A Dynamic Polymorphic Population based Algorithm: Side – Blotched Lizard Algorithm (SBLA) a reliable Algorithm to use in Real – World Problems

1. Introduction

The Side- Blotched Lizard Algorithm (SBLA) is a subpopulation-based optimization algorithm is to define the total and partial populations of lizards, taking into consideration how the distribution of each morph gradually changes as time goes by. Such lizard’s analysis with three morphs connected with the particular mating strategies [1]. The strategy takes into reflection of three polymorphism or subpopulations, blue, orange, and yellow lizards, but they only take place after it generates the initial population. The mating behavior of each morph is explained with three concepts, defensive, expansive, and sneaky [2] .The combined effort between the morphs generates a polymorphic population, able to self-balance the subpopulations of each morph without exhausting the weakest morph. The study of these lizards is particularly important because of their application to estimating insular colonization and extinction, genetic bottlenecks, ecology, and other key evolutionary issues [3]. The effects of this mechanism could be utilize the diversity of solutions on the purpose of multi-objective problem, it can be implemented to real-life problems to analysis its performance on specific perspectives.

2. Inspiration of Side – Blotched Lizard Algorithm (SBLA)

            The inspiration of SBL Algorithm which took inspiration on the different mating behavior of Side blotched lizards. Side-blotched lizards are a reptile mainly lives in the deserts of western North America [4]. These lizards are prey for much desert species. Its reproduction cycling between three colorized breeding patterns distinguished with the throat colors of side-blotched lizards as orange, blue, and yellow.They normally grow to six inches including the tail, with the males being the larger sex with bright throat colors [5].  The males exhibit three various reproductive behaviors and females exhibit two various life history strategies associated with throat colors. The presence of orange, blue, and yellow throat color is heritable in nature, since each color has their own behavior and way of surviving.

 In SBLA approach the population is divided into three subpopulations, which has their unique characteristics and weakness, blue gets overpowered by orange, orange is not capable of protecting against yellow, and yellow cannot do anything against blue, this makes the subpopulations to increase and continually decrease[6]. The search agents of the tricolor lizards can be created, eliminated, or transformed following a set of simple rules through the mating behavior. Therefore in this algorithm, the stability of the population of the side-blotched lizard and fluctuation of each color polymorphism is used as a guidance to develop the real word best optimal solutions [7].

Fig1: Inspiration of SBLA

3. Mating strategies of Side – Blotched Lizard

          The side-blotched lizards have three different mating behaviors depending on the distinct polymorphism in their throat colors such as blue, yellow and orange [8]. The mating behavior of the tricolor side- blotched lizard can be abstracted on the following points.

  • The Orange-throated males are highly dominant, largest and most aggressive who establish large territories and control areas that contain multiple females they also steal the mate of the blue lizard imposing strength, but they are vulnerable to the slippery yellow lizards. Orange-throated females lay many small eggs and are very territorial
  • The blue throated males are less aggressive and guard only one female they are better protecting them from yellow throated lizards, but are susceptible to having their females stolen by the orange lizards. The blue throated females can avoid the yellow stripe throated males but cannot withstand attacks.
  • The yellow throated males do not defend a territory, but cluster on the fringes of orange-throated lizard territories, and mate with the females on those territories while the orange-throat is absent, as the territory to defend is large. Females lay larger eggs and more liberal for each other.

4. Population color variation

In side blotched lizard populations, the coloration of the offspring is variation in a common environment. The gene flow and comparing DNA sequence among color morphs is related to the color variation [11]. Once the initial population is formed with their respective colors and the subpopulation colors are assigned, the offspring search process can start; this will go to the maximum offspring number. The offspring search agents can be formed by three major functions as

  • Created function
  • Eliminated function
  • Transformed function

4.1. Created function

The created function process is with an orange lizard, it is necessary to find for two blue lizards, that has the first and second best fitness, then we choose at random  this represent a position between the first lizard and the second lizard, blue lizards use the yellow instead, and to add a yellow lizard we need to select a position between the first and second best orange lizards, The first requirement to add a lizard is to create a new position in the population with the color matching the morph of the lizards[12].

Fig 2: Created function of SBLA

4.2. Eliminated function

The eliminated function process is when there is a negative change on the population of a morph, and there is no positive change. It gets every lizard in the population that matches the color to eliminate, once and deleted the variable of population changes on that specific color will decrease the population by one and the process will continue until the variable reaches zero [13].

Fig 3: Eliminated function of SBLA

4.3. Transformed function

The transformed function process is when the changes in the population of the color with the main population has a positive change and the one affect  by it has a negative .When is the orange season, the blue lizards will use the transform function each time their population decreases, and orange population increases.

Fig 4: Transformed function of SBLA

5. The game theory of Rock- Paper- scissors in related with mating strategies of Lizards

For side-splotched lizards, the model researchers have used is the game of rock-paper-scissors.  A big game theory of rock-paper-scissors, each variety has its pluses and minuses in the mating game [9]. Just as a rock crushes–and so beats–scissors in the game, orange-throated lizards out-compete the less aggressive blue-throated males; just as scissors cut paper, protective blue-throated lizards win against sneaky yellow-throated males; and as paper covers a rock, the yellow-throated lizards are successful against roving orange-throated males [10].

Fig 5: The game theory of Rock- paper- scissor

6. Numerical Implementation of SBLA

6.1. Initialization

A typical tri-objective design variables optimization can be presented as follows:

L= ( l1 , l2 , l3,…….) < ∞n                                                                          (1)

Let the objective functions be minimized as:

F(L) = (L1, L2, L3) →min                                                                       (2)

Where n is the number of variables and ∞n is the number of constraints. Due to the simulation of three types of lizards, their existence and breeding, we formulated the tri-objective optimization. Once the initialization is generated with their respective fitness and the subpopulation colors are implemented, the iterative search process can start; this will go from 1 to the maximum offspring numbers.

6.2. Subpopulation models

To analyze the cyclic behavior of the polymorphic populations generated by a vector of point’s that goes from 0 to the max offspring with a spacing give 𝐹𝑟𝑒𝑞uency, denoted by the two variables as

To generate every subpopulation from the total population each new offspring is denoted as

Where m is an index that goes from 1 to Subpopulation

To get the changes on the population ∆N the algorithm evaluate the subpopulation as

ΔN= Nm – Nm-1                                                 (6)

If the population gets changes, it is time to perform the delete, transform and add lizard functions.

  • Blue Lizard Search Strategy

Initially, we get the best lizard in the total population 𝐵lue lizard 𝑃population and the best of the blue lizards is selected according to their fitness, if it is the same lizard it will need to get the second-best blue lizard instead, to make an absolute difference between them and to get a delta distance ∆diff.

∆diff = absolute (Blue lizard- Blue lizard best)                       (7)

The Maximum and Minimum limit is, then formulated to calculate as below;

Max= Blue lizard population-∆diff                                        (8)

Min= Blue lizard population+ ∆diff                                       (9)

The Max number of blue lizards in the population in that specific offspring will get.

  • Orange Lizard Search Strategy

The search process is to obtain the best orange lizard according to fitness, according to the best orange one and it is defined as

Diff= Best Orange population –N

The distance is gain then we calculated by dividing the Max and Min limit Lover the number of orange lizards #𝑂, and the distance is multiplied for a random between 0 and 1.

Attaining desired movement then, the selected orange 𝑂 𝑛 can move away from the best orange                               ON= Best Orange population –N                                         (12)  

  • Yellow Lizard Search Strategy

For the yellow search strategy, the sneaking side of the lizards, they do not have territories; they enter to the orange territories to steal their females, said areas are large, making hard to defend them from yellow lizards. Once the orange lizard is selected then the yellow lizard 𝑌 𝑛 will move towards it, the operator is:

  • Yellow Lizard Search Strategy

For the yellow search strategy, the sneaking side of the lizards, they do not have territories; they enter to the orange territories to steal their females, said areas are large, making hard to defend them from yellow lizards. Once the orange lizard is selected then the yellow lizard 𝑌 𝑛 will move towards it, the operator is:

  YellP= Yell+ rand (Orgi– Yellp)                                                (13)  

 7. Advantages of SBLA

Fig 6: Advantages of SBLA

   8. Flowchart of SBLA

Fig 7: Flowchart of SBLA

9. Pseudo code of SBLA

Fig8: Pseudo code of SBLA

10. Applications of SBLA

Fig 9: Application of SBLA


[1] S. Nesmachnow, An overview of metaheuristics: accurate and efficient methods for optimisation, Int. J. Metaheuristics. 3 (2014) 320. doi:10.1504/IJMHEUR.2014.068914.

 [2] M. Dorigo, C. Blum, Ant colony optimization theory: A survey, Theor. Comput. Sci. 344 (2005) 243–278. doi:10.1016/j.tcs.2005.05.020.

[3] S. Mirjalili, A. Lewis, the Whale Optimization Algorithm, Adv. Eng. Softw. 95 (2016) 51–67. doi:10.1016/j.advengsoft.2016.01.008.

 [4] F. Fausto, A. Reyna-Orta, E. Cuevas, Á.G. Andrade, M. Perez-Cisneros, From ants to whales: metaheuristics for all tastes, Artif. Intell. Rev. (2019) 1–58. doi:10.1007/s10462-018-09676-2.

 [5] T. Bäck, F. Hoffmeister, H.-P. Schwefel, A survey of evolution strategies, in: Proc. Fourth Int. Conf. Genet. Algorithms, 1991: p. 8. doi: [7] M. Mitchell, Genetic algorithms: An overview, Complexity. 1 (1995) 31–39. doi:10.1002/cplx.6130010108.

[6]. R.A. Rutenbar, Simulated annealing algorithms: An overview, IEEE Circuits Devices Mag. 5 (1989) 19–26. doi:10.1109/101.17235.

[7] Ş.I. Birbil, S.C. Fang, An electromagnetism-like mechanism for global optimization, J. Glob. Optim. 25 (2003) 263–282. doi: 10.1023/A: 1022452626305.

[8] E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, GSA: A Gravitational Search Algorithm, Inf. Sci. (Ny). 179 (2009) 2232–2248. doi:10.1016/j.ins.2009.03.004.

[9] E. Cuevas, A. Echavarría, M.A. Ramírez-Ortegón, An optimization algorithm inspired by the States of Matter that improves the balance between exploration and exploitation, Appl. Intell. 40 (2014) 256–272. doi: 10.1007/s10489-013-0458-0.

[10] S. Mirjalili, SCA: A Sine Cosine Algorithm for solving optimization problems, Knowledge-Based Syst. 96 (2016) 120–133. doi:10.1016/j.knosys.2015.12.022.

 [11] S. Kirkpatrick, C.D. Gelatt, M.P. Vecchi, Optimization by simulated annealing, Science (80-.). 220 (1983) 671–680. doi:10.1126/science.220.4598.671.

[12] R.A. Rutenbar, Simulated Annealing Algorithms: An Overview, IEEE Circuits Devices Mag. 5 (1989) 19–26.

 [13] N. Siddique, H. Adeli, Simulated Annealing, Its Variants and Engineering Applications, Int. J. Artif. Intell.Tools. 25 (2016). doi:10.1142/S0218213016300015

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