A Modified Bat Algorithm for Solving Large-Scale Bound Constrained Global Optimization Problems

Mashwani, Wali Khan; Mehmood, Ihsan; Abu Bakar, Maharani; Koçcak, Ismail

doi:https://doi.org/10.1155/2021/6636918

Mathematical Problems in Engineering

On this page

Abstract Introduction Experimental Results and Discussion Conclusion Data Availability Conflicts of Interest Acknowledgments References Copyright Related Articles

Special Issue

Meta-Heuristic Techniques for Solving Computational Engineering Problems 2021

View this Special Issue

Research Article | Open Access

Volume 2021 | Article ID 6636918 | https://doi.org/10.1155/2021/6636918

A Modified Bat Algorithm for Solving Large-Scale Bound Constrained Global Optimization Problems

Wali Khan Mashwani,¹Ihsan Mehmood,¹Maharani Abu Bakar,²and Ismail Koçcak³

Academic Editor: Hassène Gritli

Received06 Jan 2021

Revised30 Jan 2021

Accepted12 Feb 2021

Published28 Feb 2021

Abstract

In the last two decades, the field of global optimization has become very active, and, in this regard, many deterministic and stochastic algorithms were developed for solving various optimization problems. Among them, swarm intelligence (SI) is a stochastic algorithm that is more flexible and robust and has had the ability to find an optimum solution for high-dimensional optimization and search problems. SI-based algorithms are mainly inspired by the social behavior of fish schooling or bird flocking. Among the SI-based algorithms, Bat algorithm (BA) is one of the recently developed evolutionary algorithms. It employs an echolocation behavior of microbats by varying pulse rates of emission and loudness to perform their search process. In this paper, a modified Bat algorithm (MBA) is developed. The main focus of the MBA is to further enhance the exploration and exploitation search abilities of the original Bat algorithm. The performance of the modified Bat algorithm (MBA) is examined over the benchmark functions designed for evolutionary algorithms competition in the special session of 2005 IEEE Congress on Evolutionary Computation. The used benchmark functions include the unimodal, multimodal, and hybrid benchmark functions with high dimensionality. Furthermore, the impact analysis with respect to different values of temperatures is conducted by executing the proposed algorithm twenty-five times independently by using each benchmark function with different random seeds.

1. Introduction

Global optimization has wide applications in many fields including physics, biology, engineering, economics, and business. Examples include minimizing the cost/consumption, while maximizing the profit/product is the need of the day in every time which leads human being towards the optimization process. It has been an essential part of research in applied mathematics since six or seven decades. The advancement of computers makes it possible to solve those optimization problems that were unsolvable before. The main objective of the optimization is to maximize the efficiency of the system while minimizing its cost. A scalable optimization problem can typically and generally be formulated as follows:where is the candidate solution with decision variables, comprises objective function, and are constrained functions with inequality, and are equality constrained functions. Furthermore, a solution vector is said to be globally optimal if , , and the corresponding value of is called global minimum. If and , then is single objective bound constrained function, while if , then the problem referred to as (1) is a multiobjective problem. The decision variables of the solution vector can be continuous, semicontinuous, discrete, integer, or as one of a finite set of explicit discrete categorical labels. Optimization problems can be classified based on the type of constraints, nature of design variables, physical structure of the problem, nature of the equations involved, deterministic nature of the variables, permissible value of the design variables, separability of the functions, and number of objective functions.

In the last few decades, different kinds of linear and nonlinear optimization techniques were developed to solve various linear and nonlinear optimization problems [1–5]. The optimization methods are further divided into two subclasses, local search methods and global search methods, as shown in Figure 1. The major difference between the two aforementioned subclasses is that local search methods work on single solution and provide a local optimum for the given problem, while global search methods operate on a set of solutions called population and usually provide a global optimum for given optimization problem.

Evolutionary computation (EC) is the subfield of soft computing [5, 7, 8] which studies a family of evolutionary algorithms (EAs) for global optimization. EAs are inspired by biological evolution and operate on a set of solutions which are generated uniformly and randomly undergo the crossover, mutation, selection, and survival of the fittest for next generation of evolutionary process. The four classical paradigms of EAs are the genetic algorithm (GA) [9], evolution strategy [10], evolution programming [11], and genetic programming [12]. Differential evolution [13, 14], particle swarm optimization [15], harmony search algorithm [16], gravitational search algorithm [17], biogeography-based optimization [18], ant lion optimizer [19], invasive weed optimization [20], shuffled frog leaping [21], ant colony optimization [22], artificial bee colony [23], firefly algorithm [24], Bat algorithm [25], cuckoo search [26], flower pollination algorithm [27], the whale optimization algorithm [28], grey wolf optimizer [29], salp swarm algorithm [30], ant colony optimization (ACO) [31, 32], firefly algorithms [33], and Bat algorithms [34] are all almost nature-inspired and swarm-intelligence-based algorithms.

Recently, in EC communities, hybrid swarm-intelligence-based algorithms and hybridization of nature-inspired algorithms [35] have got a great deal of attention to solve various test suites of single objective optimization and search problems [36–47]. However, proper settings of the control parameters include population size, selection rate, and operator probabilities, and other important intrinsic parameters in EAs play important role in their success while dealing with different optimization and search problems [48–50]. In this paper, a modified Bat algorithm (MBA) is developed, aiming at further improving the exploration versus exploitation issues of the baseline Bat algorithm in terms of convergence speed, convergence precision, and global searching ability. The performance of the proposed algorithm is evaluated over the benchmark functions, which are designed for the special session of evolutionary algorithms competition of the IEEE Congress on Evolutionary Computation [51]. Furthermore, experiments are carried out with different values of temperature to show their impact on the performance of the proposed algorithm for dealing with each IEEE-CEC benchmark function [51].

The rest of the paper is organized as follows: Section 2 introduces the framework of the proposed modified Bat algorithm. Section 3 demonstrates the experimental results along with characteristics of benchmark functions used in the experiments we carried out. Section 4 finally concludes this paper.

2. Modified Bat Algorithm for Global Optimization

In the last few years, swarm intelligence- (SI-) based approaches have gained much attention in both academia and industrial applications [52]. Among them, ant colony optimization (ACO) [22], artificial bee colony (ABC) [3, 23, 52–56], cuckoo search (CS) [57, 58], firefly algorithm (FA) [24, 33, 34], and cuckoo search algorithm [57–59] are commonly used SI-based methods. They are inspired by collective behaviors of human beings, insects, birds flocking, the behavior of honeybees, the brooding behavior of cuckoo species, the flashing behavior of tropical fireflies, and the flocking behavior of birds. SI-based algorithms have tackled various optimization and search problems including traveling salesman problem (TSP) [58, 59], controlling unmanned vehicles, data mining, and many others.

Bat algorithm (BA) was first developed by Yang for global optimization problems [60–62]. It was inspired by the echolocation behavior of microbats, with varying pulse rates of emission and loudness. Bats are the only mammals with wings, and they have advanced capability of echolocation. Bats, dolphins, and other animals use the echolocation technique to determine the location of objects with reflected sound. This allows the animals to move around in pitch darkness, so they can navigate, hunt, identify friends and enemies, and avoid obstacles. The typical range of frequencies for most bat species is to . The bats emit a very loud sound pulse and listen for the echo that bounces back from objects. Bats emit to 20 sound bursts every second. The pulse emission is going to increase up to 200 pulses per second while hunting prey. The wavelength of the ultrasonic sound bursts in the range from to . Recently, an improved version of BA with novel initialization techniques was introduced in [63]. The Bats harness three rules: (i) to sense distance, background barriers, and dissimilarity between prey/food, bats use echolocation; (ii) bats fly randomly with a certain velocity to a specific position with a fixed frequency with varying wavelengths to search for prey; and (iii) the loudness changes from a large to minimum constant value [64]. Three main traits of the microbat are employed to design the basic framework of BA as explained below:(i)Most of the species of microbats exercise echolocation to search for their prey.(ii)To search for prey, the microbats search with fixed frequency,, and varying wavelength, .(iii)According to Yang’s method, the mathematical formulation of microbats is as follows: where is the minimum frequency and is the maximum frequency used by the Bat while searching for its prey, denotes the location of the Bat in the search space, represents the velocity of the Bat, and is the parameter that controls the difference between the minimum and maximum frequencies of each Bat.

2.1. Exploration and Exploitation in the Proposed Algorithm

In this paper, equation (3) is used in the modified BA (MBA) and as described in equation (4) along with as reported in equation (5), where is the distance between the sound wave source and the target in order to bound the wave back as defined by equation (5).where . In the active sonar system, the distance between the sound wave source and the target that bounds the wave back as given in equation (5), where means the time difference between the sending sound wave and receiving echo and represents the sound speed in the air, where . The bats change their position according to equations (6) and (7) as per criteria given in flowchart 2.where move the bats around the current best solution. The impact analysis of temperature with sound speed in air was settled to be constant at at [65]. In general, the speed of sound varies at different temperature levels in the air. The environmental effect of temperature with different values is also examined in the proposed MBA as outlined in Algorithm 1. The flowchart of the proposed modified Bat algorithm (MBA) is described in Figure 2. The main steps of the proposed MBA are summarized as follows: Step 1. Initialization: spread bats uniformly and randomly within the search space of the problem. Step 2. Generate new bats by using equations (4) to (7). Step 3. Evaluate bats and update their global near best position (7). Step 4. Check the termination condition to decide whether to continue or terminate the process.

(1)	: population size;
(2)	: number of decision variables
(3)	: maximum Iteration.
(4)	: random number, : maximum Iteration.
(5)	Initialize bat the population ,
(6)	Compute , ,
(7)	Find the current best
(8)
(9)	while it ≤ M_itdo
(10)	Generate new solution by flying randomly.
(11)
(12)
(13)
(14)
(15)
(16)	Compute the objective function value,
(17)	ifthen
(18)	Accept .
(19)	else
(20)	Retain
(21)	end if
(22)	Update current best solution denoted by .
(23)	Move the bats around current best solution randomly.
(24)
(25)	Repeating steps 11 to 15 and update the global best solution.
(26)	;
(27)	end while

2.2. Impact of Temperature with respect to the Speed of Sound in Air

The sound waves are longitudinal, which are propagating in air with speed described as follows:

Therefore,

The speed of sound in air is directly proportional to the square root of the absolute temperature of the air. If and are the speeds of sound at temperatures and , respectively, then

We have

Applying binomial theorem and neglecting higher-order terms, we get

We have

3. Experimental Results and Discussion

Due largely to the nature of evolutionary algorithms (EAs), their behaviors and performance are mainly studied experimentally by using various test suites of optimization and search problems. For these purposes, several continuous test suites of benchmark functions have already been designed in the existing EC community over the last few years. These benchmark functions have played a crucial role in developing and scientifically studying the behavior of various existing EAs and modified enhanced versions. The benchmark functions which have recently been designed for the special session of the 2005 IEEE Congress on Evolutionary Computation are utilized in the study conducted in this paper in order to carefully assess the proposed modified Bat algorithm (MBA) and impact analysis of various temperatures used in its framework. For more details about these instances, the readers are referred to [51]. These benchmark functions that can be categorized as to are unimodal functions, to are basic multimodal functions, and are both expanded multimodal benchmark functions, and is a hybrid composition test problem. Optimization problems are classified on the basis of landscape as follows:(i)Unimodel. If the optimization problem has only one optimum that is global and local, it is called unimodal, for example, sphere function.(ii)Multimodel. If the optimization problems have more than one optimum, those may all be global, or some of them may be local, called unimodal, for example, Ackley function.

The second last column of Table 1 provides the known optimal solution of each of the benchmark functions.

3.1. PC Configuration and Programming Environment

All experiments were performed on a computer with Intel Core CPU, 2.40 GHz and 4 G RAM, under Windows 10 Pro, 64-bit OS. The proposed algorithm and all other existing algorithms used in the comparative analysis were implemented in MATLAB R2017b programming environment. The proposed algorithm was executed 25 times independently with different random seeds by using the Matlab command rand (“state,” sum ).

3.2. Parameter Settings

All experiments were performed by solving the benchmark functions with parameters settings described as follows:(i): population size.(ii): the dimension of the search space.(iii): Maximum iteration.(iv): velocity of sound at .(v): the global best.(vi): location of the Bat in the solution space.(vii): the number of independent runs.(viii): minimum frequency.(ix): maximum frequency.(x), : % different temperature in Celsius scale.(xi): distance between sound waves source and the target.(xii) and are random numbers, respectively.(xiii): time difference between the sent sound wave and echo.

Tables 2 and 3 include the numerical results provided by the proposed modified Bat algorithm in terms of minimum objective values, average objective values, standard deviation, and maximum objective function values after independent runs of twenty-five simulations with random seeds to solve each benchmark function whose characteristics are given in Table 1. All these numerical values were obtained with different values of temperatures like , , 30, and 40 in the framework of the suggested algorithms, respectively. The last columns of Tables 2 and 3 include the average CPU time in seconds elapsed by the proposed modified Bat algorithm while solving each corresponding benchmark function.

Figure 3 presents the convergence graphs displayed by the proposed algorithm to solve the benchmark functions as denoted by to . Different values , , 30, and 40 along the x-axis represent the variation in temperature values and the evolution in minimum objective function values is shown along the y-axis. Similarly, Figure 4 displays the convergence of the benchmark denoted by to with different temperature settings like , . Figure 5 displays the convergence for the test problems denoted by to in the twenty-five independent runs of executions.

4. Conclusion

Many real-life problems can be modeled as global optimization problems. Evolutionary algorithms (EAs) are population-based optimization methods that operate on a set of uniformly and randomly generated solutions in search space as specified for each optimization problem to be solved. EAs are more flexible and usually provide a high-quality set of solutions in a single simulation run, in contrast to traditional optimization methods. This paper presents a modified Bat algorithm to deal with benchmark functions that were designed for the special session of EAs competition of 2005 IEEE Congress on Evolutionary Computation (IEEE-CEC’05) [51]. The results provided by the modified Bat algorithm (MBA) seem to be more effective for dealing with most benchmark functions in terms of diversity and proximity:(i)In MBA, the basic framework of the Bat Algorithm is modified(ii)Based on the experiments that we carried out, the speed of sound varied with varying temperature(iii)The proposed algorithm has found promising results for most problems at (iv)The multimodel problems are tackled efficiently by the proposed algorithm at

In the future, we intend to conduct the following tasks:(i)To determine the efficiency, stability, and importance of the proposed MBA by using other existing unconstrained benchmark functions and some real-world problems(ii)To examine sensitivity of the different intrinsic parameters used in the framework of the proposed algorithm in order to ensure the correct use of parameters keeping in view the structure of different problems(iii)To further evaluate the robustness and efficiency of the proposed algorithm against some state-of-the-art evolutionary algorithms

Data Availability

Data are available upon request from the first author. Furthermore, the Matlab code of the benchmark functions used to conduct this study is available on https://www3.ntu.edu.sg/home/epnsugan/.

Conflicts of Interest

The authors declare that there are no conflicts of interest.

Acknowledgments

The authors thank and acknowledge the support of the Research Intensified Grant Scheme (RIGS) Fasa 1/2019, Vot Number 55192/7, Universiti Malaysia Terengganu.

References

A. V. Fiacco and G. P. McCormick, Nonlinear Programming: Sequential Unconstrained Minimization Techniques, John Wiley & Sons, New York, NY, USA, 1968.
R. E. Miller, Optimization: Foundations and Applications, John Wiley & Sons, Hoboken, NJ, USA, 1999.
G. Beni and J. Wang, “Swarm intelligence in cellular robotic systems,” in Robots and Biological Systems: Towards a New Bionics, P. Dario, G. Sandini, and P. Aebischer, Eds., pp. 703–712, Springer, Berlin, Germany, 1993.
View at: Google Scholar
A. Ruszczynski, Nonlinear Optimization, Princeton University Press, Princeton, NJ, USA, 2006.
Z. Yoshida, Nonlinear Science: The Challenge of Complex Systems, Springer Science & Business Media, Berlin, Germany, 2010.
S. Wang and Z. Ma, “Supervisory and optimal control of building HVAC systems: a review,” HVAC&R Research, vol. 14, no. 1, pp. 3–32, 2008.
View at: Publisher Site | Google Scholar
X. Yu and M. Gen, Introduction to Evolutionary Algorithms, Springer Science & Business Media, Berlin, Germany, 2010.
A. E. Eiben and J. E. Smith, Introduction to Evolutionary Computing, Springer Publishing Company, Berlin, Germany, 2nd edition, 2015.
D. E. Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Longman Publishing, Boston, MA, USA, 1st edition, 1989.
T. Bäck, Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms, Oxford University Press, New York, NY, USA, 1996.
R. Poli, W. B. Langdon, and N. F. McPhee, A Field Guide to Genetic Programming, Lulu Enterprises, UK Ltd, Morrisville, NC, USA, 2008.
J. R. Koza, Genetic Programming: On the Programming of Computers by Means of Natural Selection, MIT Press, Cambridge, MA, USA, 1992.
R. Storn and K. Price, “Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces,” Journal of Global Optimization, vol. 11, no. 4, pp. 341–359, 1997.
View at: Publisher Site | Google Scholar
K. Price, R. M. Storn, and J. A. Lampinen, Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series), Springer-Verlag, Berlin, Germany, 2005.
J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of ICNN’95—International Conference on Neural Networks, vol. 4, Perth, Australia, 1995.
View at: Google Scholar
Z. W. Geem, Music-Inspired Harmony Search Algorithm: Theory and Applications, Springer Publishing Company, Berlin, Germany, 1st edition, 2009.
S. Yazdani, H. Nezamabadi-pour, and S. Kamyab, “A gravitational search algorithm for multimodal optimization,” Swarm and Evolutionary Computation, vol. 14, pp. 1–14, 2014.
View at: Publisher Site | Google Scholar
D. Simon, “Biogeography-based optimization,” IEEE Transactions on Evolutionary Computation, vol. 12, no. 6, pp. 702–713, 2008.
View at: Publisher Site | Google Scholar
S. Mirjalili, “The ant lion optimizer,” Advances in Engineering Software, vol. 83, pp. 80–98, 2015.
View at: Publisher Site | Google Scholar
B. Xing and W.-J. Gao, “Invasive weed optimization algorithm,” in Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms, pp. 177–181, Springer, Berlin, Germany, 2014.
View at: Google Scholar
M. Eusuff, K. Lansey, and F. Pasha, “Shuffled frog-leaping algorithm: a memetic meta-heuristic for discrete optimization,” Engineering Optimization, vol. 38, no. 2, pp. 129–154, 2006.
View at: Publisher Site | Google Scholar
C. Blum, “Ant colony optimization: introduction and recent trends,” Physics of Life Reviews, vol. 2, no. 4, pp. 353–373, 2005.
View at: Publisher Site | Google Scholar
D. Pham, A. Ghanbarzadeh, E. Koc, S. Otri, S. Rahim, and M. Zaidi, The Bees Algorithm, Technical Note, Manufacturing Engineering Centre, Cardiff University, Cardiff, UK, 2005.
N. F. Johari, A. Zain, N. Mustaffa, and A. Udin, “Firefly algorithm for optimization problem,” Applied Mechanics and Materials, vol. 421, 2013.
View at: Publisher Site | Google Scholar
X.-S. Yang, “A new metaheuristic bat-inspired algorithm,” in Nature Inspired Cooperative Strategies for Optimization (NICSO 2010), pp. 65–74, Springer, Berlin, Germany, 2010.
View at: Google Scholar
X.-S. Yang and S. Deb, “Cuckoo search via Lévy flights,” in Proceedings of the 2009 World Congress on Nature & Biologically Inspired Computing, IEEE, Coimbatore, India, 2009.
View at: Google Scholar
X.-S. Yang, “Flower pollination algorithm for global optimization,” in Proceedings of the 2012 International Conference on Unconventional Computing and Natural Computation, Springer, Orleans, France, 2012.
View at: Publisher Site | Google Scholar
S. Mirjalili and A. Lewis, “The whale optimization algorithm,” Advances in Engineering Software, vol. 95, pp. 51–67, 2016.
View at: Publisher Site | Google Scholar
S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey wolf optimizer,” Advances in Engineering Software, vol. 69, pp. 46–61, 2014.
View at: Publisher Site | Google Scholar
S. Mirjalili, A. H. Gandomi, S. Z. Mirjalili, S. Saremi, H. Faris, and S. M. Mirjalili, “SALP swarm algorithm: a bio-inspired optimizer for engineering design problems,” Advances in Engineering Software, vol. 114, pp. 163–191, 2017.
View at: Publisher Site | Google Scholar
J. Kim, T. Sharma, B. Kumar, G. Tomar, K. Berry, and W. Hyung, “Research article intercluster ant colony optimization algorithm for wireless sensor network in dense environment,” International Journal of Distributed Sensor Networks, vol. 2014, Article ID 457402, 10 pages, 2014.
View at: Publisher Site | Google Scholar
W. Fang, X. Li, M. Zhang, and M. Hu, “Nature-inspired algorithms for real-world optimization problems,” Journal of Applied Mathematics, vol. 2015, Article ID 359203, 2 pages, 2015.
View at: Publisher Site | Google Scholar
X.-S. Yang, Nature-Inspired Meta-Heuristic Algorithms, Luniver Press, Frome, UK, 2010.
J. Xie, Y. Zhou, and H. Chen, “A novel bat algorithm based on differential operator and Lévy flights trajectory,” Computational Intelligence and Neuroscience, vol. 2013, Article ID 453812, 13 pages, 2013.
View at: Publisher Site | Google Scholar
X.-S. Yang, Nature-Inspired Algorithms and Applied Optimization, vol. 744, Springer, Berlin, Germany, 2017.
S. Gupta and K. Deep, “A hybrid self-adaptive sine cosine algorithm with opposition based learning,” Expert Systems with Applications, vol. 119, pp. 210–230, 2019.
View at: Publisher Site | Google Scholar
S. Gupta and K. Deep, “Improved sine cosine algorithm with crossover scheme for global optimization,” Knowledge-Based Systems, vol. 165, pp. 374–406, 2019.
View at: Google Scholar
S. Gupta and K. Deep, “Hybrid grey wolf optimizer with mutation operator,” in Soft Computing for Problem Solving, pp. 961–968, Springer, Berlin, Germany, 2019.
View at: Google Scholar
S. Gupta, K. Deep, A. A. Heidari, H. Moayedi, and H. Chen, “Harmonized SALP chain-built optimization,” Engineering with Computers, pp. 1–31, 2019.
View at: Google Scholar
S. Gupta, K. Deep, and A. P. Engelbrecht, “A memory guided sine cosine algorithm for global optimization,” Engineering Applications of Artificial Intelligence, vol. 93, Article ID 103718, 2020.
View at: Publisher Site | Google Scholar
W. K. Mashwani, A. Hamdi, M. A. Jan, and F. Khan, “Large-scale global optimization based on hybrid swarm intelligence algorithm,” Journal of Intelligent & Fuzzy Systems, vol. 39, no. 1, pp. 1257–1275, 2021.
View at: Google Scholar
W. K. Mashwani, S. N. A. Shah, S. B. Belhaouari, and A. Hamdi, “Ameliorated ensemble strategy-based evolutionary algorithm with dynamic resources allocations,” International Journal of Computational Intelligence Systems, vol. 14, no. 1, pp. 412–437, 2021.
View at: Google Scholar
W. K. Mashwani and A. Salhi, “A decomposition-based hybrid multiobjective evolutionary algorithm with dynamic resource allocation,” Applied Soft Computing, vol. 12, no. 9, pp. 2765–2780, 2012.
View at: Google Scholar
W. K. Mashwani and A. Salhi, “Multiobjective memetic algorithm based on decomposition,” Applied Soft Computing, vol. 21, pp. 221–243, 2014.
View at: Google Scholar
W. K. Mashwani, “MOEA/D with DE and PSO: MOEA/D-DE + PSO,” in Proceedings of the 31st SGAI International Conference on Innovative Techniques and Applications of Artificial Intelligence, pp. 217–221, Cambridge, UK, December 2011.
View at: Publisher Site | Google Scholar
W. K. Mashwani, “Comprehensive survey of the hybrid evolutionary algorithms,” International Journal of Applied Evolutionary Computation (IJAEC), vol. 4, no. 2, pp. 1–19, 2013.
View at: Google Scholar
W. K. Mashwani, “Hybrid multiobjective evolutionary algorithms: a survey of the state-of-the-art,” International Journal of Computer Science Issues, vol. 8, no. 6, pp. 374–392, 2011.
View at: Google Scholar
F. G. Lobo, C. F. Lima, and Z. Michalewicz, Parameter Setting in Evolutionary Algorithms, Springer Publishing Company, Berlin, Germany, 1st edition, 2007.
K. DeJong, “Parameter setting in EAS: a 30 year perspective,” in Parameter Setting in Evolutionary Algorithms, Ser. Studies in Computational Intelligence, F. G. Lobo, C. F. Lima, and Z. Michalewicz, Eds., vol. 54, pp. 1–18, Springer, Berlin, Germany, 2007.
View at: Google Scholar
D. Thierens, “Adaptive strategies for operator allocation,” in Parameter Setting in Evolutionary Algorithms, Ser. Studies in Computational Intelligence, F. G. Lobo, C. F. Lima, and Z. Michalewicz, Eds., vol. 54, pp. 77–90, Springer, Berlin, Germany, 2007.
View at: Google Scholar
P. N. Suganthan, N. Hansen, J. J. Liang et al., “Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization,” Tech. Rep., Nanyang Technological University, Singapore, 2005, Technical report.
View at: Google Scholar
H. Ahmed and J. Glasgow, “Swarm intelligence: concepts, models and applications,” Tech. Rep., School of Computing, Queens University, Kingston, Canada, 2012, Technical report.
View at: Google Scholar
J. R. Rohan, C. N. Prasad, and P. Sadiq, “An introduction to the collective behaviour of swarm intelligence,” in Proceedings of the 2017 National Conference on Contemporary Research and Innovations in Computer Science, St. Joseph’s Evening College, Bengaluru, India, December 2017.
View at: Google Scholar
X.-S. Yang, “Swarm intelligence based algorithms: a critical analysis,” Evolutionary Intelligence, vol. 7, no. 1, pp. 17–28, 2014.
View at: Publisher Site | Google Scholar
B. Yuce, M. Packianather, E. Mastrocinque, D. Pham, and A. Lambiase, “Honey bees inspired optimization method: the bees algorithm,” Insects, vol. 4, no. 4, pp. 646–662, 2013.
View at: Publisher Site | Google Scholar
L. Li and F. Liu, Group Search Optimization for Applications in Structural Design, vol. 9, Springer, Berlin, Germany, 2011.
A. Joshi, O. Kulkarni, G. Kakandikar, and V. Nandedkar, “Cuckoo search optimization—a review,” Materials Today, vol. 4, pp. 7262–7269, 2017.
View at: Google Scholar
M. Mareli and B. Twala, “An adaptive cuckoo search algorithm for optimisation,” Applied Computing and Informatics, vol. 14, no. 2, pp. 107–115, 2018.
View at: Publisher Site | Google Scholar
M. I. Solihin and M. F. Zanil, “Performance comparison of cuckoo search and differential evolution algorithm for constrained optimization,” IOP Conference Series: Materials Science and Engineering, vol. 160, Article ID 012108, 2016.
View at: Publisher Site | Google Scholar
X.-S. Yang, A New Metaheuristic Bat-Inspired Algorithm, Springer, Berlin, Germany, 2010.
X. S. Yang and X. He, “Bat algorithm: literature review and applications,” International Journal of Bio-Inspired Computation, vol. 5, no. 3, pp. 141–149, 2013.
View at: Publisher Site | Google Scholar
M. Chawla and M. Duhan, “Bat algorithm: a survey of the state-of-the-art,” Applied Artificial Intelligence, vol. 29, no. 6, pp. 617–634, 2015.
View at: Publisher Site | Google Scholar
W. H. Bangyal, J. Ahmad, H. T. Rauf, and S. Pervaiz, “An improved bat algorithm based on novel initialization technique for global optimization problem,” International Journal of Advanced Computer Science and Applications (IJACSA), vol. 9, no. 7, pp. 158–166.
View at: Google Scholar
N. Dey and A. S. Ashour, Chapter 1—Computing in Medical Image Analysis, Academic Press, Cambridge, MA, USA, 2018.
B. S. Finn, “Laplace and the speed of sound,” ISIS, vol. 55, no. 1, pp. 7–19, 1964.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2021 Wali Khan Mashwani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies

Views

981

Downloads

793

Citations