A Population Based Metaheuristic Art Inspired Algorithm: Color Harmony Algorithm (CHA) for Solving Real World Optimization Problems

1. Introduction

Colors, usually perceived a major role in the world for the numerous number of multicolored combinations to the objects. It is known that the relationship between colors and human emotions has a stable influence on how we perceive our environment [1]. A population-based metaheuristic method algorithm known as the Color Harmony Algorithm is formulated to the searching behavior of combining harmonic colors based on their relative positions around the hue color circle in the Munsell color system and harmonic templates. Color harmony is when you use color combinations side-by-side that is pleasant to the human eye [2]. Colors are most important factor to attractive image patterns. The purpose of this color schemes is to change the “look and feel” of images which is to analysis various emotions. Color theories create a logical structure for color. For example, if we have an array of fruits and vegetables, it is systematically arranged based on the color and place that shows the colors in relation to each one [3]. Since the CHA suggests that the approach to meet the requirement of optimal high solution applications and high-quality sequential color schemes.

2. Inspiaration of CHA

The word harmony can be defined as a pleasing arrangement of parts, whether it be music, poetry or color. In color harmony is something that is pleasant to the eye [4]. It stimulates the viewer and it creates an inner sense of order, to get the balance to understand the visual experience. When something is not harmonious, it’s either boring or chaotic [5]. Therefore color harmony is to delivers visual interest and a sense of order. Based on the inspiration of color sequence structed a population based art Algorithm known as Color Harmony Algorithm (CHA).

The substantive color schemes are defined as color harmonies. Color harmony is as much of a science as an art and follows very specific rules about hue, brightness and contrast. Color harmony is a different notion because human responses to color are both affective and perception, involving emotional response and judgment [6]. Hence, our responses to color and the notion of color harmony are open to the influence of a range of different factors. These factors include individual differences such as age, gender, personal preference, etc…As well as cultural, sub-cultural and socially-based differences which give rise to conditioning and learned responses about color [7]. CHA is developed based on the Munsell Color System and color harmony system. The results show that colors which boost humans brains. CHA algorithm can perform in terms of the convergence speed and the number of function evaluations and examined for various well known benchmark functions.

3. The Color wheel

            The color wheel is the basis term of the color theory, because it indicates the relationship between colors [9]. The color wheel to find color harmonies by using the rules of color combinations. The color wheel was invented in 1666 by Isaac Newton, who mapped the color spectrum onto a circle [10]. The color wheel is the basis of color theory, it distinguish the relationship between colors. A color circle, based on red, yellow and blue, is traditional in the field of art.

4. Types of Color Harmony

There are six types of color harmonies commonly used in design [11]. They are explained as follows

4.1. Complementary colors: Colors that are opposite each other on the color wheel is mentioned to be complementary colors (example: red and green).

4.2. Split complementary colors. The split-complementary color scheme is a variation of the complementary color scheme [12]. In addition to the base color, it uses the two colors adjacent to its complement.

4.3 Analogous colors. Analogous colors are any three colors which are side by side on a 12-part color wheel, such as yellow-green, yellow, and yellow-orange. Usually one of the three colors predominates.

4.4. Triadic harmonies. A triadic color scheme uses colors that are evenly spaced around the color wheel. To use a triadic harmony successfully, the colors should be carefully balanced – let one color dominate and use the two others for accent.

4.5. Tetradic harmonies. The rectangle or tetradic color scheme uses four colors arranged into two complementary pairs [13]. This rich color scheme offers plenty of possibilities for variation you should also pay attention to the balance between warm and cool colors in your design.

4.6. Monochromatic harmonies. Three shades, tones and tints of one base color. Provides a subtle and conservative color combination [14]. This is a versatile color combination that is easy to apply to design projects for a harmonious look.

5. The Munsell color system

The American art instructor and painter Albert Henry Munsell proposed a color system in the early twentieth century [15]. In the Munshell color system color relationship is based on the three color dimension known as

• Hue: Hue is an attribute which we give names to colors (e.g., red, yellow, green, etc)
• Value: Value indicates the lightness or darkness of a color,
• Chroma: Chroma indicates the degree of purity or colorfulness of a color.

6. Numerical Implementation of CHA

Initially, colors are randomly distributed to the search space and considering as the color containing a number of decision variables C(x, y) as

C (x,y) = rand ( C^l(x) – C^m (y))          x = 1,2,……N_l

                                                                y = 1 2,……N_m                                          (1)   

Where, C^l(x) and C^m (y) are the upper & lower boundaries. N_l, N_m is the total number of colors.

Once the initial population is obtained then the population diversity is greater than or equal to the initial diversity threshold value then measures the distribution colors in the the search space.

Where D is the mean of the current solutions on each dimension; dim= [d¹, d2,d3…] and Div denotes the whole population diversity.

Since harmonic colors are not particular colors then various colors are selected and combined then the new colors N_color are produced as follows:

 C¹ (x, y) = Rand₁ . C (P_x,y) + Rand₂ .C (Q_x,y)          x=1, 2…….N_color

                                                                                               Y = 1, 2… N                      (5)

                          Rand₂= 1- Rand₁                                                                                              (6)

Where C¹ is the combination of random set of numbers as Rand₁ and Rand₂ , C (P_x,y) and C(Q_x,y)   are the components of new updating hue circle colors.

In order to achieve the combination of new component set the parameter agent as

 Thus the Parameter Agents depends on four parameters such as N_color, and.).

Based on the Munsell method definition, different colors should occupy different areas to look harmonious in an image. Then the new one araised as

C^new(x,y) = Rand₁C_sel(x,y)+(1- Rand₂) C_sel(x,y)                                                   (10)

Therefore, according to the Munsell method, they have new optimal fitness contribution in combination with colors in the hue circle parameters as

Sel 1> P* N                                                                                              (11)

Sel2 <P* N                                                                                               (12)

7. Pseudo code of CHA

8. Flowchart of CHA

9. Application of CHA

10. Advantages & Disadvantages of CHA

Reference

[1] 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.

[2] 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.

[3] 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.

[4] 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.

 [5] Roli A (2003) Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Comput Surv 35(3):268–308.

[6] Khachaturyan A, Semenovsovskaya S, Vainshtein B (1981) the thermodynamic approach to the structure analysis of crystals. Acta Crystallogr Sect A 37(5):742–754.

[7].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 realparameter optimization problems.

[8].Rashedi E, Nezamabadi-pour H, Saryazdi S (2009) GSA: a gravitational search algorithm.

[9]. Inf Sci 179(13):2232–2248 Storm R, Price K (1997) Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359.

[10] Gandomi AH et al (2013) metaheuristic applications in structures and infrastructures, 1st edn. Elsevier.

[11] 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.

[12] Comput Oper Res 13(5):533–549 Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press.

[13] Ann Anbor 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.

[14] Wang GG et al (2014) Chaotic krill herd algorithm. Inf Sci 274(1):17–34 Westland S et al (2007) Color harmony. Color Des Creat 1(1):1–15.

[15] Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Gonza ´lez J et al (eds) Nature inspired cooperative strategies for optimization (NICSO 2010). Springer, Berlin, pp 65