**1. Introduction**

The Woodpecker Mating Algorithm (WMA) is the nature inspired search population-based metaheuristic algorithm that imitates the mating behavior of woodpeckers [1]. Woodpeckers are wonderful birds and there are nearly 200 various species of them. They use an effective strategy of communication known as drumming to attract the other gender for the process of mating. WMA is applicable for the challenging problems in structural optimization [2]. Optimization is the process of obtaining optimal values for the parameters of a speciﬁc system from all of the possible values to maximize or minimize its output [3]. The WMA algorithm is used to solve the real world problems in different engineering ﬁelds and the efficiency of WMA is tested and obtains better result in several benchmark functions.

**2. Inspiration of WMA**

Woodpecker Mating Algorithm (WMA) is inspired by the intelligent mating behavior of red-bellied woodpeckers. In WMA, the population of woodpeckers is divided into male and female groups. Woodpeckers use a speciﬁc strategy for communication and it is called drumming or pecking the trunks of trees [4]. Woodpeckers make holes into the trunks of trees to build nests and feed on insects [5]. However, the most important purpose of drumming is to attract mates in the mating season.

At the beginning of the mating season, male woodpeckers start drumming. The quality of the sound produced by the male has a great effect on the attraction of female woodpeckers and they try to attract and choose the best mate. Birds with the higher ability for drumming can produce stronger, higher quality drums and are regarded as ideal mates [6]. Their drum can be heard farther away and attract more female woodpeckers. The female woodpeckers are then attracted to the source, because for them a more powerful sound connects the male’s higher ability to ﬁnd food, nest and reproduce, making them a better option as mate. As a result, the size of a female woodpecker’s movement toward a male woodpecker depends on the quality of sound it hears. This process is repeated in several intervals or several days and each time, the female woodpecker gets closer to the male [7]. According to the physics laws, sound waves propagate in the environment so that other woodpeckers can hear them. Therefore, the physical quantity is deﬁned as sound intensity, on which the amount of sound received by a listener depends. Such concepts provided the inspiration for the WMA algorithm [8].

**3. Sound Intensity of Woodpecker**

The sound intensity was inspired by the concepts of sound waves physics. In physics sound intensity is defined as quality or frequency of sound produced and received as waves [9]. The sound intensity may high or low depends upon the nature of producing sound waves. In WMA the male woodpecker produce the sound of drumming or pecking tree for the purpose of attracting female for mating [10]. The male woodpecker with high sound intensity of drumming is attracted by the female and male woodpecker with low sound intensity of drumming is rejected by the female.

**4. Distinguish between Male & female Red bellied Woodpecker**

The Population of Red Bellied Woodpecker is divided into male and female for the mating purpose. At the beginning of the mating section the number of male population is high in accordance with the female [11]. With the successful mating purpose the woodpecker population is to be increased [12]. Thus the male and female woodpecker have different characteristic are distinguished as below;

**Male:**The male woodpecker has a red crown and nape, medium – sized black and white barred with a pale belly [13].**Female:**The female woodpecker has a red nape, lacking the red crown, medium –sized black and white barred with a pale belly [14].

**5. Numerical Implementation of WMA**

**Step 1**

Initialize the parameters of WMA as male and female woodpeckers are considered as candidate solutions [15]. Hence we initialize the candidate solution as random group of woodpeckers and distributed uniformly in the search space.

**Step 2**

At the beginning of each iteration, the woodpecker population is sorted on the basis of the rate of ﬁtness value according to the objective function. The woodpecker in motion is give as

Where is the position of the woodpecker, is the position of the best male woodpecker, is the random number of distribution to the interval of (0, 1) and the random coefficients of the woodpecker in each iteration.

**Step 3**

As a result, the male one produces the highest quality of drumming sounds inﬂuencing the female woodpeckers. Then the female woodpecker updates its position according to best male as

W= rand + Z (3)

Where rand is the random number of distribution and Z is the parameter value in the iteration cycle.

**Step 4**

If W i>1, then female woodpeckers are required to far away the target woodpecker and diverge from it. Then the new promising areas for better solutions are updated. If W i ≤ 1, then the female woodpeckers have to converge to the target woodpecker as

Where ß are the male woodpecker and are the sound intensity of the target woodpecker.

A woodpecker moves around the centralized target, and results in a more accurate estimated optimal solution. Therefore, parameter effect is defined as

Where TSF is the tangent sigmoid function, is the current iteration number and iter_{max} is the maximum number of iterations.

In the ﬁnal iterations, decreasing the number of male bird’s increases and accuracy of solution is

Where TH is the threshold value and the sound intensity movement is called the random running away movement of woodpecker.

**Step 5**

The Random Running Away (RRA) with the new position of woodpecker with the boundaries of lower and upper is given as

RRA = ib – (ib –ub) *Rand (9)

The woodpecker heard the sound of the drums with acceptable sound intensity. Therefore, it is in an appropriate position. Thus the Sound intensity declares to run away group of woodpeckers. The Group Run Away (GRA) is denotes as

¥ = The probability of run away coefficient. GRA is a vector as long as the problem dimensions, the elements of which are obtained through Equation as

**Step 6**

The new position of the female woodpecker sits at any random point between the best male woodpecker positions and the random woodpecker is

In this step, the new position of the woodpecker is compared with the previous position and the position of the best woodpecker [16]. If the position is better than one, it will get replaced. If the termination condition of the algorithm is met, the best solution will be selected as the optimal solution to the problem.

**6. Pseudo code of WMA**

**7. Flowchart of WMA**

**8. Application of WMA**

In WMA technique various applications are implemented. They are as follows;

- Sound Intensity [17].
- Engineering Design [18].
- Structural optimization problems [19].
- Data Retrieval [20].

**9. Advantages & Disadvantages of WMA**

**Reference**

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

[2] Chandel P (2018) Social Behaviour Inspired Optimization Algorithm: An Approach for Solving Complex Optimization Problems. HELIX 8:3985-3988. doi: 10.29042/2018-3985-3988

[3] Anvari B (2004) Book Review: Introduction to Biophotonics. By Prasad N. Prasad, John Wiley & Sons, Hoboken, New Jersey, 2003, 593 pp., ISBN 0-471-28770-9. Annals of Biomedical Engineering 32:1314-1315. doi: 10.1114/b:abme.0000039443.03525.bd

[4] Maier H, Razavi S, Kapelan Z et al. (2019) Introductory overview: Optimization using evolutionary algorithms and other metaheuristics. Environmental Modelling & Software 114:195-213. doi: 10.1016/j.envsoft.2018.11.018

[5] Qian W, Chai J, Xu Z, Zhang Z (2018) Differential evolution algorithm with multiple mutation strategies based on roulette wheel selection. Applied Intelligence 48:3612-3629. doi: 10.1007/s10489-018-1153-y

[6] Behera S, Sahoo S, Pati B (2015) A review on optimization algorithms and application to wind energy integration to grid. Renewable and Sustainable Energy Reviews 48:214-227. doi: 10.1016/j.rser.2015.03.066

[7] Kaveh A, Dadras A (2017) A novel meta-heuristic optimization algorithm: Thermal exchange optimization. Advances in Engineering Software 110:69-84. doi: 10.1016/j.advengsoft.2017.03.014

[8] Dehghani M, Mardaneh M, Montazeri Z et al. (2018) SPRING SEARCH ALGORITHM FOR SIMULTANEOUS PLACEMENT OF DISTRIBUTED GENERATION AND CAPACITORS. Electrical Engineering & Electromechanics 0:68-73. doi: 10.20998/2074-272x.2018.6.10

[9] Khabbazi A, Gargari E, Lucas C (2009) Imperialist competitive algorithm for minimum bit error rate beamforming. International Journal of Bio-Inspired Computation 1:125. doi: 10.1504/ijbic.2009.022781

[10] Gandomi A (2014) Interior search algorithm (ISA): A novel approach for global optimization. ISA Transactions 53:1168-1183. doi: 10.1016/j.isatra.2014.03.018

[11] Issa M, Hassanien A, Oliva D et al. (2018) ASCA-PSO: Adaptive sine cosine optimization algorithm integrated with particle swarm for pairwise local sequence alignment. Expert Systems with Applications 99:56-70. doi: 10.1016/j.eswa.2018.01.019

[12] Zhang Y, Jin Z (2020) Group teaching optimization algorithm: A novel metaheuristic method for solving global optimization problems. Expert Systems with Applications 148:113246. doi: 10.1016/j.eswa.2020.113246

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

[14] Chandel P (2018) Social Behaviour Inspired Optimization Algorithm: An Approach for Solving Complex Optimization Problems. HELIX 8:3985-3988. doi: 10.29042/2018-3985-3988

[15] Anvari B (2004) Book Review: Introduction to Biophotonics. By Prasad N. Prasad, John Wiley & Sons, Hoboken, New Jersey, 2003, 593 pp., ISBN 0-471-28770-9. Annals of Biomedical Engineering 32:1314-1315. Doi: 10.1114/b:abme.0000039443.03525.bd

[16] S. Mirjalili,”The ant lion optimizer,” Advances in Engineering Software, vol. 83, pp. 80-98, 2015.

[17] V. Punnathanam and P. Kotecha,”Yin-Yang-pair Optimization: A novel lightweight optimization algorithm,” Engineering Applications of Artiﬁcial Intelligence, vol. 54, pp. 62-79, 2016.

[18] A. Askarzadeh,”Bird mating optimizer: an optimization algorithm inspired by bird mating strategies,” Communications in Nonlinear Science and Numerical Simulation, vol. 19, pp. 1213-1228, 2014.

[19] X.-S. Yang, Engineering optimization: an introduction with metaheuristic applications. New Jersey: John Wiley & Sons, 2010.

[20] H. R. Maier, S. Razavi, Z. Kapelan, L. S. Matott, J. Kasprzyk, and B. A. Tolson, ”Introductory overview: Optimization using evolutionary algorithms and other metaheuristics,” Environmental modelling & software, 2018.

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