Soft Computing

, Volume 21, Issue 7, pp 1765–1784 | Cite as

Towards the right amount of randomness in quantum-inspired evolutionary algorithms

Methodologies and Application


Quantum-inspired evolutionary algorithms (QIEAs) combine the advantages of quantum-inspired bit (Q-bit), representation and operators with evolutionary algorithms for better performance. Using quantum-inspired representation the complete binary search space can be generated by collapsing a single Q-bit string repeatedly. Thus, even a population size of 1 can be taken in a QIEA implementation resulting in enormous saving in computation. Although this is correct in theory, QIEA implementations run into trouble in exploring large search spaces with this approach. The Q-bit string has to be initialized to produce each possible binary string with equal probability and then altered slowly to probabilistically favor generation of strings with better fitness values. This process is unacceptably slow when the search spaces are very large. Many ideas have been reported with EAs/QIEAs for speeding up convergence while ensuring that the algorithm does not get stuck in local optima. In this paper, the possible features are identified and systematically introduced and tested in the QIEA framework in various combinations. Some of these features increase the randomness in the search process for better exploration and the others compensate by local search for better exploitation together enabling a judicious combination tailored for particular problem being solved. This is referred to as “right-sizing the randomness” in the QIEA search. Benchmark instances of the well-known and well-studied Quadratic Knapsack Problem are used to demonstrate how effective these features are—individually and collectively. The new framework, dubbed QIEA-QKP, is shown to be much more effective than canonical QIEA. The framework can be utilized with profit on other problems and is being attempted.


Evolutionary algorithm Combinatorial optimization  Quantum-inspired evolutionary algorithm Quadratic Knapsack Problem 


  1. Bäck T (1996) Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms. Oxford University Press, OxfordMATHGoogle Scholar
  2. Billionet A, Soutif E (2004) QKP instances. [Online] Accessed 15 February 2013
  3. Caprara A, Pisinger D, Toth P (1999) Exact solution of the quadratic knapsack problem. Inf J Comput 11(2):125–137MathSciNetCrossRefMATHGoogle Scholar
  4. Dijkhuijen G, Faigle U (1993) A cutting-plane approach to he edge-weighted maximal clique problem. Eur J Oper Res 69:121–130CrossRefGoogle Scholar
  5. Engebretsen L, Holmerin J (2000) Clique is hard to approximate within n1-o(1). In: Proceedings of 27th international colloquium, ICALP 2000, vol 1853. Springer, Berlin, pp 2–12Google Scholar
  6. Ferreira CE, Martin A, deSouza CC (1996) Formulations and valid inequalities for node capacitated graph partitioning. Math Program 74:247–266MathSciNetGoogle Scholar
  7. Gallo G, Hammer P, Simeone B (1980) Quadratic knapsack problems. Math Program Study 12:132–149MathSciNetCrossRefMATHGoogle Scholar
  8. Han K-H (2006) On the analysis of the quantum-inspired evolutionary algorithm with a single individual. In: Proceedings of CEC’06, Vancouver, Canada, pp 2622–2629Google Scholar
  9. Han K-H, Kim J-H (2002) Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans Evolut Comput 6(6):580–593MathSciNetCrossRefGoogle Scholar
  10. Han K-H, Kim J-H (2003) On setting the parameters of quantum-inspired evolutionary algorithm for practical application. In: Proceedings of CEC 2003, vol 1, pp 178–194Google Scholar
  11. Han K-H, Kim J-H (2004) Quantum-inspired evolutionary algorithms with a new termination criterion, h-epsilon gate, and two-phase scheme. IEEE Trans Evolut Comput 8(2):156–169CrossRefGoogle Scholar
  12. Han K, Park K, Lee C, Kim J (2001) Parallel quantum-inspired genetic algorithm for combinatorial optimization problem. In: Proceedings of CEC 2001, vol 2, pp 1422–1429Google Scholar
  13. Imabeppu T, Nakayama S, Ono S (2008) A study on a quantum-inspired evolutionary algorithm based on pair swap. Artif Life Robot 12:148–152CrossRefGoogle Scholar
  14. Johnson E, Mehrotra A, Nemhauser G (1993) Min-cut clustering. Math Program 62:133–151MathSciNetCrossRefMATHGoogle Scholar
  15. Julstorm BA (2005) Greedy, genetic and greedy genetic algorithms for the quadratic knapsack problem. In: Proceedings of GECCO 2005, Washingtom DC, USA, pp 607–614Google Scholar
  16. Kellerer H, Pferschy U, Pisinger D (2004) Knapsack problems. Springer, BerlinCrossRefMATHGoogle Scholar
  17. Kim Y, Kim JH, Han KH (2006) Quantum-inspired multiobjective evolutionary algorithm for multiobjective 0/1 knapsack problems. In: Proceedings of CEC 2006, pp 2601–2606Google Scholar
  18. Laghhunn DL (1970) Quadratic binary programming with applications to capital budgetting problems. Oper Res 18:454–461Google Scholar
  19. Li Z, Rudolph G, Li K (2009) Convergence performance comparison of quantum-inspired multi-objective evolutionary algorithms. Comput Math Appl 57:1843–1854MathSciNetCrossRefMATHGoogle Scholar
  20. Lu TC, Yu GR (2013) An adaptive population multi-objective quantum-inspired evolutionary algorithm for multi-objective 0/1 knapsack problems. Inf Sci 243:39–56MathSciNetCrossRefMATHGoogle Scholar
  21. Mahdabi P, Jalili S, Abadi M (2008) A multi-start quantum-inspired evolutionary algorithm for solving combinatorial optimization problems. In: Proceedings of GECCO ’08, pp 613–614Google Scholar
  22. Nowotniak R, Kucharski J (2012) GPU-based tuning of quantum-inspired genetic algorithm for a combinatorial optimization problem. Bull Pol Acad Sci Tech Sci 60(2):323–330Google Scholar
  23. Park K, Lee K, Park S (1996) An extended formulation approach to the edge weighted maximal cliqur problem. Eur J Oper Res 95:671–682CrossRefMATHGoogle Scholar
  24. Patvardhan C, Narayan A, Srivastav A (2007) Enhanced quantum evolutionary algorithms for difficult knapsack problems. In: Proceedings of PReMI’07. Springer, Berlin, pp 252–260Google Scholar
  25. Patvardhan C, Prakash P, Srivastav A (2012) A novel quantum-inspired evolutionary algorithm for the quadratic knapsack problem. Int J Math Oper Res 4(2):114–127MathSciNetCrossRefGoogle Scholar
  26. Patvardhan C, Bansal S, Srivastav A (2014a) Solution of “Hard” knapsack instances using quantum inspired evolutionary algorithm. Int J Appl Evolut Comput 5(1):52–68CrossRefGoogle Scholar
  27. Patvardhan C, Bansal S, Srivastav A (2014b) Balanced quantum-inspired evolutionary algorithm for multiple knapsack problem. Int J Intell Syst Appl 11:1–11Google Scholar
  28. Pisinger D (2007) The quadratic knapsack problem—a survey. Discrete Appl Math 155:623–648MathSciNetCrossRefMATHGoogle Scholar
  29. Platel M D, Schliebs S, Kasabov N (2007) A versatile quantum-inspired evolutionary algorithm. In: Proceedings of CEC’07, pp 423–430Google Scholar
  30. Platel MD, Schliebs S, Kasabov N (2009) Quantum-inspired evolutionary algorithm: a multimodel EDA. IEEE Trans Evolut Comput 13(6):1218–1232CrossRefGoogle Scholar
  31. Qin Y, Zhang G, Li Y, Zhang H (2012) A comprehensive learning quantum-inspired evolutionary algorithm. In: Qu X, Yang Y (eds) LNCS, IBI 2011, Part-II, CCIS 268, pp 151–157Google Scholar
  32. Rhys J (1970) A selection problem of shared fixed costs and network flows. Manag Sci 17:200–207CrossRefMATHGoogle Scholar
  33. Tayarani-N M-H, Akbarzadeh-T M-R (2008) A sinusoid size ring structure quantum evolutionary algorithm. In: Proceedings of IEEE conference on cybernetics and intelligent systems, pp 1165–1170Google Scholar
  34. Witzall C (1975) Mathematical methods of site selection for electronic message system (EMS). In: Technical report, NBS internal report Washington, DC. Operational Research SectionGoogle Scholar
  35. Xie X, Liu J (2007) A mini-swarm for the quadratic knapsack problem. In: Proceedings of IEEE swarm intelligence symposium, Honolulu, USA, pp 190–197Google Scholar
  36. Zhang G, Gheorghe M, Wu CZ (2008) A quantum-inspired evolutionary algorithm based on p systems for knapsack problem. Fund Inf 87(1):93–116MathSciNetMATHGoogle Scholar
  37. Zhang G (2011) Quantum-inspired evolutionary algorithms: a survey and empirical study. J Heurist 17(3):303–351CrossRefMATHGoogle Scholar
  38. Zhang G, Gheorghe M, Li Y (2012) A membrane algorithm with quantum-inspired subalgorithms and its application to image processing. Nat Comput 11:701–707MathSciNetCrossRefMATHGoogle Scholar
  39. Zhao Z, Peng X, Peng Y, Yu, E (2006) An effective repair procedure based on quantum-inspired evolutionary algorithm for 0/1 knapsack problems. In: Proceedings of the 5th WSEAS int. conf. on instrumentation, measurement, circuits and systems, Hangzho, pp 203–206Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Faculty of EngineeringDayalbagh Educational InstituteAgraIndia
  2. 2.Institut für InformatikChristian-Albrechts-Universität zu KielKielGermany
  3. 3.AgraIndia

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