In the last 3 decades, metaheuristic algorithms have received more popularity because of their superior performance to solve large and complex optimization problems. Most of these algorithms are inspired by biological phenomena, social behavior of animals, science and art. Among these four sources, the last one is utilized only by one algorithm. In this paper, we propose another novel art-inspired population-based metaheuristic, called color harmony algorithm (CHA), for solving the global optimization problems. The proposed method models its search behavior through combining harmonic colors based on their relative positions around the hue circle in the Munsell color system and harmonic templates. We utilize simultaneously four different fitness information to construct the hue groups, which improve search ability of the algorithm. CHA has two different phases including the concentration phase and the dispersion phase which are employed to explore and exploit the search space. The performance of the proposed method has been examined using several benchmark test functions commonly used in the literature. To show the effectiveness and robustness of the proposed method, the results are compared with those obtained using ten well-known metaheuristic algorithms. Also, the Wilcoxon Signed-Rank test is conducted to measure the pair-wise statistical performances of the algorithms. The results indicate that besides the simplicity of the proposed algorithm, CHA can outperform the other considered algorithms in terms of the convergence speed and the number of function evaluations.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Price excludes VAT (USA)
Tax calculation will be finalised during checkout.
Awad NH et al (2016) Problem definitions and evaluation criteria for the CEC 2017 special session and competition on single objective real-parameter numerical optimization
Blum C, Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv 35(3):268–308
Cheng S, Shi Y (2011) Diversity control in particle swarm optimization. In: 2011 IEEE symposium on swarm intelligence (SIS). IEEE
Cochrane S (2014) The Munsell color system: a scientific compromise from the world of art. Stud Hist Philos Sci Part A 47:26–41
Cohen-Or D et al (2006) Color harmonization. ACM Trans Graph 25(3):624–630
Das A (2015) Guide to signals and patterns in image processing. Springer, Berlin
Derrac J et al (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evolut Comput 1(1):3–18
Dorigo M, Stützle T (2004) Ant colony optimization. MIT Press, Cambridge
Fogel LJ (1999) Intelligence through simulated evolution: forty years of evolutionary programming. Wiley, New York, p 162
Gandomi AH, Alavi AH (2012) Krill herd: a new bio-inspired optimization algorithm. Commun Nonlinear Sci Numer Simul 17(12):4831–4845
Gandomi AH et al (2013) Metaheuristic applications in structures and infrastructures, 1st edn. Elsevier, Amsterdam
Geem Z, Kim J, Loganathan GV (2001) A new Heuristic optimization algorithm: harmony search. Simulation 76(2):60–68
Glover F (1986) Future paths for integer programming and links to artificial intelligence. Comput Oper Res 13(5):533–549
Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, AnnAnbor
Jamil M, Yang X-S (2013) A literature survey of benchmark functions for global optimisation problems. Int J Math Model Numer Optim 4(2):150–194
Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Glob Optim 39(3):459–471
Kennedy J, Eberhart R (1995) Particle swarm optimization. In: IEEE international conference on neural networks, proceedings. IEEE, Perth, WA, Australia
Khachaturyan A, Semenovsovskaya S, Vainshtein B (1981) The thermodynamic approach to the structure analysis of crystals. Acta Crystallogr Sect A 37(5):742–754
Matsuda Y (1995) Color design. Asakura Shoten 2(4):10
Rao RV, Savsani VJ, Balic J (2012a) Teaching–learning-based optimization algorithm for unconstrained and constrained real-parameter optimization problems. Eng Optim 44(12):1447–1462
Rao RV, Savsani VJ, Vakharia DP (2012b) Teaching–learning-based optimization: an optimization method for continuous non-linear large scale problems. Inf Sci 183(1):1–15
Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm. Inf Sci 179(13):2232–2248
Storn R, Price K (1997) Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Talbi E-G (2009) Metaheuristics: from design to implementation. Wiley, New York, p 593
Tokumaru M, Muranaka N, Imanishi S (2002) Color design support system considering color harmony. In: Proceedings of the 2002 ieee international conference on fuzzy systems, 2002. FUZZ-IEEE’02. IEEE
Wang G, Guo L (2013) A novel hybrid bat algorithm with harmony search for global numerical optimization. J Appl Math 2013:21
Wang GG et al (2014) Chaotic krill herd algorithm. Inf Sci 274(1):17–34
Westland S et al (2007) Colour harmony. Colour Des Creat 1(1):1–15
Wolpert DH, Macready WG (1997) No free lunch theorems for optimization. IEEE Trans Evol Comput 1(1):67–82
Xhafa F, Abraham A (2008) Metaheuristics for scheduling in industrial and manufacturing applications, vol 128, 1st edn. Springer, Berlin
Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: González J et al (eds) Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, pp 65–74
Yang XS, Deb S (2009) Cuckoo search via Lévy flights. In: World congress on nature & biologically inspired computing, 2009. NaBIC 2009. IEEE
Conflict of interest
The authors declare that there is no conflict of interest
Human and animal rights
This article does not contain any studies with human participants performed by any of the authors.
Communicated by V. Loia.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
The precise sizes of gray areas in Fig. 4 are as follows: the large areas of X, V and Y type cover 26% of the hues; the small areas of i, L, I and Y type cover 5% of the hues; the large area of L type covers 22%; the area of T type covers 50%; The angle between the bisectors of the two areas of I, X and Y type is 180◦, and for L type it is 90° (Cohen-Or et al. 2006).
Rights and permissions
About this article
Cite this article
Zaeimi, M., Ghoddosian, A. Color harmony algorithm: an art-inspired metaheuristic for mathematical function optimization. Soft Comput 24, 12027–12066 (2020). https://doi.org/10.1007/s00500-019-04646-4
- Color harmony algorithm
- Population-based optimization
- Global optimization