An improved differential harmony search algorithm for function optimization problems

Methodologies and Application
  • 50 Downloads

Abstract

To overcome the drawbacks of the harmony search (HS) algorithm and further enhance its effectiveness and efficiency, an improved differential HS (IDHS) is proposed to solve numerical function optimization problems. The proposed IDHS has a novel improvisation scheme that integrates DE/best/1/bin and DE/rand/1/bin from the differential evolution (DE) algorithm to enhance its local search and exploration capabilities and a new pitch adjustment rule that benefits from the best solution in the harmony memory to increase its convergence speed. With dynamically adjusted parameters, the proposed IDHS can balance exploitation and exploration throughout the search process. The numerical results of an experiment with classic testing functions and those of a comparative experiment show that IDHS outperforms eight algorithms in the HS family and three widely used population-based algorithms in different families, including DE, particle swarm optimization, and improved fruit fly optimization algorithm. IDHS demonstrates fast convergence and an especially good capability to handle difficult high-dimensional optimization problems.

Keywords

Harmony search algorithm Differential evolution Meta-heuristics Global optimization 

Notes

Acknowledgements

This research is partially supported by National Natural Science Foundation of China (71771096; 71531009).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

References

  1. Abedinpourshotorban H, Hasan S, Shamsuddin SM, As’ Sahra NF (2016) A differential-based harmony search algorithm for the optimization of continuous problems. Expert Syst Appl 62:317–332CrossRefGoogle Scholar
  2. Amaya I, Cruz J, Correa R (2015) Harmony search algorithm: a variant with self-regulated fretwidth. Appl Math Comput 266:1127–1152MathSciNetGoogle Scholar
  3. Ashrafi SM, Dariane AB (2013) Performance evaluation of an improved harmony search algorithm for numerical optimization: melody search (MS). Eng Appl Artif Intell 26(4):1301–1321CrossRefGoogle Scholar
  4. Castelli M, Silva S, Manzoni L, Vanneschi L (2014) Geometric selective harmony search. Inf Sci 279:468–482MathSciNetCrossRefMATHGoogle Scholar
  5. Chakraborty P, Roy GG, Das S, Jain D, Abraham A (2009) An improved harmony search algorithm with differential mutation operator. Fundam Inform 95(4):401–426MathSciNetMATHGoogle Scholar
  6. Chatterjee A, Ghoshal SP, Mukherjee V (2012) Solution of combined economic and emission dispatch problems of power systems by an opposition-based harmony search algorithm. Int J Electr Power Energy Syst 39(1):9–20CrossRefGoogle Scholar
  7. Chen J, Pan QK, Li JQ (2012) Harmony search algorithm with dynamic control parameters. Appl Math Comput 219(2):592–604MathSciNetMATHGoogle Scholar
  8. Chen K, Zhou F, Liu A (2018) Chaotic dynamic weight particle swarm optimization for numerical function optimization. Knowl Based Syst 139:23–40CrossRefGoogle Scholar
  9. Cheng MY, Prayogo D, Wu YW, Lukito MM (2016) A Hybrid Harmony Search algorithm for discrete sizing optimization of truss structure. Autom Constr 69:21–33CrossRefGoogle Scholar
  10. Cobos C, Estupiñán D, Pérez J (2011) GHS + LEM: global-best harmony search using learnable evolution models. Appl Math Comput 218(6):2558–2578MathSciNetMATHGoogle Scholar
  11. El-Abd M (2013) An improved global-best harmony search algorithm. Appl Math Comput 222:94–106MATHGoogle Scholar
  12. Erdal F, Doğan E, Saka MP (2011) Optimum design of cellular beams using harmony search and particle swarm optimizers. J Constr Steel Res 67(2):237–247CrossRefGoogle Scholar
  13. Fesanghary M, Asadi S, Geem ZW (2012) Design of low-emission and energy-efficient residential buildings using a multi-objective optimization algorithm. Build Environ 49:245–250CrossRefGoogle Scholar
  14. Gandhi TK, Chakraborty P, Roy GG, Panigrahi BK (2012) Discrete harmony search based expert model for epileptic seizure detection in electroencephalography. Expert Syst Appl 39(4):4055–4062CrossRefGoogle Scholar
  15. Gao WF, Liu SY (2012) A modified artificial bee colony algorithm. Comput Oper Res 39(3):687–697CrossRefMATHGoogle Scholar
  16. García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15(6):617–644CrossRefMATHGoogle Scholar
  17. Geem ZW (2006) Optimal cost design of water distribution networks using harmony search. Eng Optim 38(03):259–277CrossRefGoogle Scholar
  18. Geem ZW (2008) Novel derivative of harmony search algorithm for discrete design variables. Appl Math Comput 199(1):223–230MathSciNetMATHGoogle Scholar
  19. Geem ZW (2009) Harmony search optimisation to the pump-included water distribution network design. Civ Eng Environ Syst 26(3):211–221CrossRefGoogle Scholar
  20. Geem ZW (2011) Discussion on “Combined heat and power economic dispatch by harmony search algorithm” by A. Vasebi et al. Int J Electr Power Energy Syst 29(2007):713–719. Int J Electr Power Energy Syst 33(7):1348–1348Google Scholar
  21. Geem ZW, Sim KB (2010) Parameter-setting-free harmony search algorithm. Appl Math Comput 217(8):3881–3889MathSciNetMATHGoogle Scholar
  22. Geem ZW, Kim J, Loganathan G (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68 ?CrossRefGoogle Scholar
  23. Kamboj VK, Bath SK, Dhillon JS (2016) Implementation of hybrid harmony search/random search algorithm for single area unit commitment problem. Int J Electr Power Energy Syst 77:228–249CrossRefGoogle Scholar
  24. Kaveh A, Ahangaran M (2012) Discrete cost optimization of composite floor system using social harmony search model. Appl Soft Comput 12(1):372–381CrossRefGoogle Scholar
  25. Keshtegar B, Hao P, Wang Y, Li Y (2017) Optimum design of aircraft panels based on adaptive dynamic harmony search. Thin Walled Struct 118:37–45CrossRefGoogle Scholar
  26. Khalili M, Kharrat R, Salahshoor K, Sefat MH (2014) Global dynamic harmony search algorithm: GDHS. Appl Math Comput 228(9):195–219MathSciNetMATHGoogle Scholar
  27. Landa-Torres I, Manjarres D, Salcedo-Sanz S, Del Ser J, Gil-Lopez S (2013) A multi-objective grouping harmony search algorithm for the optimal distribution of 24-hour medical emergency units. Expert Syst Appl 40(6):2343–2349CrossRefGoogle Scholar
  28. Lee KS, Geem ZW (2004) A new structural optimization method based on the harmony search algorithm. Comput Struct 82(9):781–798CrossRefGoogle Scholar
  29. Lee KS, Geem ZW (2005) A new meta-heuristic algorithm for continuous engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194:3902–3933CrossRefMATHGoogle Scholar
  30. Li G, Cui L, Fu X, Wen Z, Lu N, Lu J (2017) Artificial bee colony algorithm with gene recombination for numerical function optimization. Appl Soft Comput 52:146–159CrossRefGoogle Scholar
  31. Mahdavi M, Fesanghary M, Damangir E (2007) An improved harmony search algorithm for solving optimization problems. Appl Math Comput 188(2):1567–1579MathSciNetMATHGoogle Scholar
  32. Manjarres D, Landa-Torres I, Gil-Lopez S, Del Ser J, Bilbao MN, Salcedo-Sanz S, Geem ZW (2013) A survey on applications of the harmony search algorithm. Eng Appl Artif Intell 26(8):1818–1831CrossRefGoogle Scholar
  33. Mokhtari H, Salmasnia A (2015) A Monte Carlo simulation based chaotic differential evolution algorithm for scheduling a stochastic parallel processor system. Expert Syst Appl 42(20):7132–7147CrossRefGoogle Scholar
  34. Nearchou AC (2007) Balancing large assembly lines by a new heuristic based on differential evolution method. Int J Adv Manuf Technol 34(9–10):1016–1029CrossRefGoogle Scholar
  35. Omran MGH, Mahdavi M (2008) Global-best harmony search. Appl Math Comput 198(2):643–656MathSciNetMATHGoogle Scholar
  36. Onwubolu G, Davendra D (2006) Scheduling flow shops using differential evolution algorithm. Eur J Oper Res 171(2):674–692CrossRefMATHGoogle Scholar
  37. Ouyang HB, Gao LQ, Li S, Kong XY, Wang Q, Zou DX (2017) Improved harmony search algorithm: LHS. Appl Soft Comput 53:133–167CrossRefGoogle Scholar
  38. Ovaska SJ, VanLandingham HF, Kamiya A (2002) Fusion of soft computing and hard computing in industrial applications: an overview. IEEE Trans Syst Man Cybern Part C (Appl Rev) 32(2):72–79CrossRefGoogle Scholar
  39. 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(3):830–848Google Scholar
  40. Pandi VR, Panigrahi BK (2011) Dynamic economic load dispatch using hybrid swarm intelligence based harmony search algorithm. Expert Syst Appl 38(7):8509–8514CrossRefGoogle Scholar
  41. Park J, Kwon S, Kim M, Han S (2017) A cascaded improved harmony search for line impedance estimation in a radial power system. IFAC-PapersOnLine 50(1):3368–3375Google Scholar
  42. Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evolut Comput 13(2):398–417CrossRefGoogle Scholar
  43. Shabani M, Mirroshandel SA, Asheri H (2017) Selective refining harmony search: a new optimization algorithm. Expert Syst Appl 81:423–443CrossRefGoogle Scholar
  44. Shan D, Cao G, Dong H (2013) LGMS-FOA: an improved fruit fly optimization algorithm for solving optimization problems. Math Probl Eng 108768:1–9.  https://doi.org/10.1155/2013/108768 MATHGoogle Scholar
  45. Shen Q, Jiang JH, Jiao CX, Shen GL, Yu RQ (2004) Modified particle swarm optimization algorithm for variable selection in MLR and PLS modeling: QSAR studies of antagonism of angiotensin II antagonists. Eur J Pharm Sci 22(2):145–152Google Scholar
  46. Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359Google Scholar
  47. Tsoulos IG, Tzallas A, Tsalikakis D (2016) PDoublePop: an implementation of parallel genetic algorithm for function optimization. Comput Phys Commun 209:183–189CrossRefMATHGoogle Scholar
  48. Valdez F, Vazquez JC, Melin P, Castillo O (2017) Comparative study of the use of fuzzy logic in improving particle swarm optimization variants for mathematical functions using co-evolution. Appl Soft Comput 52:1070–1083CrossRefGoogle Scholar
  49. Valian E, Tavakoli S, Mohanna S (2014) An intelligent global harmony search approach to continuous optimization problems. Appl Math Comput 232:670–684MathSciNetGoogle Scholar
  50. Villarrubia G, De Paz JF, Chamoso P, De la Prieta F (2018) Artificial neural networks used in optimization problems. Neurocomputing 272:10–16Google Scholar
  51. Wang G, Guo L (2013) A novel hybrid bat algorithm with harmony search for global numerical optimization. J Appl Math Article ID 696491, 1–21Google Scholar
  52. Wang CM, Huang YF (2010) Self-adaptive harmony search algorithm for optimization. Expert Syst Appl 37(4):2826–2837Google Scholar
  53. Wang L, He J, Zeng YR (2012) A differential evolution algorithm for joint replenishment problem using direct grouping and its application. Expert Syst 29(5):429–441CrossRefGoogle Scholar
  54. Wang L, Yang R, Xu Y, Niu Q, Pardalos PM, Fei M (2013) An improved adaptive binary harmony search algorithm. Inf Sci 232:58–87MathSciNetCrossRefGoogle Scholar
  55. Wang L, Shi Y, Liu S (2015) An improved fruit fly optimization algorithm and its application to joint replenishment problems. Expert Syst Appl 42(9):4310–4323CrossRefGoogle Scholar
  56. Wang L, Liu R, Liu S (2016) An effective and efficient fruit fly optimization algorithm with level probability policy and its applications. Knowl-Based Syst 97:158–174Google Scholar
  57. Xiang WL, An MQ, Li YZ, He RC, Zhang JF (2014) An improved global-best harmony search algorithm for faster optimization. Expert Syst Appl 41(13):5788–5803CrossRefGoogle Scholar
  58. Yadav P, Kumar R, Panda SK, Chang CS (2012) An intelligent tuned harmony search algorithm for optimization. Inf Sci 196:47–72CrossRefGoogle Scholar
  59. Yu WJ, Ji JY, Gong YJ, Yang Q, Zhang J (2018) A tri-objective differential evolution approach for multimodal optimization. Inf Sci 423:1–23MathSciNetCrossRefGoogle Scholar
  60. Zeng YR, Peng L, Zhang JL, Wang L (2016) An effective hybrid differential evolution algorithm incorporating simulated annealing for joint replenishment and delivery problem with trade credit. Int J Comput Int Sys 9(6):1001–1015CrossRefGoogle Scholar
  61. Zeng Y, Zeng Y, Choi B, Wang L (2017) Multifactor-influenced energy consumption forecasting using enhanced back-propagation neural network. Energy 127:381–396CrossRefGoogle Scholar
  62. Zhao F, Liu Y, Zhang C, Wang J (2015) A self-adaptive harmony PSO search algorithm and its performance analysis. Expert Syst Appl 42(21):7436–7455CrossRefGoogle Scholar
  63. Zhou YP, Tang LJ, Jiao J, Song DD, Jiang JH, Yu RQ (2009) Modified particle swarm optimization algorithm for adaptively configuring globally optimal classification and regression trees. J Chem Inf Model 49(5):1144–1153CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of ManagementHuazhong University of Science and TechnologyWuhanChina

Personalised recommendations