Solving multi-objective optimization problems using self-adaptive harmony search algorithms

  • Yin-Fu HuangEmail author
  • Sih-Hao Chen
Methodologies and Application


In recent years, there have been many multi-objective evolutionary algorithms proposed to solve multi-objective optimization problems. These evolutionary algorithms generate many solutions for iterations and move to the true Pareto optimal region gradually. As expected, since the harmony search algorithm can also iterate over a large number of solutions (in HM memory) and moves to the true Pareto optimal region, we use it to solve multi-objective optimization problems. In this paper, the proposed system architecture can be divided into two phases. In the first phase, we aim to search feasible solution regions as widely as possible in the entire process. In the second phase, we focus on searching optimized solutions stepwise in the feasible solution regions. Since the proposed algorithm uses many parameters, we adjust some of them in a self-adaptive way and call the algorithm self-adaptive. In the experiments, we use the eleven well-known multi-objective problems and three many-objective problems to examine the proposed algorithm and other existing algorithms, based on five performance indicators. As a result, our algorithm achieves better performances than the others in inverted generational distance, hypervolume, and spread indicators.


Harmony search algorithm Optimization method Pareto optimization Multi-objective optimization Self-adaptive 



This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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.


  1. Chen B, Zeng W, Lin Y, Zhang D (2015) A new local search-based multiobjective optimization algorithm. IEEE Trans Evol Comput 19(1):50–73CrossRefGoogle Scholar
  2. Cheng R, Li M, Tian Y, Xiang X, Zhang X, Yang S, Jin Y, Yao X (2018) Benchmark functions for CEC’2018 competition on many-objective optimization. Technical report CEC2018, pp 1–22Google Scholar
  3. Chitara D, Niazi KR, Swarnkar A, Gupta N, (2016) Multimachine power system stabilizer tuning using harmony search algorithm. In: Proceedings of international conference on electrical power and energy systems, Bhopal, IndiaGoogle Scholar
  4. Dai X, Yuan X, Zhang Z (2015) A self-adaptive multi-objective harmony search algorithm based on harmony memory variance. Appl Soft Comput 35:541–557CrossRefGoogle Scholar
  5. Deb K, Jain H (2014) An evolutionary many-objective optimization algorithm using reference-point-based nondominated sorting approach, part I: solving problems with box constraints. IEEE Trans Evol Comput 18(4):577–601CrossRefGoogle Scholar
  6. Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist nondominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Schoenauer M et al (eds) Parallel problem solving from nature. Springer, Berlin, pp 849–858Google Scholar
  7. Deb K, Thiele L, Laumanns M, Zitzler E (2001) Scalable test problems for evolutionary multi-objective optimization. In: Abraham A, Jain L, Goldberg R (eds) Evolutionary multiobjective optimization. Springer, Berlin, pp 105–145Google Scholar
  8. Deb K, Pratap A, Agrawal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  9. Doush IA, Bataineh MQ (2015) Hybedrized NSGA-II and MOEA/D with harmony search algorithm to solve multi-objective optimization problems. In: Proceedings of international conference on neural information processing, Istanbul, TurkeyGoogle Scholar
  10. Feng Z, Guo H, Liu Z, Xu L, She J (2017) Hybridization of harmony search with Nelder–Mead algorithm for combined heat and power economic dispatch problem. In: Proceedings of the 36th Chinese control conference, Dalian, ChinaGoogle Scholar
  11. Geem ZW, Kim JH, Loganathan GV (2001) A new heuristic optimization algorithm: harmony search. Simulation 76(2):60–68CrossRefGoogle Scholar
  12. Huang YF, Wang CT (2014) Classification of painting genres based on feature selection. In: Park JJ, Chen SC, Gil JM, Yen NY (eds) Multimedia and ubiquitous engineering. Springer, Berlin, pp 159–164CrossRefGoogle Scholar
  13. Li M, Yang S, Liu X (2014) Shift-based density estimation for Pareto-based algorithms in many-objective optimization. IEEE Trans Evol Comput 18(3):348–365CrossRefGoogle Scholar
  14. Li K, Deb K, Zhang Q, Kwong S (2015) Combining dominance and decomposition in evolutionary many-objective optimization. IEEE Trans Evol Comput 19(5):694–716CrossRefGoogle Scholar
  15. Li M, Yang S, Liu X (2016) Pareto or non-Pareto: bi-criterion evolution in multiobjective optimization. IEEE Trans Evol Comput 20(5):645–665CrossRefGoogle Scholar
  16. Mahto T, Mukherjee V (2017) Fractional order fuzzy PID controller for wind energy-based hybrid power system using quasi-oppositional harmony search algorithm. IET Gener Transm Distrib 11(13):3299–3309CrossRefGoogle Scholar
  17. Tian Y, Zhang X, Cheng R, Jin Y (2016) A multiobjective evolutionary algorithm based on an enhanced inverted generational distance metric. In: Proceedings of the IEEE congress on evolutionary computation, Vancouver, BC, CanadaGoogle Scholar
  18. Tian Y, Cheng R, Zhang X, Jin Y (2017) PlatEMO: a MATLAB platform for evolutionary multi-objective optimization. IEEE Comput Intell Mag 12(4):73–87CrossRefGoogle Scholar
  19. Van Veldhuizen DA, Lamont GB (1998) Multiobjective evolutionary algorithm research: a history and analysis. TR-98-03, pp 1–88Google Scholar
  20. Van Veldhuizen DA, Lamont GB (2000) On measuring multiobjective evolutionary algorithm performance. In: Proceedings of the IEEE congress on evolutionary computation, La Jolla, CA, USAGoogle Scholar
  21. Wang YN, Wu LH, Yuan XF (2010) Multi-objective self-adaptive differential evolution with elitist archive and crowding entropy-based diversity measure. Soft Comput 14(3):193–209CrossRefGoogle Scholar
  22. Wu J, Yi J, Gao L, Li X (2017) Cooperative path planning of multiple UAVs based on PH curves and harmony search algorithm. In: Proceedings of the IEEE 21st international conference on computer supported cooperative work in design, Wellington, New ZealandGoogle Scholar
  23. Zhang Q, Li H (2007) MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712–731CrossRefGoogle Scholar
  24. Zhang Q, Zhou A, Zhao S, Suganthan PN, Liu W, Tiwari S (2008) Multiobjective optimization test instances for the CEC-2009 special session and competition. Technical report CES-487, pp 1–30Google Scholar
  25. Zhang S, Wang H, Yang D, Huang M (2015) Hybrid multi-objective genetic algorithm for multi-objective optimization problems. In: Proceedings of the 27th Chinese control and decision conference, Qingdao, ChinaGoogle Scholar
  26. Zhang H, Zhou A, Song S, Zhang Q, Gao X, Zhang J (2016) A self-organizing multiobjective evolutionary algorithm. IEEE Trans Evol Comput 20(5):792–806CrossRefGoogle Scholar
  27. Zhou A, Jin Y, Zhang Q, Sendhoff B, Tsang E (2006) Combining model-based and genetics-based offspring generation for multi-objective optimization using a convergence criterion. In: Proceedings of the IEEE congress on evolutionary computation, Vancouver, BC, CanadaGoogle Scholar
  28. Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195CrossRefGoogle Scholar
  29. Zitzler E, Laumanns M, Thiele L (2001) SPEA2: improving the strength Pareto evolutionary algorithm. TIK-Report 103, pp 1–20Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer Science and Information EngineeringNational Yunlin University of Science and TechnologyTouliuTaiwan, ROC

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