8):5360–5366. https://doi.org/10.1016/j.asoc.2011.05.023

    Article  Google Scholar 

  15. Moser H (2005) Exact algorithms for generalizations of vertex cover. Thesis, Friedrich-Schiller University

  16. Karakostas G (2004) A better approximation ratio for the vertex cover problem. ECCC Report TR04–084

  17. Amritkar A, Sturler E, Swirydowicz K, Tafti D, Ahuja K (2015) Recycling Krylov subspaces for CFD applications and a new hybrid recycling solver. J Comput Phys 303:222–237

    Article  MathSciNet  MATH  Google Scholar 

  18. Khan W (2022) Numerical simulation of Chun-Hui He’s iteration method with applications in engineering. Int J Numer Method H 32(3):944–955. https://doi.org/10.1108/HFF-04-2021-0245

    Article  Google Scholar 

  19. Barari A, Ghotbi A, Farrokhzad F, Ganji D (2008) Variational iteration method and homotopy-perturbation method for solving different types of wave equations. J Appl Sci 8:120–126. https://doi.org/10.3923/jas.2008.120.126

    Article  Google Scholar 

  20. Momani S, Odibat Z (2007) Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations. Comput Math Applicat 54:910–919

    Article  MathSciNet  MATH  Google Scholar 

  21. He JH (2006) New interpretation of homotopy perturbation method. Int J Mod Phys B 20:2561–2568

    Article  Google Scholar 

  22. He JH (2000) Variational iteration method for autonomous ordinary differential systems. Applied Math Comput 114:115–123

    MathSciNet  MATH  Google Scholar 

  23. He JH (1999) Homotopy perturbation technique. Comput Methods Appl Mech Engr 178:257–262

    Article  MathSciNet  MATH  Google Scholar 

  24. He JH (2005) A new iterative method for solving algebraic equations. Appl Math Comput 135:81–84

    Google Scholar 

  25. He CH (2016) An introduction to an ancient Chinese algorithm and its modification. Int J Numer Method H 26(8):2486–2491

    Article  Google Scholar 

  26. Kenny V, Matthew N, Spencer S (2014) Heuristic algorithms. https://optimization.mccormick.northwestern.edu/index.php/Heuristic_algorithms. Accessed 2 February 2022

  27. Russell S, Nowig P (2003) Artificial intelligence: a modern approach. Pearson Education, New Jersey

    Google Scholar 

  28. Luke S (2013) Essentials of metaheuristics. Lulu Publisher

  29. Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv 35:268–308

    Article  Google Scholar 

  30. Alba E, Luque G, Nesmachnow S (2013) Parallel metaheuristics: recent advances and new trends. Int Trans Oper Res 20(1):1–48

    Article  MATH  Google Scholar 

  31. Al-Shaikh A, Mahafzah B, Alshraideh M (2021) Hybrid harmony search algorithm for social network contact tracing of COVID-19. Soft Comput. https://doi.org/10.1007/s00500-021-05948-2

    Article  Google Scholar 

  32. Mahafzah B, Jabri R, Murad O (2021) Multithreaded scheduling for program segments based on chemical reaction optimizer. Soft Comput 25(4):2741–2766. https://doi.org/10.1007/s00500-020-05334-4

    Article  Google Scholar 

  33. Bouchekara HREH (2020) Most valuable player algorithm: a novel optimization algorithm inspired from sport. Oper Res Int J 20:139–195. https://doi.org/10.1007/s12351-017-0320-y

    Article  Google Scholar 

  34. Al-Shaikh A, Mahafzah B, Alshraideh M (2019) Metaheuristic approach using grey wolf optimizer for finding strongly connected components in digraphs. J Theor Appl Inf Technol 97(16):4439–4452

    Google Scholar 

  35. Liu C, Du Y (2019) A membrane algorithm based on chemical reaction optimization for many-objective optimization problems. Knowl Based Syst 165:306–320. https://doi.org/10.1016/j.knosys.2018.12.001

    Article  Google Scholar 

  36. Masadeh R, Mahafzah B, Sharieh A (2019) Sea lion optimization algorithm. Int J Adv Comput Sci Appl 10(5):388–395

    Google Scholar 

  37. Masadeh R, Sharieh A, Mahafzah B (2019) Humpback whale optimization algorithm based on vocal behavior for task scheduling in cloud computing. Int J Adv Sci Technol 13(3):121–140

    Google Scholar 

  38. Faris H, Aljarah I, Al-Betar M, Mirjalili S (2018) Grey wolf optimizer: a review of recent variants and applications. Neural Comput & Applic 30(2):413–435. https://doi.org/10.1007/s00521-017-3272-5

    Article  Google Scholar 

  39. Martín-Moreno R, Vega-Rodríguez M (2018) Multi-objective artificial bee colony algorithm applied to the bi-objective orienteering problem. Knowl Based Syst 154:93–101. https://doi.org/10.1016/j.knosys.2018.05.005

    Article  Google Scholar 

  40. Mirjalili SZ, Mirjalili S, Saremi S, Faris H, Aljarah I (2018) Grasshopper optimization algorithm for multi-objective optimization problems. Appl Intell 48(4):805–820. https://doi.org/10.1007/s10489-017-1019-8

    Article  Google Scholar 

  41. Zhou Y, He F, Hou N, Qiu Y (2018) Parallel ant colony optimization on multi-core SIMD CPUs. Future Gener Comput Syst 79(2):473–487. https://doi.org/10.1016/j.future.2017.09.073

    Article  Google Scholar 

  42. Barham R, Aljarah I (2017) Link prediction based on whale optimization algorithm. In: proceedings of 2017 International conference on new trends in computing sciences, pp 55–60. https://doi.org/10.1109/ICTCS.2017.41

  43. Zhou Y, He F, Qiu Y (2017) Dynamic strategy based parallel ant colony optimization on GPUs for TSPs. Sci China Inf Sci 60(6):068102. https://doi.org/10.1007/s11432-015-0594-2

    Article  Google Scholar 

  44. Barham R, Sharieh A, Sliet A (2016) Chemical reaction optimization for max flow problem. Int J Adv Comput Sci Appl 7(8):189–196

    Google Scholar 

  45. Biyanto T, Fibrianto H, Nugroho G, Listijorini E, Budiati T, Huda H (2016) Duelist algorithm: an algorithm inspired by how duelist improve their capabilities in a duel. In: proceedings of international conference in swarm intelligence: advances in swarm intelligence, pp 39–47. https://doi.org/10.1007/978-3-319-41000-5_4

  46. Eswarawaka R, Mahammad SK, Reddy BE (2015) Genetic annealing with efficient strategies to improve the performance for the NP-hard and routing problems J. Exp Theor Artif Intell 27:779–788

    Article  Google Scholar 

  47. Chakraborty U, Konar D, Chakraborty C (2014) A GA based approach to find minimal vertex cover. Int J Comput Appl, National Conference cum Workshop on Bioinformatics and Computational Biology 3:5–7. https://doi.org/10.13140/2.1.3223.6326

  48. Truong TK, Li K, Xu Y (2013) Chemical reaction optimization with greedy strategy for the 0–1 knapsack problem. Appl Soft Comput 13:1774–1780

    Article  Google Scholar 

  49. Lam A, Li V (2010) Chemical-reaction-inspired metaheuristic for optimization. IEEE Trans Evol Comput 14(3):381–399. https://doi.org/10.1109/TEVC.2009.2033580

    Article  Google Scholar 

  50. Lam A, Li V (2010) Chemical reaction optimization for cognitive radio spectrum allocation. In: Proceeding of IEEE Global Telecommunications Conference, pp 1–5. https://doi.org/10.1109/GLOCOM.2010.5684065

  51. Hu B, Guo K, Wang X, Zhang J, Zhou D (2021) RRL-GAT: graph attention network-driven multi-label image robust representation learning. IEEE Internet Things J. https://doi.org/10.1109/JIOT.2021.3089180

    Article  Google Scholar 

  52. Khan M, Jabeen F, Ghouzali S, Rehman Z, Naz S, Abdul W (2021) Metaheuristic algorithms in optimizing deep neural network model for software effort estimation. IEEE Access 9:60309–60327. https://doi.org/10.1109/ACCESS.2021.3072380

    Article  Google Scholar 

  53. Hassan Sh (2020) The implication of deep neural networks in solving optimization problems for network security. Int J Comput Appl Technol 176(20):6–13

    Google Scholar 

  54. Doulah M (2019) Application of machine learning algorithms in bioinformatics. J Proteom Bioinform 3(1):1–11

    Google Scholar 

  55. Guo T, Han C, Tang S, Ding M (2019) Solving combinatorial problems with machine learning methods. In: Du DZ, Pardalos P, Zhang Z (eds) Nonlinear combinatorial optimization. Springer Optim Its Appl, vol 147. Springer, Cham

    Google Scholar 

  56. Nagy B, Szokol P (2021) A genetic algorithm for the minimum vertex cover problem with interval-valued fitness. Acta Polytech. Hungarica 18(4):105–123

    Article  Google Scholar 

  57. Wael M (2021) Shrink: an efficient construction algorithm for minimum vertex cover problem. Inf Sci Lett 10(2):255–261

    Article  Google Scholar 

  58. Truong TK, Li K, Xu Y, Ouyang A, Tang X (2013) An artificial chemical reaction optimization algorithm for multiple-choice knapsack problem. In: Proceedings of the International conference on artificial intelligence, pp 1–5.

  59. Szeto W, Liu Y, Ho S (2016) Chemical reaction optimization for solving a static bike repositioning problem. Transp Res 47:104–135

    Google Scholar 

  60. Islam R, Mahmud R, Pritom R (2020) Transportation scheduling optimization by a collaborative strategy in supply chain management with TPL using chemical reaction optimization. Neural Comput & Applic 32:3649–3674. https://doi.org/10.1007/s00521-019-04218-5

    Article  Google Scholar 

  61. Islam R, Smrity R, Chatterjee S, Mahmud R (2020) Optimization of protein folding using chemical reaction optimization in HP cubic lattice model. Neural Comput & Applic 32:3117–3134. https://doi.org/10.1007/s00521-019-04447-8

    Article  Google Scholar 

  62. Nguyen T, Li Z, Zhang S, Truong T (2014) A hybrid algorithm based on particle swarm and chemical reaction optimization. Expert Syst Appl 41:2134–2143

    Article  Google Scholar 

  63. Dam TL, Li K, Fournier-Viger P (2016) Chemical reaction optimization with unified tabu search for the vehicle routing problem. Soft Comput 20:1–13

    Google Scholar 

  64. Nayak J, Paparao S, Naik B, Seetayya N, Pradeep P, Behera HS, Pelusi D (2019) Chemical reaction optimization: A survey with application and challenges. In: Nayak J, Abraham A, Krishna B, Chandra Sekhar G, Das A (eds), Soft computing in data analytics. Adv Intell Syst Comput vol 758. Springer, Singapore

  65. Eremeev A, Khachay M, Kochetov Y, Pardalos P (2018) Optimization problems and their applications. 7th International conference, Russia, July 8–14, 2018

  66. Thomas I (1980) Greek mathematical works. Harvard University Press, London

    Google Scholar 

  67. McKinnon K, Millar C, Mongeau M (1996) Global optimization for the chemical and phase equilibrium problem using interval analysis. In: Floudas C, Pardalos P (Eds) State of the art in global optimization: computation methods and applications, 365–382

  68. Bearden J (2006) A new secretary problem with rank-based selection and cardinal payoffs. J Math Psychol 50:58–59. https://doi.org/10.1016/j.jmp.2005.11.003

    Article  MathSciNet  MATH  Google Scholar 

  69. Talbi E (2009) Metaheuristics: from design to implementation. Wiley Publishing, New Jersey

    Book  MATH  Google Scholar 

  70. Sinthiya M, Chidambaram M (2016) A study on best first search. Int J Eng Res 3(6):588–597

    Google Scholar 

  71. Neri F, Cotta C (2012) Memetic algorithms and memetic computing optimization: a literature review. Swarm Evol Comput 2:1–14. https://doi.org/10.1016/j.swevo.2011.11.003

    Article  Google Scholar 

  72. Alonso JI, de la Ossa L, Gámez JA, Puerta JM (2018) On the use of local search heuristics to improve GES-based bayesian network learning. Appl Soft Comput 64:366–376. https://doi.org/10.1016/j.asoc.2017.12.011

    Article  Google Scholar 

  73. Chen X, Ong Y-S, Lim M-H, Tan KC (2011) A multi-facet survey on memetic computation. IEEE Trans Evol Comput 15:591–607. https://doi.org/10.1109/tevc.2011.2132725

    Article  Google Scholar 

  74. Johnson D, Trick M (1996) Cliques, coloring, and satisfiability: Second DIMACS implementation challenge. DIMACS Series, Providence RI, 26: american Mathematical Society

  75. Mascia F (2015) DIMACS benchmark set. http://iridia.ulb.ac.be/~fmascia/maximum_clique/DIMACS-benchmark. Accessed 10 January 2020

  76. Xu K (2014) BHOSLIB: Benchmarks with hidden optimum solutions for graph problems (maximum clique, maximum independent set, minimum vertex cover and vertex coloring) – hiding exact solutions in random graphs. http://www.nlsde.buaa.edu.cn/~kexu/benchmarks/graph-benchmarks.html. Accessed 10 January 2020

  77. Asmaran M, Sharieh A, Mahafzah B (2019) Chemical reaction optimization algorithm to find maximum independent set in a graph. Int J Adv Comput Sci Appl 10(9):76–91

    Google Scholar 

  78. Murad O, Jabri R, Mahafzah B (2019) A metaheuristic approach for static scheduling based on chemical reaction optimizer. J Theor Appl Inf 97(21):3144–3165

    Google Scholar 

  79. Lam A, Li V (2012) Chemical reaction optimization: a tutorial. Memet Comput 4(1):3–17. https://doi.org/10.1007/s12293-012-0075-1

    Article  Google Scholar 

  80. Lam A, Li V, Yu J (2012) Real-coded chemical reaction optimization. IEEE Trans Evol Comput 16(3):339–353. https://doi.org/10.1109/TEVC.2011.2161091

    Article  Google Scholar 

  81. Adamchik V (2009) Algorithmic complexity. https://www.cs.cmu.edu/~adamchik/15-122/lectures/complexity/complexity.pdf. Accessed 3 January 2020

  82. Goodrich M, Tamassia R, Goldwasser M (2014) Data structures and algorithms in JAVA. John Wiley and Sons, USA

    Google Scholar 

  83. Chandu D (2014) A parallel genetic algorithm for generalized vertex cover problem. Int J Comput Sci Inf Tech Res 5(6):7686–7689

    Google Scholar 

  84. Vasconcelos J, Ramírez J, Takahashi R, Saldanha R (2001) Improvements in genetic algorithms. IEEE Trans Magn 37:3414–3417. https://doi.org/10.1109/20.952626

    Article  Google Scholar 

  85. Geeen K, Tashman L (2009) Percentage error: what denominator? Foresight. Int J Appl Forecast 12:36–40

    Google Scholar 

  86. Meyer T (2012) Root mean square error compared to, and contrasted with, standard deviation. Surv Land Inf Sci 72:107–108

    Google Scholar 

  87. Grama A, Gupta A, Karypis G, Kumar G (2003) Introduction to parallel computing. Addison Wesley, England

    MATH  Google Scholar 

  88. Rukhin A (2009) Weighted means statistics in interlaboratory studies. Metrologia 46(3):323–331

    Article  Google Scholar 

  89. Abdullah M, Abuelrub E, Mahafzah B (2011) The chained-cubic tree interconnection network. Int Arab J Inf Technol 8(3):334–343

    Google Scholar 

  90. Baddar S, Mahafzah B (2014) Bitonic sort on a chained-cubic tree interconnection network. J Parallel Distrib Comput 74(1):1744–1761. https://doi.org/10.1016/j.jpdc.2013.09.008

    Article  Google Scholar 

  91. Mahafzah B, Alshraideh M, Abu-Kabeer T, Ahmad E, Hamad N (2012) The optical chained-cubic tree interconnection network: Topological structure and properties. Comput Electr Eng 38(2):330–345. https://doi.org/10.1016/j.compeleceng.2011.11.023

    Article  MATH  Google Scholar 

  92. Mahafzah B, Al-Zoubi I (2018) Broadcast communication operations for hyper hexa-cell interconnection network. Telecommun Syst 67(1):73–93. https://doi.org/10.1007/s11235-017-0322-3

    Article  Google Scholar 

  93. Al-Adwan A, Zaghloul R, Mahafzah B, Sharieh A (2020) Parallel quicksort algorithm on OTIS hyper hexa-cell optoelectronic architecture. J Parallel Distrib Comput 141:61–73. https://doi.org/10.1016/j.jpdc.2020.03.015

    Article  Google Scholar 

  94. Al-Adwan A, Sharieh A, Mahafzah B (2019) Parallel heuristic local search algorithm on OTIS hyper hexa-cell and OTIS mesh of trees optoelectronic architectures. Appl Intell 49(2):661–688. https://doi.org/10.1007/s10489-018-1283-2

    Article  Google Scholar 

  95. Al-Adwan A, Mahafzah B, Sharieh A (2018) Solving traveling salesman problem using parallel repetitive nearest neighbor algorithm on OTIS-hypercube and OTIS-mesh optoelectronic architectures. J Supercomput 74(1):1–36. https://doi.org/10.1007/s11227-017-2102-y

    Article  Google Scholar 

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  1. Autonomous Systems Department, Faculty of Artificial Intelligence, Al-Balqa Applied University, Al-Balqa, Jordan

    Hebatullah Khattab

  2. Computer Science Department, King Abdullah II School of Information Technology, The University of Jordan, Amman, 11942, Jordan

    Basel A. Mahafzah & Ahmad Sharieh

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  1. Hebatullah Khattab
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Khattab, H., Mahafzah, B.A. & Sharieh, A. A hybrid algorithm based on modified chemical reaction optimization and best-first search algorithm for solving minimum vertex cover problem. Neural Comput & Applic 34, 15513–15541 (2022). https://doi.org/10.1007/s00521-022-07262-w

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