Skip to main content
SpringerLink
Log in

An efficient modified harmony search algorithm with intersect mutation operator and cellular local search for continuous function optimization problems

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

This paper proposes a modified harmony search (MHS) algorithm with an intersect mutation operator and cellular local search for continuous function optimization problems. Instead of focusing on the intelligent tuning of the parameters during the searching process, the MHS algorithm divides all harmonies in harmony memory into a better part and a worse part according to their fitness. The novel intersect mutation operation has been developed to generate new -harmony vectors. Furthermore, a cellular local search also has been developed in MHS, that helps to improve the optimization performance by exploring a huge search space in the early run phase to avoid premature, and exploiting a small region in the later run phase to refine the final solutions. To obtain better parameter settings for the proposed MHS algorithm, the impacts of the parameters are analyzed by an orthogonal test and a range analysis method. Finally, two sets of famous benchmark functions have been used to test and evaluate the performance of the proposed MHS algorithm. Functions in these benchmark sets have different characteristics so they can give a comprehensive evaluation on the performance of MHS. The experimental results show that the proposed algorithm not only performs better than those state-of-the-art HS variants but is also competitive with other famous meta-heuristic algorithms in terms of the solution accuracy and efficiency.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Boussaid I, Lepagnot J, Siarry P (2013) A survey on optimization metaheuristics. Inf Sci 237:82–117

    Article  MathSciNet  MATH  Google Scholar 

  2. Holland JH (1975) Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence

  3. Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359

    Article  MathSciNet  MATH  Google Scholar 

  4. Zou DX, Wu JH, Gao LQ, Li S (2013) A modified differential evolution algorithm for unconstrained optimization problems. Neurocomputing 120:469–481

    Article  Google Scholar 

  5. Kennedy J, Eberhart R (1995) Particle swarm optimization, proceedings of IEEE International Conference on neural networks (ICNN’95) in

  6. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39:459–471

    Article  MathSciNet  MATH  Google Scholar 

  7. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents, Systems, Man, and Cybernetics. IEEE Transactions on Part B: Cybernetics 26:29–41

    Google Scholar 

  8. Yang X-S, Deb S (2009) Cuckoo search via Lévy flights nature & biologically inspired computing, 2009. NaBIC World Congress on IEEE, pp 210–214

  9. Kirkpatrick S (1984) annealing, Optimization by simulated Quantitative studies. J Stat Phys 34:975–986

    Article  MathSciNet  Google Scholar 

  10. Lam AY, Li VO (2010) Chemical-reaction-inspired metaheuristic for optimization. IEEE Trans Evol Comput 14:381–399

    Article  Google Scholar 

  11. Geem ZW, Kim JH, Loganathan G (2001) A new heuristic optimization algorithm: harmony search. Simulation 76:60–68

    Article  Google Scholar 

  12. Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188:1567–1579

    Article  MathSciNet  MATH  Google Scholar 

  13. Geem ZW (2009) Particle-swarm harmony search for water network design. Eng Optim 41:297–311

    Article  Google Scholar 

  14. Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82:781–798

    Article  Google Scholar 

  15. Panchal A (2009) Harmony search in therapeutic medical physics, in: Music-inspired Harmony search algorithm. Springer, pp 189–203

  16. Alia O, Mandava R, Ramachandram D, Aziz ME (2009) Dynamic fuzzy clustering using harmony search with application to image segmentation. In: Signal Processing and Information Technology (ISSPIT) IEEE International Symposium on IEEE, pp 538–543

  17. Zarei O, Fesanghary M, Farshi B, Saffar RJ, Razfar MR (2009) Optimization of multi-pass face-milling via harmony search algorithm. J Mater Process Tech 209:2386–2392

    Article  Google Scholar 

  18. Liu L, Zhou H (2013) Hybridization of harmony search with variable neighborhood search for restrictive single-machine earliness/tardiness problem. Inform Sci 226:68–92

    Article  MathSciNet  MATH  Google Scholar 

  19. Cuevas E (2013) Block-matching algorithm based on harmony search optimization for motion estimation. Appl Intell 39:165–183

    Article  Google Scholar 

  20. Arul R, Ravi G, Velusami S (2013) Chaotic self-adaptive differential harmony search algorithm based dynamic economic dispatch. Int J Electr Power Energy Syst 50:85–96

    Article  Google Scholar 

  21. Kulluk S, Ozbakir L, Baykasoglu A (2012) Training neural networks with harmony search algorithms for classification problems. Eng Appl Artif Intell 25:11–19

    Article  Google Scholar 

  22. Mun S, Cho YH (2012) Modified harmony search optimization for constrained design problems. Expert Systems with Applications 39:419–423

    Article  Google Scholar 

  23. Chen J, Pan QK, Li JQ (2012) Harmony search algorithm with dynamic control parameters. Applied Mathematics and Computation 219:592–604

    Article  MathSciNet  MATH  Google Scholar 

  24. Omran MGH, Mahdavi M (2008) Global-best harmony search. Appl Math Comput 198:643–656

    Article  MathSciNet  MATH  Google Scholar 

  25. Wang L, Li LP (2013) An effective differential harmony search algorithm for the solving non-convex economic load dispatch problems. Int J Electr Power Energy Syst 44:832–843

    Article  Google Scholar 

  26. Banerjee A, Mukherjee V, Ghoshal S (2013) An opposition-based harmony search algorithm for engineering optimization problems. Ain Shams Eng J

  27. Wang H, Ouyang H, Gao L, Qin W (2014) Opposition-based learning harmony search algorithm with mutation for solving global optimization problems, In: Control and Decision Conference (2014 CCDC), The 26th Chinese, IEEE, pp 1090–1094

  28. Zou D, Gao L, Wu J, Li S (2010) Novel global harmony search algorithm for unconstrained problems. Neurocomputing 73:3308–3318

    Article  Google Scholar 

  29. Im SS, Yoo DG, Kim JH (2013) Smallest-small-world cellular harmony search for optimization of unconstrained benchmark problems. J Appl Math:2013

  30. Al-Betar MA, Khader AT, Awadallah MA, Alawan MH, Zaqaibeh B (2013) Cellular Harmony Search for Optimization Problems. J Appl Math:2013

  31. Ashrafi SM, Dariane AB (2013) Performance evaluation of an improved harmony search algorithm for numerical optimization: Melody Search (MS). Eng Appl Artif Intell 26:1301–1321

    Article  Google Scholar 

  32. Al-Betar MA, Awadallah MA, Khader AT, Abdalkareem ZA (2015) Island-based harmony search for optimization problems. Expert Systems with Applications 42:2026–2035

    Article  Google Scholar 

  33. Pan QK, Suganthan PN, Tasgetiren MF, Liang JJ (2010) A self-adaptive global best harmony search algorithm for continuous optimization problems. Appl Math Comput 216:830–848

    Article  MathSciNet  MATH  Google Scholar 

  34. Yadav P, Kumar R, Panda SK, Chang CS (2012) An Intelligent Tuned Harmony Search algorithm for optimisation. Inform Sci 196:47–72

    Article  Google Scholar 

  35. Kattan A, Abdullah R (2013) A dynamic self-adaptive harmony search algorithm for continuous optimization problems. Appl Math Comput 219:8542–8567

    Article  MathSciNet  MATH  Google Scholar 

  36. Enayatifar R, Yousefi M, Abdullah AH, Darus AN (2013) LAHS: a novel harmony search algorithm based on learning automata. Commun Nonlinear Sci 18:3481–3497

    Article  MathSciNet  Google Scholar 

  37. Kumar V, Chhabra JK, Kumar D (2014) Parameter adaptive harmony search algorithm for unimodal and multimodal optimization problems. J Comput Sci-Neth 5:144–155

    Article  MathSciNet  Google Scholar 

  38. Zhou YZ, Li XY, Gao L (2013) A differential evolution algorithm with intersect mutation operator. Appl Soft Comput 13:390–401

    Article  Google Scholar 

  39. Schiff JL (2011) Cellular automata: a discrete view of the world. Wiley

  40. Alba E, Dorronsoro B (2005) The exploration/exploitation tradeoff in dynamic cellular genetic algorithms. IEEE Trans Evol Comput 9:126–142

    Article  Google Scholar 

  41. Alba E, Alfonso H, Dorronsoro B (2005) Advanced models of cellular genetic algorithms evaluated on SAT, Gecco. Genetic and Evolutionary Computation Conference 1 and 2:1123–1130

    Google Scholar 

  42. Shi Y, Liu HC, Gao L, Zhang GH (2011) Cellular particle swarm optimization. Inform Sci 181:4460–4493

    Article  MathSciNet  MATH  Google Scholar 

  43. Im SS, Yoo DG, Kim JH (2013) Smallest-Small-World Cellular Harmony Search for Optimization of Unconstrained Benchmark Problems

  44. Al-Betar MA, Khader AT, Awadallah MA, Alawan MH, Zaqaibeh B (2013) Cellular Harmony Search for Optimization Problems

  45. Yang X-S, Deb S (2010) Engineering optimisation by cuckoo search. International Journal of Mathematical Modelling and Numerical Optimisation 1:330–343

    Article  MATH  Google Scholar 

  46. Yang X-S, Deb S (2013) Multiobjective cuckoo search for design optimization. Comput Oper Res 40:1616–1624

    Article  MathSciNet  Google Scholar 

  47. Yao X, Liu Y, Lin GM (1999) Evolutionary programming made faster. Ieee T Evolut Comput 3:82–102

    Article  Google Scholar 

  48. Liang J, Qu B, Suganthan P, Hernández-Díaz AG (2013) Problem definitions and evaluation criteria for the CEC 2013 special session on real-parameter optimization, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, China and Nanyang Technological University, Singapore, Technical Report, 201212

  49. Zhu J, Chew DA, Lv S, Wu W (2013) Optimization method for building envelope design to minimize carbon emissions of building operational energy consumption using orthogonal experimental design (OED). Habitat International 37:148–154

    Article  Google Scholar 

  50. Rice J (2006) Mathematical statistics and data analysis. Cengage Learning

  51. Castelli M, Silva S, Manzoni L, Vanneschi L (2014) Geometric Selective Harmony Search. Inform Sci 279:468–482

    Article  MathSciNet  Google Scholar 

  52. Zambrano-Bigiarini M, Clerc M, Rojas R (2013) Standard Particle Swarm Optimisation 2011 at CEC-2013: A baseline for future PSO improvements. In: Evolutionary Computation (CEC), IEEE Congress on IEEE, pp 2337–2344

  53. Nepomuceno FV, Engelbrecht AP (2013) A self-adaptive heterogeneous pso for real-parameter optimization. In: Evolutionary Computation (CEC), IEEE Congress on IEEE, pp 361–368

  54. Qin A, Li X (2013) Differential evolution on the CEC-2013 single-objective continuous optimization testbed. In: Evolutionary Computation (CEC), IEEE Congress on IEEE, pp 1099–1106

  55. Zhang C, Gao L (2013) An effective improvement of JADE for real-parameter optimization. In: Advanced Computational Intelligence (ICACI), Sixth International Conference on IEEE, pp 58–63

  56. Tanabe R, Fukunaga A (2013) Evaluating the performance of SHADE on CEC 2013 benchmark problems. In: Evolutionary Computation (CEC) IEEE Congress on IEEE, pp 1952–1959

Download references

Acknowledgments

The authors would like to thank anonymous reviewers for their helpful comments. This research work is supported by the National Basic Research Program of China (973 Program) under grant no. 2014CB046705 and the National Natural Science Foundation of China (NSFC) under Grant Nos. 51375004, 51435009 and 51421062.

Author information

Authors and Affiliations

  1. The State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan, 430074, People’s Republic of China

    Jin Yi, Liang Gao, Xinyu Li & Jie Gao

Authors
  1. Jin Yi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Liang Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xinyu Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jie Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xinyu Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yi, J., Gao, L., Li, X. et al. An efficient modified harmony search algorithm with intersect mutation operator and cellular local search for continuous function optimization problems. Appl Intell 44, 725–753 (2016). https://doi.org/10.1007/s10489-015-0721-7

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-015-0721-7

Keywords

Search

Navigation