Bat Algorithm: A Survey of the State-of-the-Art

Abstract

The area of metaheuristic optimization algorithms has been attracting researchers for many years. These algorithms have built in capability to explore a large region of the solution space, are computationally robust, efficient and can avoid premature convergence. They have been extensively tested and applied on many hard optimization problems where conventional computing techniques perform unsatisfactorily. They are capable of solving general N-dimensional, linear, nonlinear and complex global optimization problems. One of the latest entrants in this field is the Bat algorithm which is based on the echolocation behaviour of bats. It has been proven to have good convergence properties on different benchmark functions and seems promising for dealing with optimization problems. The aim of this paper is to provide a survey of the state of the art on Bat algorithm. A concise effort has been made so that the readers get a rapid insight into some of the applications upon which bat algorithm has been applied till date in specialized fields of science and engineering. Some of the variants of the bat algorithm as reported in the literature have also been discussed.

INTRODUCTION

The increasing popularity of Metaheuristic Optimization Algorithms (MOA) has attracted a great deal of attention in engineering and industry (Blum and Roli 2003). In the past 50 years or so, these algorithms have been brought out one after another. Some of the most distinguished among them, such as genetic algorithm (GA) designed by Goldberg (1989), particle swarm optimization (PSO) developed by Kennedy and Eberhart (1995), and simulated annealing (SA) formulated by Kirkpatrick, Gelatt, and Veechi (1983) have solved many problems that are difficult to be solved using conventional mathematical optimization techniques. The traditional mathematical methods of optimization encounter limitations of high computational complexity, applicability to only particular classes of objective functions and getting struck in local minima. This invoked the need of developing a new class of solution methods that can overcome these shortcomings. Thus, more and more researchers turned to MOA for different kinds of hard-to-solve problems. Most of them are inspired by the natural evolution, survival of the fittest, and utilize a collective learning process of a population of individuals. The power and beauty of almost all modern MOA such as firefly algorithm (FA) developed by Yang (2009), cuckoo search (CS) formulated by Yang and Deb (2009), biogeography based optimization (BBO) designed by Simon (2008), and many others comes from the fact that they imitate the best characteristics in the environment, particularly those of bioinspired systems that have evolved through natural selection over millions of years.

Researchers have suggested that nature is a great source of ideas for the development of intelligent systems and has provided solutions to many complicated problems. One of the newest entrants in this league of nature-inspired MOA is the Bat Algorithm (BA) developed by Yang (2010a) based on the echolocation behavior of bats. Bats are fascinating animals and their advanced capability of echolocation has attracted the attention of researchers from different fields. Echolocation works as a type of sonar. Bats, mainly microbats, emit a loud and short pulse of sound, wait for it to strike an object and, after a fraction of time, the echo returns to their ears. Thus, bats can compute how far they are from an object. In addition, the amazing orientation mechanism makes bats able to distinguish the difference between an obstacle and prey, allowing them to hunt even in complete darkness.

BAT ALGORITHM

In this section we illustrate the basic concepts, pseudocode, and various attributes of BA.

Basic Concepts

BA, introduced by Yang (2010a, b), is based on the echolocation behavior of bats. Bats are the only mammals that can fly. There are many different species of bats and they are of different sizes. Among them, microbats extensively use echolocation. They emit loud sound pulses and listen for the echo that bounces off from surrounding objects. Bats emit sound pulses of constant frequency in the range of 25 KHz to 150 KHz. Each ultrasonic sound burst lasts for a very short time, typically 5 ms to 20 ms. Microbats normally emit about 10–20 sound bursts every second. The rate of emission of these sound pulses is increased (to about 200 pulses per second) when they fly close to their prey. While searching for prey, bats produce loud sound pulses (in the range of 110 dB), but when bats get closer to their prey, they become quieter. Such echolocation capabilities of microbats can be associated with the objective function to be optimized and optimization algorithms can be formulated that mimic this bat behavior to find the optimal solution.

The following assumptions (Yang 2010b) are made to approximate the bat echolocation properties to solve an optimization problem.

1. All bats use echolocation to sense distance, and they also “know” the difference between food/prey and background barriers in some magical way.

2. Bats fly randomly with velocity v_i at position x_i with a fixed frequency in the range f_max to f_min, varying wavelength λ and loudness A_o to search for prey.

3. Depending upon the proximity of their target, bats can automatically adjust the wavelength (or frequency) of their emitted pulses and adjust the rate of pulse emission, .

4. It is assumed that their loudness varies from a large (positive) A_o to a minimum constant value A_min.

New solutions are generated by adjusting frequencies, loudness, and pulse emission rates of the bats, whether the proposed solution is accepted depends on the quality of the solutions controlled or characterized by loudness and pulse rate, which are in turn related to the closeness or the fitness of the locations/solution to the global optimal solution. For BA to be used in simulation analysis, rules are defined as to how their positions and velocities are updated in d-dimensional search space. The new solutions, and velocities, at time step t are given by

(1)

(2)

where is the current global best location (solution), which is located after comparing all the solutions among all the n bats at each iteration t. Frequency is used to adjust the velocity change and is given by

(3)

where , are the minimum/maximum frequency of the pulse emitted by the bats, is a random vector drawn from a uniform distribution. Initially, each bat is randomly assigned a frequency, which is drawn uniformly from [, ]. Once a solution is selected among the current fittest solution, a new solution for each bat is generated locally using random walk given by

(4)

where is a random number in the range [−1, 1] and is the average loudness of all the bats at this time step. BA can be considered to be a combination of PSO and intensive local search controlled by loudness and pulse emission rate.

Once a bat has found prey, its loudness decreases while the rate of pulse emission increases. The bat moves toward optimal solution according to two design equations given by Equations (5) and (6) as

(5)

(6)

where and are constants. The value of lies between 0 and 1, i.e., , whereas that of is greater than 0, i.e., is the loudness of the bat at time step and is the loudness of the bat at time step is the rate of pulse emission at time step and is the initial rate of pulse emission. As the time step t approaches infinite average loudness of the bat goes to zero while the rate of pulse emission approaches initial rate of pulse emission. This can be expressed as

(7)

Pseudocode of Bat Algorithm

Pseudocode (Yang and Gandomi 2012) of BA is straightforward and can be implemented in any programming language as follows:

• Objective function ,

• Initialize the bat population and

• Define pulse frequency at

• Initialize pulse rates and the loudness

• while ( Max number of iterations)

• Generate new solutions by adjusting frequency,

• and updating velocities and locations/solutions

• if (rand > r_i)

• Select a solution among the best solutions

• Generate a local solution around the selected best solution

• end if

• Generate a new solution by flying randomly

• if (rand < A_i & f(x_i) < f(x_*))

• Accept the new solutions

• Increase and reduce

• end if

• Rank the bats and find the current best

• end while

• Postprocess results and visualization

Attributes of BA

BA is simple, easy to implement, and flexible. It has been successfully applied to a wide range of applications. High efficiency of BA can be attributed to the following three features comprising frequency tuning, automatic zooming, and parameter control (Yang 2013).

Frequency Tuning

BA uses echolocation and frequency/wavelength tuning to solve optimization problems. Though echolocation is not directly used to mimic the true function in reality, frequency variations are used. This capability provides some functionality that might be similar to the key feature used in PSO and harmony search (HS). It uses a good combination of major advantages of these algorithms and, thus, is potentially more powerful than they are.

Automatic Zooming

Compared to other MOA, BA has distinct advantages. It has the inbuilt capability to automatically transit into areas where there is possibility of obtaining promising solutions. This transition or zooming is accompanied by the automatic switching from diversified explorative move to local intensified exploitative move. BA shows high convergence rate, in early stages of the iterations, compared to other algorithms.

Parameter Control

Parameter control is of utmost importance for any MOA to work efficiently. The performance of an algorithm depends largely on the parameters of the algorithm. In BA, parameter control can be done in such a manner that the values of the parameters that include the loudness and rate of pulse emission can be varied as the iterations proceed. This way, the BA provides inbuilt mechanism to automatically move from exploration stage to exploitation stage when the optimal solution is approaching.

APPLICATIONS

Even though BA was introduced very recently in 2010, the range of published studies available online utilizing this novel algorithm has been increasing day by day. In most of the cases, if not all, the results and quality of the solutions, obtained using this algorithm, outperformed or matched those obtained using other well-known MOA. Various applications in engineering sciences employing BA are presented in this section.

Biomedical Engineering

The aim of parameter estimation is to determine the parameters of the model that give the best fit to a set of experimental data. The parameter estimation task is challenging and computationally expensive because of highly nonlinear dynamics and the limited measurability of biological systems. Lin, Chou, Yang, Tsai, and Lee (2012) discussed a general methodology to adaptively select the values of the model parameters for the reconstruction of biological system dynamics and developed an improved optimization algorithms based on BA. It incorporates both the effects of chaotic dynamics and Levy flights. It was assumed that the observed time series are originated by a primary system with unknown parameters and it was used to drive a secondary system, so that both systems are coupled. The parameters of the secondary system were adaptively optimized by the proposed chaotic Levy flight BA to make it follow the dynamics of the primary system.

Full-body human pose estimation from video sequences finds applications in numerous areas such as cartoon character animation, human gait analysis, sports biomechanics, robotics, human computer interface, and gesture recognition. This problem of estimating the full-body human pose in video sequences was addressed by Akhtar, Ahmad, and Rahman (2012) using BA. It was formulated as a 31-dimensional nonlinear optimization problem. The performance of BA was compared with particle filter (PF), annealed particle filter (APF), and PSO using a standard dataset. The most likely/appropriate pose (MAP) error results suggested that the BA has performed better than the other three employed algorithms. Experimentally, it is found that with the increase in bat population, the tracking accuracy is increased at the expense of computational burden.

Computer Science Engineering

Bat Intelligent Hunting (BIH) developed by Kim (2010) provides a framework for solving various optimization problems. It models the prey-hunting behaviors of bats. Bats locate and capture prey without using their eyesight by utilizing echolocation and constant absolute target approach (CATD) techniques. BIH implements these concepts to converge toward the optimal solution and was employed to solve the multiprocessor scheduling problem. This problem deals with assigning a given set of tasks to a set of processors in order to optimize specified objectives, one with voltage scaling taking energy into account, and another without voltage scaling with energy not considered as the objective. In both problems, multiple objective optimizations were performed by the authors using the normalized weighted additive utility function, in which a set of importance of objective values (weights) were used to identify a set of efficient solutions.

Komarasamy and Wahi (2012) proposed a new optimization algorithm based on K-means algorithm and bat algorithm (KMBA). This algorithm does not require the user to give in advance the number of cluster and cluster center, it resolves the K-means (KM) cluster problem. This method finds the cluster center, which is generated by using the BA, and then it forms the cluster by using the KM. It uses the better results of both KM and BA to form a cluster and, thus, avoids the shortcomings of both KM and BA. The experiments were performed on three different datasets and showed the robustness and efficiency of the new algorithm. The new algorithm improves the convergence speed of BA and helps KM remain independent on the initial centers.

Electrical Engineering

To optimize the mono- and multiobjective optimization problems related to the brushless DC wheel motor BA was used by Bora, Coelho, and Lebensztajn (2012).The aim was to design a Brushless DC wheel motor by maximizing the efficiency, taking into account five optimization parameters: bore stator diameter, current density in the conductors, magnetic induction in the air gap, magnetic induction both in the teeth, and in the back iron. The constraints that must be obeyed included total mass, inner diameter, magnetic maximum current, temperature, and determinant used in the slot height calculation. For the multiobjective counterpart, the total mass constraint was curved to a minimization objective. The results obtained were compared with other optimization approaches such as GA, PSO, and ant colony optimization (ACO). They were superior to earlier published results.

Biswal et al. (2013) obtained the optimal solution of the economic load dispatch (ELD) problem in which operating cost of a thermal power plant was optimized using BA. Numerical results obtained on three and six generating unit test systems showed that the proposed method had good convergence property and better quality of solution than PSO and intelligent water drops (IWD) techniques. The main advantage of this technique was that it was easy to implement and was capable of finding feasible near-global optimal solution with less computational effort.

Niknam et al. (2013) proposed a multiobjective self-adaptive learning bat-inspired algorithm to solve a practical reserve constrained dynamic environmental/economic dispatch problem. The constraints that were considered for the problem comprised valve-point effects, ramp rate limits, and transmission losses. To ensure secure real-time power system operations, the system operator schedules sufficient resources to meet energy demand and operating reserve requirements simultaneously. The proposed problem was a complex nonlinear nonsmooth and nonconvex multiobjective optimization problem whose complexity was increased when considering the mentioned constraints. Authors utilized metaheuristic bat-inspired algorithm to achieve the set of nondominated (Pareto-optimal) solutions. The initial population of the proposed framework was generated by a chaos-based strategy. A tournament crowded selection approach was implemented to choose the population such that the Pareto optimal front was distributed uniformly. It also ensured that the extreme points of the trade-off surface were obtained simultaneously.

Kumaravel and Kumar (2012) designed a self-tuning proportional integral (PI) controller using the Bats echolocation algorithm-based neural controller for a static synchronous compensator (STATCOM). The backpropagation algorithm (BPA) was used to adapt the PI controller gains with the system impedance. The convergence speed of the BPA was increased by the Bats echolocation algorithm. A simulation result for the proposed model showed that the PI controller gains were adjusted in a very short period. Similarly, the satisfactory dynamic responses were achieved for different loading conditions. It was found that the dynamic responses were better than the fixed-gain PI controller and PSO-based self-tuning PI controller.

Yammani, Maheswarapu, and Matam (2013) utilized BA for optimal placement and size of the distributed energy resources (DERs), which included wind, solar, and fuel cell as renewable energy resources. These energy resources also include some artificial models such as gas turbines, microturbines, diesel engines, and internal combustion reciprocating engines. The objective functions that were taken into account were voltage profile improvement and system loss reduction. The BA was tested on 37 bus distribution systems with different load models such as residential, industrial, commercial, and mixed loads and the results obtained were found to be satisfactory.

Electronics Engineering

Localization is one of the key techniques of wireless sensor networks (WSN). The goal of localization is to assign geographical coordinates to each device with unknown position in the deployment area. Goyal and Patterh (2013) proposed the application of BA for distributed iterative node localization in WSN. It performed quite well in terms of nodes localized and localization accuracy. The simulation result showed that the mean localization error continues to decrease as the number of anchor nodes and transmission range were increased. However, it decreases as we increase the number of sensor nodes and the field size.

In traditional image-matching techniques, the fitness for every pixel in the search space has to be computed, which is very cumbersome and time consuming. Due to these shortcomings, a new Bat algorithm with mutation (BAM) was developed by Zhang and Wang (2012) to solve the image-matching problem. This approach accelerates the convergence speed, while maintaining the strong robustness of the basic BA. The experimental results showed that the proposed approach was more effective and feasible in image matching than some of the other MOA.

Feature selection aims to find the most important information from a given set of features. Based on the bats behavior, feature selection was applied for the first time by Nakamura et al. (2012). It combined the power of exploration of the bats together with the speed of the optimum path forest classifier to find the set of features that maximizes the accuracy in a validating set. Authors proposed a binary version of the BA for feature selection purposes called binary bat algorithm (BBA), in which the search space was modeled as a n- cube, where n stands for the number of features. In such case, the optimal (near-optimal) solution is chosen among the 2n possibilities, and it corresponds to one hypercube’s corner. Experiments conducted on five public datasets demonstrated that the proposed method outperformed PSO, FA, and Gravitational Search Algorithm (GSA).

Industrial and Production Engineering

Kaveh and Zakian (2013) presented an improvement on BA to carry out size optimization of skeletal structures consisting of trusses and frames. Various optimization problems comprising size, shape, and topology were implemented to demonstrate the ability of the present enhanced BA. These design examples were associated with different constraints that included displacement, frequency, and stress. Static and time history dynamic loadings were also considered. Both discrete and continuous optimization problems were studied. Results indicated the efficiency of the BA for design optimization of skeletal structures.

Bat algorithm-based scheduling tool (BAST) was developed by Musikapun and Pongcharoen (2012) for solving the multistage multimachine, multiproduct, scheduling problem. The aim was to minimize both the earliness and tardiness penalties cost, correctly sequence the operations required to manufacture components, and to satisfy the assembly precedence relationship. Experimentally, it was found that the quality of the solutions obtained from BAST can be improved significantly after applying the necessary parameters setting identified by the statistical tools. The results obtained using BA optimized setting outperformed those using nonoptimized setting.

Taherian, Kakhki, and Aghaebrahimi (2013) proposed a model that was based on improved Support Vector Machine (SVR) network. It was used for price forecasting in the Iranian power market in 2013. In this model, first the input data was clustered by the fuzzy c-means technique. This made it possible to separate the data based on the type of load or day of the year. Then, proper training data were used by the improved SVR network for short-term price forecasting. BA was used for optimizing the parameters of SVR network. The results were compared with those of conventional neural networks methods, which were based on gradient and common SVR. It was found that the results obtained from applying the model showed high accuracy of the proposed model.

Mechanical Engineering

Yang, Karamanoglu, and Fong (2012) demonstrated that BA is efficient in finding the optimal shape to heat transfer design problems in microelectronic applications. BA was used to solve topology optimization problems. The first problem included the design and development of a tensional and compression spring. The objective was to minimize the weight of the spring. The constraints to be obeyed included minimum deflection, maximum shear stress, and geometrical limits. The second problem was optimal design of a speed reducer or a gearbox. Here, the objective was to minimize the total weight of the speed reducer. In this case, the constraints to be followed included deflection, bending stress, and various limits on stresses in shafts. For both test problems, BA found the optimal solutions, which were either better than or the same as the solutions found so far in the literature.

Exergy is the maximum useful energy that can be obtained from a system at a given state and in a known environment. Enthalpy and entropy changes in the system are determined using exergy analysis. Lemma and Hashim (2011) demonstrated the use of fuzzy systems for capturing exergy destruction variations in the main components of an industrial gas turbine. The fuzzy models were trained applying locally linear model tree algorithm followed by BA, which was applied for the first time in the area of thermal systems. The results indicated that BA is indeed very powerful in nonlinear model identification. The models can be used for performance optimization and condition monitoring.

Gandomi et al. (2012) applied BA to three benchmark constraint engineering problems: pressure vessel design, welded beam design, and spring design. The simulations indicated that BA was very efficient and the results obtained were superior to GA, PSO, and HS.

Software Engineering

A classifier is aimed to discover the hidden class level of the unknown data. Mishra, Shaw, and Mishra (2012) proposed a model for classification using BA to update the weights of a functional link artificial neural network (FLANN) classifier. The proposed model using BA, called BAT-FLANN, was compared with FLANN and PSO-FLANN. It was observed that the proposed classification technique was superior and faster than FLANN and PSO-FLANN. Higher accuracy in BAT- FLANN was observed using BA due to wide knowledge of bat echolocation signals and their specific features.

Khan and Sahai (2012) used BA to train standard and e-Learning datasets for classification purposes. Training procedures involved selecting the optimal values of the parameters, such as weights between the hidden layer and the output layer, spread parameters of the hidden layer base function, center vectors of the hidden layer, and bias parameters of the neurons of the output layer. A comparison of algorithms for training feedforward neural networks was done. Tests were done on two gradient descent algorithms: backpropagation and Levenberg–Marquardt, and three population-based heuristics: BA, GA, and PSO. Experimental results showed that BA outperformed all other algorithms in training feedforward neural networks.

Khan and Sahai (2011) proposed a new Levy flight bat algorithm (LBA) based on the hunting strategy of microbats, and results were compared with a neural network backpropagation (NNBP) algorithm. LBA was found to be superior to NNBP for nonlinear neural network type objective function. It converged more quickly and deals with neural network weight training more naturally. Parameter setting had been minimal for this algorithm, with only population size being adjusted and minimal manipulation of constants for specific problem being tested.

Other Applications

A system for screening company workplaces with high ergonomic risk was formed by Khan, Nikov, and Sahai (2011). In this work, fuzzy modification of BA was obtained for clustering of company workplaces. Clusters of workplaces with low, moderate, and high ergonomic risk were obtained. Workplaces with moderate and high ergonomic risk levels were eliminated and pertinent solutions were proposed. This method results in reduction of computational effort and fast screening of workplaces with major ergonomic problems within a company.

Further, Yang and Gandomi (2012) used BA to solve various engineering problems such as three-bar truss design, speed reducer design, parameter identification of structures, cantilever stepped beam, heater exchanger design, and car side problem. For most problems, the optimal solutions obtained by BA were far better than the best solutions reported in the literature.

VARIANTS OF BA

This section describes different variants of the BA. These variants have been proposed in the literature to incorporate either the capabilities of other evolutionary computation techniques, such as hybrid versions of BA or the adaptation of BA parameters. The main endeavor is to improve the performance of the original BA. Various variants of BA are described as follows.

Hybridized BA with HS

A hybrid metaheuristic algorithm combining the advantages of both the HS algorithm and the BA was proposed by Wang and Guo (2013) for solving unimodal and multimodal numerical optimization problems. An improvement was applied to mutate between bats using HS during the process of bats updating. Using the original configuration of BA, authors generated the new harmonies based on the newly generated bat each iteration after the bat’s position has been updated. The newly generated bat was substituted by the harmony vector only if it had better fitness. This method avoided all bats getting trapped in inferior local optimal regions. It enabled the bats to have more diverse exemplars to learn from, because the bats were updated with each iteration and also formed new harmonies to search in a larger search space. This new method speeded up the global convergence rate without losing the strong robustness of the basic BA. Experimentally, it was found that HS/BA makes good use of the information available in previous solutions more effectively to obtain better quality solutions compared to the other MOA such as BA, GA, HS, and PSO. Based on the results of the ten approaches on the test problems, HS/BA significantly improved the performances of the HS and BA on most multimodal and unimodal problems.

Differential Operator and Levy Flights BA

BA based on differential operator and Levy flights trajectory was proposed by Xie, Zhou, and Chen (2013).The aim was to improve the convergence rate and precision of the original BA. A differential operator was introduced to accelerate the convergence speed of the proposed algorithm. It was similar to the mutation strategy “DE/best/2” in a differential algorithm. Levy flights trajectory was incorporated to ensure the diversity of the population against premature convergence. It made the algorithm effectively jump out of local minima. Testing was done on 14 benchmark functions. The simulation results showed not only that the proposed algorithm was feasible and effective, but that it also had superior approximation capabilities in high-dimensional space.

Hybridized BA with Fuzzy Logic

Reddy and Manoj (2012) presented a novel method to determine the optimum capacitor locations using fuzzy approach and capacitor sizing problem for loss minimization using the BA method. It incorporated the advantages of both fuzzy logic and BA. The proposed method was tested on IEEE-15 and IEEE-34 bus systems. The method places capacitors at a fewer number of locations with optimum sizes and offered much savings in investment and maintenance. By installing capacitors at all potential locations, the real power loss was reduced significantly. Compared to the conventional methods, the fuzzy inference system (FIS) considers loss reduction and voltage profile simultaneously to decide the most suitable nodes for the capacitor. The results obtained showed 53.05% reduction in power losses for 15-bus system and a 28.47% reduction in power losses for 34-bus system when compared to uncompensated line.

Multiobjective BA

Yang (2011) extended his original BA to solve multiobjective optimization problems. He called this advanced version multiobjective bat algorithm (MOBA).This algorithm was tested and validated against a subset of multiobjective test functions. It was then applied to solve multiobjective design problems on structural engineering such as welded beam design. Simulation results showed that the proposed algorithm worked efficiently. It could deal with highly nonlinear problems with complex constraints and diverse Pareto optimal sets.

BA with Differential Evolution

The Bat algorithm was hybridized with differential evolution strategies by Fister Jr., Fister, and Yang (2013). It was named the hybrid bat algorithm (HBA) by the authors. Differential evolution (DE) was used as a local search part of BA. Solutions of the original BA were modified using a “DE/rand/1/bin” strategy. This hybridization significantly improved the results of the original BA.

BA with Mutation

The Bat algorithm with mutation (BAM) for path planning with an uninhabited combat air vehicle (UCAV) was developed by Wang et al. (2012) to provide path planning ability in complicated combat field environments. A modification was applied to the original BA by mutating between bats during the process of the new solution updating. This makes it possible for the UCAV to find the safe path by connecting the chosen nodes while avoiding the threat areas and costing minimum fuel. This new approach accelerates the global convergence speed while maintaining the strong robustness of the basic BA. BAM was compared with BA and different population-based optimization methods such as GA and PSO and, experimentally, was found to be more effective and feasible in UCAV path-planning than the other models.

Modified BA

Modified Bat algorithm (MBA) was developed by Damodaram and Valarmathi (2012) to overcome the difficulty and complexity in detecting and predicting phishing websites. They introduced MBA to get an optimal solution for the search of fake websites. MBA was compared with PSO and the original BA and was found to be superior in terms of both accuracy and convergence rate.

Directed Artificial BA

A new bioinspired swarm algorithm named directed artificial bat algorithm (DABA) was developed by Rekaby (2013). The algorithm simulates the bat echo emitting and the reflection capturing to be able to create a figure from the entities around it. This behavior is used for prey catching. DABA is an artificial algorithm, so it gives the computational meaning/mapping of real bat’s hunting concepts. Experiments were applied to compare DABA versus the artificial bee colony (ABC) algorithm. The used test problem was the traveling salesman problem. Standard benchmark assessment data from an online repository was used in the research’s experiments. It was found that DABA provided better solutions with the same number of cycles and using the same generation size, between 5% to 10% fitness values enhancements, compared to the ABC algorithm.

Simplified Adaptive BA Based on Frequency

A simplified adaptive BA based on frequency was proposed by Chen, Zhou, and Lu (2013), in which frequency was adjusted dynamically with a nonlinear function when the number of iterations was increased to avoid the problems of premature convergence and low precision. Inertia weight of location is determined using normal distribution, and then the frequency of the microbats’ emitted pulses adjusts to the change of random position and optimal location of the microbats. The experimental results showed that the proposed algorithm had not only great advantages of convergence property over standard BA, but also effectively avoids being trapped in local optimal solution.

Improved BA

Yilmaz and Kucuksille (2013) proposed three modifications to the standard BA in order to improve its exploration and exploitation capability. The version was named improved bat algorithm (IBA). The first modification increases the exploration capabilities at the beginning of cycles and then increases exploitation capabilities toward the end of the cycles; the second modification increases local search ability (exploitation), and the third modification decreases lack of exploration capability of BA. BA and IBA were compared on ten different benchmark test functions. IBA produced better performance compared to BA on 25 of the 26 test implementations of ten different test functions. It was observed that IBA exhibits superior performance ranging from 3.66 to 1.43 × 1061 times compared to BA.

Hybrid BA with Path Relinking

A hybrid bat algorithm with path relinking (HBA-PR) was proposed by Zhou, Xie, and Zheng (2013) to solve the capacitated vehicle routing problem (CVRP). The HBA-PR was constructed based on the framework of continuous BA; the greedy randomized adaptive search procedure (GRASP) and path relinking were effectively integrated into the standard BA. For further improvement in the performance, single-point intensified search and random subsequences were operated with certain loudness (probability). Experimental results and comparisons showed that the HBA-PR was very effective for CVRP.

Cooperation of Biology Related Algorithms

Akhmedova and Semenkin (2013) introduced a new metaheuristic called cooperation of biology related algorithms (COBRA), based on five nature-inspired algorithms: PSO, FA, CS, BA, and wolf pack search algorithm. The proposed algorithm was validated and compared with its component algorithms and its performance was evaluated on 28 test functions. Simulations and comparison showed that COBRA was superior to these existing algorithms when dimension grows and complicated problems are solved. It was a self-tuning method and hence had no need in controlling the population size, whereas this was the most essential parameter for the aforementioned algorithms. Also, fine-tuning of parameters for a specific problem was not necessary.

Other Variants

There are numerous other variants of BA in addition to those that have been illustrated in the previous section. These include chaotic Levy flight BA developed by Lin, Chou, Yang, and Tsai (2012) for parameter estimation in nonlinear dynamic biological system; BIH developed by Kim (2010) provided a framework for solving the multiprocessor scheduling problem; KMBA developed by Komarasamy and Wahi (2012) presented a combination of K-means and BA for efficient clustering; BAM was developed by Zhang and Wang (2012) to solve image-matching problem; BBA was developed by Nakamura et al. (2012) for solving the feature selection problem; LBA was developed by Khan and Sahai (2011) for training feedforward neural networks in e-Learning context, and a fuzzy bat-clustering method was developed by Khan, Nikov, and Sahai (2011) for ergonomic screening of office workplaces. Active research on variants of BA is still in progress and more variants are expected to be published in years to come.

CONCLUSIONS

Bats are mysterious creatures that utilize echolocation to locate and capture prey without visually observing their environments. In this article an attempt has been made to provide the state-of-the-art survey on BA. This algorithm models the prey hunting behavior of bats to find solutions in optimization problems. It employs frequency tuning and has dynamic control of exploration and exploitation by varying pulse emission rates and loudness during iterations. The fine adjustment of these parameters affects its convergence rate. It has attracted many researchers from various fields of engineering sciences who are working on solving optimization problems. Ever since its inception in 2010, it has successfully been applied to solve numerous industrial and distinct engineering applications and seems to be a very promising algorithm. However, the algorithm is still in its infancy stage and further development and research are needed to enhance its overall performance characteristics.