Applied Intelligence

, Volume 46, Issue 3, pp 684–702 | Cite as

A complex-valued encoding wind driven optimization for the 0-1 knapsack problem

  • Yongquan Zhou
  • Zongfan Bao
  • Qifang Luo
  • Sen Zhang


This paper presents a complex-valued encoding wind driven optimization (CWDO) with a greedy strategy for the 0-1 knapsack problem. We introduce a complex-value encoding method, which can be viewed as an effective global optimization strategy, and a greedy strategy, which can be viewed as an enhanced local search strategy into wind driven optimization. These strategies increase the diversity of the population and avoid premature convergence. This paper presents three types of test cases for evaluation: standard, small-scale, and large-scale test cases. The experimental results show that the proposed algorithm is suitable for these three cases. Compared to the complex valued cuckoo search algorithm, greedy genetic algorithm, wind driven optimization, binary cuckoo search algorithm, bat algorithm and particle swarm optimization, the performance, stability, and robustness of the CWDO algorithm is better. The simulation results show that the CWDO algorithm is an effective and feasible method for solving the 0-1 knapsack problem.


Complex-valued encoding Wind driven optimization (WDO) Greedy strategy Knapsack problem 



The authors would like to thank the anonymous reviewers for their careful review and constructive comments. This work was supported by National Science Foundation of China (Grant No. 61463007, 61563008).


  1. 1.
    Martello S, Pisinger D, Toth P (2000) New trends in exact algorithms for the 0–1 knapsack problem. Eur J Oper Res 123(2):325–332MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Zhou Y, Li L, Ma M (2016) A Complex-valued Encoding Bat Algorithm for Solving 0–1 Knapsack Problem. Neural Process Lett 44:407430Google Scholar
  3. 3.
    Kulkarni AJ, Shabir H (2016) Solving 0–1 knapsack problem using cohort intelligence algorithm. Int J Mach Learn Cybern 7(1):427–441CrossRefGoogle Scholar
  4. 4.
    Gherboudj A, Layeb A, Chikhi S (2012) Solving 0-1 knapsack problems by a discrete binary version of cuckoo search algorithm. Int J Bio-Inspired Computqq 4(2):229–236CrossRefGoogle Scholar
  5. 5.
    Du D, Zu Y (2015) Greedy Strategy Based Self-adaption Ant Colony Algorithm for 0/1 Knapsack ProblemUbiquitous Computing Application and Wireless Sensor, Netherlands, pp 663–670Google Scholar
  6. 6.
    Bayraktar Z, Komurcu M, Werner DH (2010) Wind Driven Optimization (WDO). A novel nature-inspired optimization algorithm and its application to electromagnetics. Antennas and Propagation Society International Symposium (APSURSI), 2010 IEEE. IEEEGoogle Scholar
  7. 7.
    Bayraktar Z, Komurcu M, Bossard J, et al. (2013) The wind driven optimization technique and its application in electromagnetics. IEEE Trans Antennas Propag 61(3):2745–2757MathSciNetCrossRefGoogle Scholar
  8. 8.
    Bhandari AK, Singh VK, Kumar A, et al. (2014) Cuckoo search algorithm and wind driven optimization based study of satellite image segmentation for multilevel thresholding using Kapur’s entropy. Expert Syst Appl 41 (5):3538–3560CrossRefGoogle Scholar
  9. 9.
    Sun J, Wang X, Huang M, et al. (2013) A Cloud Resource Allocation Scheme Based on Microeconomics and Wind Driven Optimization. In: 2013 8th China Grid Annual Conference (China Grid). IEEE, pp 34–39Google Scholar
  10. 10.
    Boulesnane A, Meshoul S (2014) A new multi-region modified wind driven optimization algorithm with collision avoidance for dynamic environments. Advances in Swarm Intelligence. Springer International Publishing, pp 412–421Google Scholar
  11. 11.
    Kuldeep B, Singh VK, Kumar A, et al. (2015) Design of two-channel filter bank using nature inspired optimization based fractional derivative constraints. ISA Trans 54:101–116CrossRefGoogle Scholar
  12. 12.
    Mahto SK, Choubey A, Suman S Linear array synthesis with minimum side lobe level and null control using wind driven optimization. In: 2015 International Conference on Signal Processing And Communication Engineering System (SPACES). IEEE, pp. 191–195Google Scholar
  13. 13.
    Chen DB, Li HJ, Li Z (2009) Particle swarm optimization based on complex-valued encoding and application in function optimization. Comput Appl 45(10):59–61Google Scholar
  14. 14.
    Riehl H (1978) Introduction to the Atmosphere. McGraw HillGoogle Scholar
  15. 15.
    Ahrens CD (2003) Meteorology Today: An Introduction to Weather, Climate, and the Environment, 7th ed. Thomson–Brook/Cole, BelmontGoogle Scholar
  16. 16.
    Zhao-hui Z, Zhang Y, Qiu Y-H (2003) Genetic algorithm based on complex-valued encoding. IET Control Theory Appl 1:021Google Scholar
  17. 17.
    Zhao JF, Huang TL, Pang F, et al. (2009) Genetic algorithm based on greedy strategy in the 0-1 knapsack problem. In: 3rd International Conference on Genetic and Evolutionary Computing, 2009. WGEC’09. IEEE, pp 105–107Google Scholar
  18. 18.
    Zhou Y, Zheng H (2013) A novel complex valued cuckoo search algorithm. Sci World J 2013(2013). Article ID 597803, 6 pagesGoogle Scholar
  19. 19.
    He YC, Liu KQ, Zhang CJ, et al. (2007) Greedy genetic algorithm for solving knapsack problems and its application. Commun Eng Des Mag 28:2655–2657Google Scholar
  20. 20.
    Bhattacharjee KK, Sarmah SP (2016) Modified swarm intelligence based techniques for the knapsack problem. Appl Intell:1–22Google Scholar
  21. 21.
    Mirjalili S, Mirjalili SM, Yang XS (2014) Binary bat algorithm. Neural Comput & Applic 25(3-4):663–681CrossRefGoogle Scholar
  22. 22.
    Hembecker F, Lopes HS, Godoy JW (2007) Particle swarm optimization for the multidimensional knapsack problem. Adaptive and Natural Computing Algorithms:358–365Google Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Yongquan Zhou
    • 1
    • 2
  • Zongfan Bao
    • 1
  • Qifang Luo
    • 1
    • 2
  • Sen Zhang
    • 1
  1. 1.College of Information Science and EngineeringGuangxi University for NationalitiesNanningChina
  2. 2.Schools Key Laboratory of Guangxi Highs Complex System and Computational IntelligenceNanningChina

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