**1.
Introduction**

** **The Bat algorithm is a
metaheuristic algorithm for global optimization. It was inspired by the
echolocation behavior of microbats, with varying pulse rates of emission and loudness.
The Bat algorithm was developed by Xin-She Yang in 2010. Metaheuristic
algorithms such as particle swarm optimization and simulated annealing are now
becoming powerful methods for solving many tough optimization problems [1]. The
vast majority of heuristic and metaheuristic algorithms have been derived from
the behavior of biological systems and/or physical systems in nature. For
example, particle swarm optimization was developed based on the swarm behavior
of birds and fish, while simulated annealing was based on the annealing process
of metals. New algorithms are also emerging recently, including harmony search
and the firefly algorithm. The former was inspired by the improvising process
of composing a piece of music, while the latter was formulated based on the
flashing behavior of fireflies. Each of these algorithms has certain advantages
and disadvantages [2]. For example, simulating annealing can almost guarantee
to find the optimal solution if the cooling process is slow enough and the
simulation is running long enough; however, the fine adjustment in parameters
does affect the convergence rate of the optimization process [3].

**2. Bat Echolocation Behavior**

A focal bat (left) emits an echolocation signal (blue). Echoes (pink) return simultaneously from a potential prey item and a tree obstacle. A second insect emits an acoustic signal (red), and a conspecific echolocate nearby (green). Note that each of these acoustic stimuli could serve as signal or as noise, depending on the focal animal’s current behavioral goals [4].

**3.
Bat Search Algorithm (BSA)**

Bat algorithm is based on the echolocation behavior of microbats with varying pulse rates of emission and loudness. The idealization of the echolocation of microbats can be summarized as follows: Each virtual bat flies randomly with a velocity at position (solution) with a varying frequency or wavelength and loudness [5]. As it searches and finds its prey, it changes frequency, loudness and pulse emission rate. Search is intensified by a local random walk. Selection of the best continues until certain stop criteria are met. This essentially uses a frequency-tuning technique to control the dynamic behavior of a swarm of bats, and the balance between exploration and exploitation can be controlled by tuning algorithm-dependent parameters in bat algorithm [6].

**3.1.
Rules of Bat BSA**

- All bats use ecolocation to sense distance, and they also know the difference between food/prey and background barriers in some magical way [7].
- Bats fly randomly with velocity at position with a fixed frequency varying loudness to search for prey.
- Although the loudness can vary in many ways [8].

**3.2.
Bat Behavior**

- Echolocation is the some bats have evolved a highly sephisticated sense of hearing.
- They emit sounds that bounce off of objects in their path, sending echoes back to the bats [9].
- From these echoes, the bats can determine the size of objects, distance how fast they are travelling [10].

**3.3.
Steps for BSA**

- Initialize
- Update position and velocity
- Generate random number
- Fitness values

**3.3.1.
Initialization**

In initialization, the parameters of an algorithm are initialized, after that it generates an initial population using random distribution, and at last, the best solution is illustrated from that initial population [11].

**3.3.2.
Update position and velocity**

Calculate the fitness function of the selected objective functions with the initial position, the velocity and weights. Set the best particle from the initially evaluated solution. It involves process randomization, and new solution generation (position update), which sorts and compares among best possible outcomes [12]. Now the feasibility rule must be carried out to obtain a new population. In this step, the population is updated based on injective scheme (one-to-one), where the solution after implementing the rough set scheme is compared with corresponding one obtained by the bat procedures [13].

**3.3.3.
Generate Random Number**

** **A long-term lack of
improvement regarding the best result during the run was one of the most
reliable indicators of the stagnation. If the fitness value did not improve
over a number of generations, this probably means that the search process got
stuck within a local optimum [14].

**3.3.4.
Fitness values**

Focused on fitness training in regard to cycling. Incorporation of strength training in cyclist’s preparatory periods has received more attention over the last two decades. Most of the serious and competitive cyclists also include strength training in their training programs. It is also evident in some previous research that adding strength training to an endurance training program can increase endurance performance [15].

**3.4. Flow Chart**

**4.
Numerical Expression for BSA**

BSA is applied to this equation,

**5. Applications of BSA**

- Image processing
- Fuzzy logic and other applications
- Continuous optimization in engineering[17]
- Inverse problem, parameter estimation
- Combinatorial optimization and scheduling
- Classifications, clustering and Data mining[18]
- Biology and medical problem
- Economic dispatch problem
- Feature selection
- Multilevel image thresholding

**6. Advantages of BSA**

- Simple, Flexible, and Easy to implement.
- Solve a wide range of problems and highly non linear problems efficiently.
- Provides very quick convergence at a very initial stage by switching from exploration to exploitation.
- The loudness and pulse emission rates essentially provide a mechanism for automatic control and auto-zooming into the region [19].
- It gives promising optimal solutions.
- Works well with complicated problems [20].

**Reference**

[1] Zhang, J. and Wang, G. (2012). Image Matching Using a Bat Algorithm with Mutation. Applied Mechanics and Materials, 203, pp.88-93.

[2] Kaveh, A. and Kooshkebaghi, M. (2019). Artificial Coronary Circulation System; A new bio-inspired metaheuristic algorithm. Scientia Iranica, 0(0), pp.0-0.

[3] Ali, E. (2014). Optimization of Power System Stabilizers using BAT search algorithm. International Journal of Electrical Power & Energy Systems, 61, pp.683-690.

[4] Mirjalili, S., Mirjalili, S. and Yang, X. (2013). Binary bat algorithm. Neural Computing and Applications, 25(3-4), pp.663-681.

[5] Bangyal, W., Ahmad, J., Tayyab, H. and Pervaiz, S. (2018). An Overview of Mutation Strategies in Bat Algorithm. International Journal of Advanced Computer Science and Applications, 9(8).

[6] Yadav, P., Sharma, P. and Gupta, S. (2015). Bat Search Algorithm Based Hybrid PSO Approaches to Optimize the Location of UPFC in Power System. International Journal on Electrical Engineering and Informatics, 7(3), pp.475-488.

[7] Rodrigues, D., Pereira, L., Nakamura, R., Costa, K., Yang, X., Souza, A. and Papa, J. (2014). A wrapper approach for feature selection based on Bat Algorithm and Optimum-Path Forest. Expert Systems with Applications, 41(5), pp.2250-2258.

[8] Oshaba, A., Ali, E. and Abd Elazim, S. (2015). PI controller design for MPPT of photovoltaic system supplying SRM via BAT search algorithm. Neural Computing and Applications, 28(4), pp.651-667.

[9] Gai-GeWanga,b,c,∗, HaiCheng EricChud, SeyedaliMirjalili. Three-dimensional path planning for UCAV using an improved bat algorithm. AerospaceScienceand Technology 49(2016)231–238.

[10] Rizk M. Rizk-Allah1,3 · Aboul Ella Hassanien2,3. New binary bat algorithm for solving 0–1 knapsack problem. Received: 3 April 2017 / Accepted: 11 July 2017.

[11] B. Venkateswara Rao, G.V. Nagesh Kumar. Optimal power flow by BAT search algorithm for generation reallocation with unified power flow controller. Electrical Power and Energy Systems 68 (2015) 81–88.

[12] Jiann-Horng Lin, Chao-Wei Chou, Chorng-Horng Yang, Hsien-Leing Tsai. A Chaotic Levy Flight Bat Algorithm for Parameter Estimation in Nonlinear Dynamic Biological Systems. Department of Information Management, I-Shou University, Taiwan.

[13] Arulanand Natarajan*. A comparative study of cuckoo search and bat algorithm for Bloom filter optimisation in spam filtering. Int. J. Bio-Inspired Computation, Vol. 4, No. 2, 2012.

[14] T. Yuvaraj *, K. Ravi, K.R. Devabalaji.DSTATCOM allocation in distribution networks

considering load variations using bat algorithm. Received 8 May 2015; revised 5 August 2015; accepted 28 August 2015.

[15] Yassine Saji1 • Mohammed Essaid Riffi1 .A novel discrete bat algorithm for solving the travelling salesman problem .Received: 25 November 2014 / Accepted: 10 June 2015.

[16] Asma CHAKRI , Rabia KHELIF , Mohamed BENOUARET , Xin-She YANG , New directional bat algorithm for continuous optimization problems, Expert Systems With Applications (2016).

[17] Z. Cui, Y. Cao, X. Cai, J. Cai, J. Chen, Optimal LEACH protocol with modified bat algorithm for big data sensing systems in Internet of Things, J. Parallel Distrib. Comput. (2018).

[18] K. Premkumar a, *, B.V. Manikandan b. Bat algorithm optimized fuzzy PD based speed controller for brushless direct current motor. Engineering Science and Technology, an International Journal (2015).

[19] Chiranjeevi Karri *, Umaranjan Jena. Fast vector quantization using a Bat algorithm for image compression. Engineering Science and Technology, an International Journal (2015).

[20] Haopeng Zhang and Qing Hui. Cooperative Bat Searching Algorithm: A Combined Perspective from Multiagent Coordination and Swarm Intelligence. 2017 13th IEEE Conference on Automation Science and Engineering (CASE) Xi’an, China, August 20-23, 2017.

In section 4 please provide the explanation about the mathematical notations. Doing so would help the reader.

For more details please contact decoderzmt@gmail.com

Thanks for your detailed explanation. It helps me a lot for my research.

🙂