A novel cuckoo search technique for solving discrete optimization problems

  • Ashish JainEmail author
  • Narendra S. Chaudhari
Original Article


During the past decade, swarm intelligence (SI) techniques have received considerable recognition among researchers to solve continuous optimization problems. However, only few significant works have been reported in the literature to solve discrete optimization problems using SI techniques. Therefore, this paper proposes an improved SI technique, namely, discrete cuckoo search. As an application, the proposed technique is employed to solve a transposition cipher, and then the efficiency of the proposed technique is compared to the existing genetic algorithms. The obtained results indicate that the performance of the proposed technique is superior to genetic algorithms (as compared to genetic algorithm, cuckoo search is roughly 1.5 times faster and recovers 12% more number of key elements). Hence, the proposed technique can be utilized to solve various discrete optimization problems, e.g., for optimal placement of phaser measurement units in a power system, traveling salesman problem, graph coloring problem etc.


Cuckoo search Genetic algorithm Discrete optimization Automated cryptanalysis Classical ciphers 


  1. Bansal JC, Sharma H, Jadon SS, Clerc M (2014) Spider monkey optimization algorithm for numerical optimization. Memet Comput 6(1):31–47CrossRefGoogle Scholar
  2. Bastos Filho CJ, de Lima Neto FB, Lins AJ, Nascimento AI, Lima MP (2008) A novel search algorithm based on fish school behavior. In: IEEE international conference on systems, man and cybernetics, 2008. SMC 2008. IEEE, pp 2646–2651Google Scholar
  3. Bhateja AK, Bhateja A, Chaudhury S, Saxena P (2015) Cryptanalysis of vigenere cipher using cuckoo search. Appl Soft Comput 26:315–324CrossRefGoogle Scholar
  4. Boryczka U, Dworak K (2014a) Cryptanalysis of transposition cipher using evolutionary algorithms. In: Hwang D, Jung JJ, Nguyen NT (eds) Computational collective intelligence. Technologies and applications. ICCCI 2014. Lecture Notes in Computer Science, Springer, vol 8733, pp 623–632Google Scholar
  5. Boryczka U, Dworak K (2014b) Genetic transformation techniques in cryptanalysis. In: Nguyen NT, Attachoo B, Trawiński B, Somboonviwat K (eds) Intelligent information and database systems. ACIIDS 2014. Lecture Notes in Computer Science, vol 8398. Springer, pp 147–156Google Scholar
  6. Carneiro RF, Bastos-Filho CJ (2016) Improving the binary fish school search algorithm for feature selection. In: IEEE Latin American conference on computational intelligence (LA-CCI), 2016. IEEE, pp 1–6Google Scholar
  7. Chetty S, Adewumi AO (2014) Comparison study of swarm intelligence techniques for the annual crop planning problem. IEEE Trans Evolut Comput 18(2):258–268CrossRefGoogle Scholar
  8. Clark A (1994) Modern optimisation algorithms for cryptanalysis. In: Proceedings of the 1994 second Australian and New Zealand conference on intelligent information systems, 1994. IEEE, pp 258–262Google Scholar
  9. Clark AJ (1998) Optimisation heuristics for cryptology. Ph.D. thesisGoogle Scholar
  10. Cuevas E, Cienfuegos M, Zaldívar D, Pérez-Cisneros M (2013) A swarm optimization algorithm inspired in the behavior of the social-spider. Expert Syst Appl 40(16):6374–6384CrossRefGoogle Scholar
  11. Danziger M, Henriques MAA (2012) Computational intelligence applied on cryptology: a brief review. IEEE Latin Am Trans 10(3):1798–1810CrossRefGoogle Scholar
  12. Dasgupta P, Das S (2015) A discrete inter-species cuckoo search for flowshop scheduling problems. Comput Oper Res 60:111–120MathSciNetCrossRefzbMATHGoogle Scholar
  13. Faraoun KM (2014) A genetic strategy to design cellular automata based block ciphers. Expert Syst Appl 41(17):7958–7967CrossRefGoogle Scholar
  14. Goldberg DE (2006) Genetic algorithms. Pearson Education India, DelhiGoogle Scholar
  15. Gonzalez TF (2007) Handbook of approximation algorithms and metaheuristics. CRC Press, Boca RatonCrossRefzbMATHGoogle Scholar
  16. Heydari M, Senejani MN (2014) Automated cryptanalysis of transposition ciphers using cuckoo search algorithm. Int J Comput Sci Mob Comput 3(1):140–149Google Scholar
  17. Holden J (2017) The mathematics of secrets: cryptography from caesar ciphers to digital encryption. Princeton University Press, PrincetonCrossRefzbMATHGoogle Scholar
  18. Jain A, Chaudhari NS (2014) Cryptanalytic results on knapsack cryptosystem using binary particle swarm optimization. In: International joint conference SOCO14-CISIS14-ICEUTE14, Springer, Berlin, pp 375–384Google Scholar
  19. Jain A, Chaudhari NS (2015a) Evolving highly nonlinear balanced boolean functions with improved resistance to DPA attacks. In: Network and system security, Springer, Berlin, pp 316–330Google Scholar
  20. Jain A, Chaudhari NS (2015b) A new heuristic based on the cuckoo search for cryptanalysis of substitution ciphers. In: Neural information processing, Springer, Berlin, pp 206–215Google Scholar
  21. Jain A, Chaudhari NS (2017a) An improved genetic algorithm for developing deterministic OTP key generator. Complexity, Wiley & Hindawi (7436709, 2017), pp 1–17Google Scholar
  22. Jain A, Chaudhari NS (2017b) A novel cuckoo search strategy for automated cryptanalysis: a case study on the reduced complex knapsack cryptosystem, Int J Syst Assur Eng Manag 1–20.
  23. Jhajharia S, Mishra S, Bali S (2013) Public key cryptography using neural networks and genetic algorithms. In: 2013 Sixth international conference on contemporary computing (IC3). IEEE, pp 137–142Google Scholar
  24. Karaboga D (2005) An idea based on honey bee swarm for numerical optimization. Techical report, Technical report-tr06, Erciyes university, engineering faculty, computer engineering departmentGoogle Scholar
  25. Kramer O (2017) Genetic algorithm essentials, vol 679. Springer, BerlinzbMATHGoogle Scholar
  26. Li JQ, Pan QK, Tasgetiren MF (2014) A discrete artificial bee colony algorithm for the multi-objective flexible job-shop scheduling problem with maintenance activities. Appl Math Model 38(3):1111–1132MathSciNetCrossRefGoogle Scholar
  27. Li X, Ma S (2017) Multiobjective discrete artificial bee colony algorithm for multiobjective permutation flow shop scheduling problem with sequence dependent setup times. IEEE Trans Eng Manag 64(2):149–165CrossRefGoogle Scholar
  28. Mantegna RN (1994) Fast, accurate algorithm for numerical simulation of levy stable stochastic processes. Phys Rev E 49(5):4677CrossRefGoogle Scholar
  29. Marinakis Y, Marinaki M, Migdalas A (2016) A hybrid discrete artificial bee colony algorithm for the multicast routing problem. In: European conference on the applications of evolutionary computation, Springer, Berlin, pp 203–218Google Scholar
  30. Matthews RA (1993) The use of genetic algorithms in cryptanalysis. Cryptologia 17(2):187–201CrossRefGoogle Scholar
  31. Menezes AJ, Van Oorschot PC, Vanstone SA (1996) Handbook of applied cryptography. CRC Press, Boca RatonCrossRefzbMATHGoogle Scholar
  32. Michalewicz Z (2013) Genetic algorithms + data structures = evolution programs. Springer, BerlinzbMATHGoogle Scholar
  33. Mucherino A, Seref O (2007) Monkey search: a novel metaheuristic search for global optimization. AIP Conf Proc 953:162–173CrossRefGoogle Scholar
  34. Mulholland H, Jones CR (2013) Fundamentals of statistics. Springer, BerlinGoogle Scholar
  35. Osaba E, Yang XS, Diaz F, Lopez-Garcia P, Carballedo R (2016) An improved discrete bat algorithm for symmetric and asymmetric traveling salesman problems. Eng Appl Artif Intell 48:59–71CrossRefGoogle Scholar
  36. Osaba E, Yang XS, Diaz F, Onieva E, Masegosa AD, Perallos A (2017) A discrete firefly algorithm to solve a rich vehicle routing problem modelling a newspaper distribution system with recycling policy. Soft Comput 21(18):5295–5308CrossRefGoogle Scholar
  37. Ouaarab A, Ahiod B, Yang XS (2014a) Discrete cuckoo search algorithm for the travelling salesman problem. Neural Comput Appl 24(7–8):1659–1669CrossRefGoogle Scholar
  38. Ouaarab A, Ahiod B, Yang XS (2014) Improved and discrete cuckoo search for solving the travelling salesman problem. In: Yang XS (eds) Cuckoo search and firefly algorithm. Studies in Computational Intelligence, vol 516. Springer, ChamGoogle Scholar
  39. Riffi ME, Saji Y, Barkatou M (2017) Incorporating a modified uniform crossover and 2-exchange neighborhood mechanism in a discrete bat algorithm to solve the quadratic assignment problem. Egypt Inform J 18(3):221–232CrossRefGoogle Scholar
  40. Sadiq AT, Ali L, Kareem H (2014) Attacking transposition cipher using improved cuckoo search. J Adv Comput Sci Technol Res 4(1):22–32Google Scholar
  41. Saji Y, Riffi ME (2016) A novel discrete bat algorithm for solving the travelling salesman problem. Neural Comput Appl 27(7):1853–1866CrossRefGoogle Scholar
  42. Sharma A, Sharma H, Bhargava A, Sharma N (2016) Optimal design of pida controller for induction motor using spider monkey optimization algorithm. Int J Metaheuristics 5(3–4):278–290CrossRefGoogle Scholar
  43. Shlesinger MF, Zaslavsky GM, Frisch U (1994) Lévy flights and related topics in physics. In: Nice, 27–30 June, Springer, BerlinGoogle Scholar
  44. Sokouti M, Sokouti B, Pashazadeh S, Feizi-Derakhshi MR, Haghipour S (2013) Genetic-based random key generator (grkg): a new method for generating more-random keys for one-time pad cryptosystem. Neural Comput Appl 22(7–8):1667–1675CrossRefGoogle Scholar
  45. Song J, Yang F, Wang M, Zhang H (2008) Cryptanalysis of transposition cipher using simulated annealing genetic algorithm. In: Advances in Computation and Intelligence, Springer, Berlin, pp 795–802Google Scholar
  46. Soto R, Crawford B, Galleguillos C, Barraza J, Lizama S, Muñoz A, Vilches J, Misra S, Paredes F (2015) Comparing cuckoo search, bee colony, firefly optimization, and electromagnetism-like algorithms for solving the set covering problem. In: Computational science and its applications–ICCSA 2015, Springer, Berlin, pp 187–202Google Scholar
  47. Stinson DR (2005) Cryptography: theory and practice. CRC Press, Boca RatonzbMATHGoogle Scholar
  48. Toemeh R, Arumugam S (2007) Breaking transposition cipher with genetic algorithm. Electron Elect Eng 79(7):75–78Google Scholar
  49. Wang Y, Wong KW, Li C, Li Y (2012) A novel method to design s-box based on chaotic map and genetic algorithm. Phys Lett A 376(6):827–833CrossRefzbMATHGoogle Scholar
  50. Yang XS (2010a) Firefly algorithm, stochastic test functions and design optimisation. Int J Bio Inspir Comput 2(2):78–84CrossRefGoogle Scholar
  51. Yang XS (2010b) A new metaheuristic bat-inspired algorithm. In: González JR, Pelta DA, Cruz C, Terrazas G, Krasnogor N (eds) Nature inspired cooperative strategies for optimization (NICSO 2010). Studies in Computational Intelligence, Springer, vol 284, pp 65–74Google Scholar
  52. Yang XS (2014) Nature-inspired optimization algorithms. Elsevier, AmsterdamzbMATHGoogle Scholar
  53. Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: World congress on nature and biologically inspired computing, 2009 (NaBIC 2009). IEEE, pp 210–214Google Scholar
  54. Yang XS, Deb S (2010) Engineering optimisation by cuckoo search. Intern J Math Model Numer Optim 1(4):330–343zbMATHGoogle Scholar
  55. Yang XS, Cui Z, Xiao R, Gandomi AH, Karamanoglu M (2013) Swarm intelligence and bio-inspired computation: theory and applications. Elsevier, WalthamCrossRefGoogle Scholar
  56. Yazdani M, Jolai F (2016) Lion optimization algorithm (loa): a nature-inspired metaheuristic algorithm. J Comput Des Eng 3(1):24–36Google Scholar
  57. Zhang L, Shan L, Wang J (2017) Optimal feature selection using distance-based discrete firefly algorithm with mutual information criterion. Neural Comput Appl 28(9):2795–2808CrossRefGoogle Scholar
  58. Zhong Y, Lin J, Wang L, Zhang H (2017) Hybrid discrete artificial bee colony algorithm with threshold acceptance criterion for traveling salesman problem. Inf Sci 421:70–84MathSciNetCrossRefGoogle Scholar

Copyright information

© The Society for Reliability Engineering, Quality and Operations Management (SREQOM), India and The Division of Operation and Maintenance, Lulea University of Technology, Sweden 2018

Authors and Affiliations

  1. 1.Discipline of Computer Science and EngineeringIndian Institute of Technology IndoreIndoreIndia
  2. 2.Discipline of Computer Science and EngineeringVisvesvaraya National Institute of Technology NagpurNagpurIndia

Personalised recommendations