Academia.eduAcademia.edu

Outline

Title
Abstract
Introduction
Experimental Results
Conclusions
References
All Topics
Engineering
Electrical and Electronic Engineering

Modified Bat Algorithm

Profile image of Ecir Ugur KucuksilleEcir Ugur Kucuksille

2014, Electronics and Electrical Engineering

https://doi.org/10.5755/J01.EEE.20.2.4762
visibility

…

description

8 pages

Abstract

Heuristic optimization algorithms which are inspired by nature have become very popular for solving real world problems recently. The use of these algorithms increases day by day in the literature because of their flexible structures and non-containing confusing mathematical terms. One of these algorithms is Bat Algorithm (BA). BA is a heuristic algorithm based on echolocation characteristic of bats and developed by the mimics of bats' foraging behaviour. In this study exploration mechanism of the algorithm is improved by modifying the equation of pulse emission rate and loudness of bats. The performance of Modified Bat Algorithm (MBA) is verified by 15 benchmark functions and the results were exhibited as comparative. The results of MBA are superior in terms of solution quality on optimization problems compared to BA.

Related papers

Improved Bat Algorithm (IBA) on Continuous Optimization Problems
Ecir Ugur Kucuksille

Lecture Notes on Software Engineering, 2013

Heuristic optimization techniques have became very popular techniques and have widespread usage areas. Since they do not include mathematical terms, heuristic methods have been carried out on many fields by researchers. Main purpose of these techniques is to achieve good performance on problem of interest. One of these techniques is Bat Algorithm (BA). BA is an optimization algorithm based on echolocation characteristic of bats and developed by mimics of bats' foraging behavior. In this study, exploration and exploitation mechanisms of BA are improved by three modifications. Performance of proposed and standard version of algorithm is compared on ten basic benchmark test problems. Results indicate that proposed version is better than standard version in terms of solution quality.

View PDFchevron_right
An Improved Bat Algorithm based on Novel Initialization Technique for Global Optimization Problem
hafiz tayyab

International Journal of Advanced Computer Science and Applications

Bat algorithm (BA) is a nature-inspired metaheuristic algorithm which is widely used to solve the real world global optimization problem. BA is a population-based intelligent stochastic search technique that emerged from the echolocation features of bats and created from the mimics of bats foraging behavior. One of the major issue faced by the BA is frequently captured in local optima while handling the complex real-world problems. In this study, a new variant of BA named as improved bat algorithm (I-BAT) is proposed. Improved bat algorithm modifies the standard BA by enhancing its exploitation capabilities, and secondly for initialization of swarm, a quasirandom sequence Torus has been applied to overcome the issue of convergence and diversity. Population initialization is a vital factor in BA, which considerably influences the diversity and convergence of swarm. In order to improve the diversity and convergence, quasi-random sequences are more useful to initialize the population rather than the random distribution. The proposed strategy is applied to standard benchmark functions that are extensively used in the literature. The experimental results illustrate the superiority of the proposed technique. The simulation results verify the efficiency of proposed technique for swarm over the benchmark algorithm that is implemented for the function optimization.

View PDFchevron_right
Multi-Modal Bat Algorithm with Improved Search (MMBAIS)
Reshu Chaudhary

Journal of Computational Science, 2017

Bat Algorithm (BA), is a relatively new nature inspired metaheuristic algorithm, which works on the echolocation capabilities of micro-bats. Although being highly efficient, it suffers from pre-mature convergence. To overcome this limitation, this paper proposes a multimodal variant of BA, called Multi-Modal Bat Algorithm (MMBA), which includes the foraging behaviour of bats. The standard BA exhibits a random movement for catching its prey. This work also proposes an enhancement to these exploration capabilities of bat, called Bat Algorithm with Improved Search (BAIS). Each of these variants is tested for its efficacy against BA over 30 benchmark functions. An integration of both these modifications, the Multi-Modal Bat Algorithm with Improved Search (MMBAIS), is also subsequently compared against the same 30 benchmark functions. Results established the superiority of MMBAIS over BA. Experimental comparison of MMBAIS with a recent variant of BA also revealed the efficiency of MMBAIS.

View PDFchevron_right
Bat Algorithm
Lagouge Tartibu

Metaheuristic Optimization: Nature-Inspired Algorithms Swarm and Computational Intelligence, Theory and Applications, 2020

Bat algorithm is an innovative or population-based technique which belongs to the swarm intelligence. It is also referred to as a metaheuristic algorithm developed by Yang [1]. The bat algorithm as a unique algorithm provides a suitable solution technique than numerous and prevalent classical and heuristic algorithms. The algorithm is used for quick decision making and for solving complex problems in diverse fields of operations ranging from engineering, business, transportation, and other fields of human endeavor. It is important to understand the communication and navigational pattern of bats while defining the algorithm since the algorithm is based on the micro-bats echolocation (EL) [1]. EL is an enchanting and captivating sonar propensity produced bats. The appealing wave of sound made by the bats is a great strength they often exhibit while searching for prey. The wave of sound is a formula they adopt not only in food search but serves other purposes [2]. For instance, while searching for food in a completely dark environment, there might be obstacles or dangers on their way to the food source. This can easily be detected in some magical manner as they can sense and discern possible danger on their way to the food source as shown in Fig. 8.1 [3]. The structure and flying position of a bat is shown in Fig. .1. BA is therefore a very powerful algorithm as it uses the frequency-tuning methodology for range intensification of the solutions in the population. At the same time, the BA system implements the instinctive skyrocketing or zooming procedure to maintain stability during the food search or exploration process. In developing the BA, the pattern of direction finding, manipulation, and exploration during prey hunting is taken into consideration by mimicking the disparities in terms of emission rates of pulse and intensity of sound released by the bats while hunting or searching for prey. The algorithm demonstrates a high level of efficiency with a distinctive swift start process (Fig. .2).

View PDFchevron_right
New Modified Controlled Bat Algorithm for Numerical Optimization Problem
Richard Etengu

Computers, Materials & Continua

Bat algorithm (BA) is an eminent meta-heuristic algorithm that has been widely used to solve diverse kinds of optimization problems. BA leverages the echolocation feature of bats produced by imitating the bats' searching behavior. BA faces premature convergence due to its local search capability. Instead of using the standard uniform walk, the Torus walk is viewed as a promising alternative to improve the local search capability. In this work, we proposed an improved variation of BA by applying torus walk to improve diversity and convergence. The proposed. Modern Computerized Bat Algorithm (MCBA) approach has been examined for fifteen well-known benchmark test problems. The finding of our technique shows promising performance as compared to the standard PSO and standard BA. The proposed MCBA, BPA, Standard PSO, and Standard BA have been examined for well-known benchmark test problems and training of the artificial neural network (ANN). We have performed experiments using eight benchmark datasets applied from the worldwide famous machine-learning (ML) repository of UCI. Simulation results have shown that the training of an ANN with MCBA-NN algorithm tops the list considering exactness, with more superiority compared to the traditional methodologies. The MCBA-NN algorithm may be used effectively for data classification and statistical problems in the future.

View PDFchevron_right
Swarm bat algorithm with improved search (SBAIS)
Hema Banati

Soft Computing, 2018

Bat algorithm (BA) is a powerful nature-inspired swarm algorithm which finds applicability to a diverse range of problem domains. Though it is efficient, it suffers from two handicaps: possibility of being trapped in local optima and lost convergence speed as the algorithm progresses. This paper proposes swarm bat algorithm with improved search (SBAIS). SBAIS gains superior exploration capabilities by employing swarming characteristics inspired by shuffled complex evolution (SCE) algorithm. Best bats of the population are kept in a super-swarm, while all other bats are partitioned according to SCE. The super-swarm uses the search mechanism of bat algorithm with improved search to perform refined search around the best solution, which makes sure that the convergence speed of the algorithm is not lost. Every other swarm gets one solution from the super-swarm before starting their evolution process. These swarms evolve using standard bat algorithm, helping the algorithm to escape any possible local optima. SBAIS further keeps a check on the overall diversity of the population. If the diversity drops below a given threshold value, new random solutions are added to the population. Performance of SBAIS is validated by comparing it to BA and fourteen recent variants of bat algorithm over 30 standard benchmark optimization functions, CEC'05 and CEC'14 function sets. Results established the superiority of SBAIS over the compared algorithms.

View PDFchevron_right
Modified Bat Algorithm (MBA) on non-linear programming
Alkailany Mohammed

Heuristic optimization techniques have became very general techniques and have diffuse know areas. Main purpose of these techniques is to achieve good performance on problem. One of these techniques is Bat Algorithm (BA). BA is an optimization algorithm based on echolocation usually of bats and promoted by simulate of bats' behavior. In this study, exploration and exploitation mechanisms of bat algorithm are improved by Using descent directions(Powell). Performance of proposed and standard version of algorithm is compared on eight basic criterion test problems. Results indicate that proposed version is preferable than standard version in terms of standard deviation and other parameters.

View PDFchevron_right
http://dx.doi.org/10.5755/j01.eee.20.2.4762 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 20, NO. 2, 2014 Modified Bat Algorithm S. Yılmaz1, E. Ugur Kucuksille2, Y. Cengiz3 1 Department of Mechatronics Engineering, Pamukkale University, Denizli, 20020, Turkey 2 Department of Computer Engineering, Suleyman Demirel University, Isparta, 32260, Turkey 3 Department of Electronics and Communication Engineering, Suleyman Demirel University, Isparta, 32260, Turkey [email protected] 1Abstract—Heuristic optimization algorithms which are methods are divided into six different groups as biological- inspired by nature have become very popular for solving real based, physical-based, social-based, swarm-based, musical- world problems recently. The use of these algorithms increases based and chemical-based [6], [7]. Genetic Algorithm [8] day by day in the literature because of their flexible structures and Differential Evolution Algorithm [9] are grouped as and non-containing confusing mathematical terms. One of these algorithms is Bat Algorithm (BA). BA is a heuristic biology-based algorithm; Gravitational Search Algorithm algorithm based on echolocation characteristic of bats and [10] and Electromagnetism Algorithm [11] are grouped as developed by the mimics of bats’ foraging behaviour. In this physics-based algorithm; Tabu Search [12] is grouped as study exploration mechanism of the algorithm is improved by social-based algorithm; Particle Swarm Optimization [13], modifying the equation of pulse emission rate and loudness of Ant Colony Optimization [14] are grouped as swarm-based bats. The performance of Modified Bat Algorithm (MBA) is algorithm; Harmony Search Algorithm [3] is grouped as verified by 15 benchmark functions and the results were exhibited as comparative. The results of MBA are superior in music-based algorithm; Artificial Chemical Reaction terms of solution quality on optimization problems compared Algorithm [15] is grouped as chemical-based algorithm. to BA. There are two crucial components in modern metaheuristics: Exploration and exploitation [3]. Index Terms—Optimization, bat algorithm, swarm Exploration is investigation capability of obscure various intelligence, bio-inspired computing. spaces so as to detect global optimum point, while exploitation refers to effort to find optimum point by using I. INTRODUCTION previous best solutions’ knowledge. A good response of an Over the last few decades evolutionary optimization algorithm depends on well-balanced of these components algorithms has been utilized in large numbers of field. The [16], [17]. In the case of too little exploration but intensive main goal of the works is to perform faster and more exploitation, algorithm can get trapped into local optimum successful optimization process. In contrast to traditional points. On the other hand too much exploration but scarce computational systems, evolutionary computation provides a exploitation could cause the algorithm to converges slowly more robust and efficient approach for solving complex and decreases overall search performance [3], [16]. Some of real-world problems [1]. Generally, evolutionary the studies indicate that it’s advantageous to adopt “explore optimization algorithms which simulate the evolution first, exploit later” approach to obtain necessary data about phenomenon of biological colony can be used to solve some search space before exploitation is applied [18]. complicated optimization problems. According to the Bats have the mechanism called echolocation which operating mechanism of evolutionary algorithms, they are guides their hunting strategies. The echolocation capability based on the existing individuals of the previous generation of microbats is fascinating, as these bats can find their prey and searches at random without guidance [2]. The and discriminate different types of insects even in complete optimization process of real world problems by evolutionary darkness. BA is an algorithm inspired by echolocation algorithm is quite similar to the simplified animal social characteristic of bats proposed by Yang [19]. behaviors. In this proposed study, it is aimed that algorithm explores Heuristic Algorithms mostly inspired by social behaviour the search space more efficiently by improving exploration of animals do not guarantee optimal solution due to their component of BA. Each bat which searches the space has random-based structure. However these algorithms are one pulse emission rate (r) and loudness (A) in standard methods which generally have a tendency to find good version of BA. In MBA loudness and pulse rate, which acts solutions. The word “Heuristic” refers to “solution by trial as a balance, are equalized to number of problem dimension. and error method” and the word “meta” refers to “high Thus it’s provided that bats search the space effectively. In level”. Hence metaheuristic algorithms solve optimization order to examine performance of the proposed algorithm problems via high level techniques [3]–[5]. Heuristic (MBA), it is applied on unimodal, multimodal and shifted benchmark functions with different dimensions and the Manuscript received July 10, 2013; accepted November 29, 2013. results are compared with BA. 71 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 20, NO. 2, 2014 The rest of this paper is organized as follows. Section II collision and reflection of these spread signals [20]. In BA, summarizes BA. The studies of BA in literature are the echolocation characteristics are idealized within the presented in Section III. The MBA is expressed in Section framework of the following rules by benefitting such IV. Section V contains benchmark functions and results. features of bats [19]: Finally conclusion is presented in Section VI. 1. All bats use echolocation to sense distance, and they also ‘know’ the difference between food/prey and II. BAT ALGORITHM background barriers in some magical way; BA, proposed by Yang [19], is a meta-heuristic algorithm 2. Bats fly randomly with velocity vi at position xi inspired by fascinating abilities of bats such as finding their with a frequency fmin, varying wavelength and loudness A0 prey and discriminating different types of insects even at to search for prey. They can automatically adjust the complete darkness. The advanced echolocation capability of wavelength (or frequency) of their emitted pulses and bats makes them fascinating. Such abilities inspired to adjust the rate of pulse emission r [0,1], depending on researchers on many fields. Bats use typical sonar called as the proximity of their target; echolocation to detect prey and to avoid obstacles. Bats, in 3. Although the loudness can vary in many ways, we particular micro-bats, are able to recognize positions of the assume that the loudness varies from a large (positive) A0 objects by spreading high and short audio signals and by to a minimum constant value Amin. TABLE I. BENCHMARK FUNCTIONS USED IN EXPERIMENTS. Function Search range Min Formulation ௡ f1 [-5.12,5.12] 0 ଵ =  ௜ଶ ௜ୀଵ ௡ f2 [-5.12,5.12] 0 ଶ =  ௜ଶ ௜ୀଵ ௡ f3 [-1,1] 0 ଷ = |௜ |௜ାଵ ௜ୀଵ ௡ ଶ f4 [-100,100] 0 ସ =  ௜ + 0.5 ௜ୀଵ ௡ ௡ f5 [-2pi,2pi] -1 ହ = −−1 ௡ cos ଶ ௜ exp −  ௜ −  ଶ  ௜ୀଵ ௜ୀଵ ଶ௠ ௡ ௜ଶ f6 [0,pi] * ଺ = −  sin(௜ ) sin   ௜ୀଵ  1 ௡ ௡ ௜ f7 [-600,600] 0 ଻ =  ௜ଶ −  cos  +1 4000 ௜ୀଵ ௜ୀଵ √ ௡ f8 [-5.12,5.12] 0 ଼ =  ௜ଶ − 10 cos2௜ + 10 ௜ୀଵ ௡ f9 [-500,500] 0 ଽ = 418.982 +  −௜  |௜ | ௜ୀଵ 1 ௡ 1 ௡ f10 [-32.768,32.768] 0 ଵ଴ = −20 exp −0.2  ௜ଶ − exp   2௜  + 20 +  ௜ୀଵ ௜ୀଵ ௡ିଵ f11 [-2.048,2.048] 0 ଵଵ =  100௜ାଵ − ௜ ଶ + ௜ − 1 ଶ ௜ୀଵ ௡ f12 [-100,100] 0 ଵଶ =  ௜ଶ ௜ୀଵ ௡ f13 [-5.12,5.12] 0 ଵଷ =  ௜ଶ − 10 cos2௜ + 10 ௜ୀଵ 1 ௡ 1 ௡ f14 [-32.768,32.768] 0 ଵସ = −20 exp −0.2  ௜ଶ − exp   2௜  + 20 +  ௜ୀଵ ௜ୀଵ 1 ௡ ௡ ௜ f15 [-600,600] 0 ଵହ =   ଶ −  cos  +1 4000 ௜ୀଵ ௜ ௜ୀଵ √ Note: ‫ ݔ = ݖ‬− ‫ ݋‬and ‘o’ is randomly generated shifted vector located in search range; * -4.687, -9.66, -99.28 for d=5, 10, 100 respectively A. Algorithm 1. (Bat Algorithm) 5. while(t<maximum number of iterations) 1. Objective function: f(x), x=(x1,….xd)t 6. Generate new solutions by adjusting frequency, and 2. Initialize bat population xi and velocity vi i=1,2,..n updating velocities and location/solutions. 3. Define pulse frequency fi at xi 7. if(rand> ri) 4. Initialize pulse rate ri and loudness Ai 8. Select a solution among the best solutions 72 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 20, NO. 2, 2014 9. Generate a local solution around the selected best region which includes food/prey for bats, the bats randomly solution spread to the search space at first iteration since they have 10. end if no idea where the preys are in space at the beginning. The 11. if(rand< Ai and f(xi)< f(x*)) fitness value of each bat defines the quality of food source 12. Accept new solutions where it locates. Initial population is randomly generated 13. Increase ri, reduce Ai from real-valued vectors with d dimension and n number, by 14. end if taking into account lower and upper boundaries. (2nd line in 15. Ranks the bats and find current best x* Algorithm 1) 16. end while 17. Display results. , = + rand(0,1) − , (1) B. Initialization of Bat Population where i = 1,2,…n, j = 1,2,….d, xminj and xmaxj are lower and Since the search space in the problem is assumed as a upper boundaries for dimension j respectively. TABLE II. THE COMPETITIVE PERFORMANCE OF BA AND MBA ON UNIMODAL FUNCTIONS. Fun Dim Best Worst Mean Median SD Significant 5 BA 1.15e-01 3.67e-00 7.82e-01 6.06e-01 6.89e-01 MBA 7.52e-04 5.88e-03 3.16e-03 3.43e-03 1.42e-03 + 10 BA 1.09e-00 7.49e-00 3.84e-00 3.92e-00 1.58e-00 MBA 3.73e-03 1.60e-02 8.80e-03 7.74e-03 3.34e-03 + f1 30 BA 1.26e+01 4.13e+01 2.33e+01 2.10e+01 6.87e-00 MBA 1.07e-02 1.95e-01 4.61e-02 3.06e-02 4.38e-02 + 60 BA 3.83e+01 8.83e+01 5.53e+01 5.58e+01 1.15e+01 MBA 5.87e-00 2.30e+01 1.08e+01 1.02e+01 3.70e-00 + 5 BA 9.66e-02 9.86e-00 2.17e-00 1.73e-00 2.36e-00 MBA 1.15e-03 1.79e-02 7.63e-03 7.74e-03 4.06e-03 + 10 BA 2.09e-00 3.43e+01 1.82e+01 1.68e+01 8.77e+00 MBA 1.66e-02 1.07e-01 4.73e-02 4.38e-02 2.20e-02 + f2 30 BA 1.68e+02 6.99e+02 3.83e+02 3.75e+02 1.15e+02 MBA 5.68e-01 2.64e+01 6.82e-00 3.94e-00 6.74e-00 + 60 BA 1.07e+03 2.26e+03 1.70e+03 1.67e+03 3.14e+02 MBA 9.36e+01 7.61e+02 4.02e+02 3.75e+02 1.42e+02 + 5 BA 4.23e-06 4.23e-03 6.86e-04 3.97e-04 8.76e-04 MBA 4.64e-05 1.21e-03 3.00e-04 2.25e-04 2.46e-04 + 10 BA 3.62e-05 1.69e-02 3.09e-03 1.29e-03 4.09e-03 MBA 6.12e-04 1.07e-02 3.53e-03 3.35e-03 2.18e-03 . f3 30 BA 9.98e-05 2.57e-02 2.53e-03 8.60e-04 4.87e-03 MBA 3.27e-03 4.83e-01 1.07e-01 5.85e-02 1.08e-01 . 60 BA 8.26e-05 7.86e-03 2.25e-03 1.67e-03 1.98e-03 MBA 9.19e-03 1.01e-00 2.58e-01 2.00e-01 2.21e-01 . 5 BA 3.16e-16 6.24e-10 4.85e-11 8.01e-12 1.17e-10 MBA 8.36e-15 8.52e-11 9.06e-12 2.45e-12 1.62e-11 + 10 BA 4.39e-14 3.62e-10 3.50e-11 1.18e-11 6.78e-11 MBA 6.16e-16 4.14e-10 2.21e-11 2.21e-11 7.60e-11 + f4 30 BA 4.90e-16 1.30e-09 5.62e-11 3.18e-12 2.32e-10 MBA 5.14e-17 4.87e-11 1.0e-11 3.61e-12 1.44e-11 + 60 BA 5.00e-14 3.54e-10 2.52e-11 6.31e-12 6.39e-11 MBA 7.59e-16 4.54e-11 6.82e-12 1.40e-12 1.12e-11 + 5 BA 1.30e-193 2.54e-159 4.24e-160 1.30e-193 9.49e-160 MBA 1.30e-193 2.54e-159 8.49e-161 1.30e-193 4.57e-160 + 10 BA -1.11e-04 -8.9556e-15 -4.85e-06 -6.01e-08 2.00e-05 MBA -9.92e-01 -9.60e-01 -9.80e-01 -9.80e-01 7.64e-03 + f5 30 BA -1.47e-24 -2.69e-55 -4.97e-26 -2.32e-39 2.64e-25 MBA -9.89e-01 -1.00e-005 -7.07e-01 -9.72e-01 4.16e-01 + 60 BA -6.78e-43 0 -2.26e-44 -6.69e-124 1.21e-43 MBA -2.26e-24 0 -7.55e-26 0 4.06e-25 + which homogeneously dispersed in frequency band C. Generation of Frequency, Velocity and New Solutions [fmin,fmax]. Because of f frequency controls pace and range of The pulse frequency, which emits by bats, ranges between movement, the update process of bats’ position/solution and upper and lower bounds. As seen in 3rd line in Algorithm 1, velocity is similar to Particle Swarm Optimization (PSO) pulse frequency is randomly assigned to different values [19]. For the future iterations, frequency and consequently 73 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 20, NO. 2, 2014 velocity and position of a bat are evaluated as follows: a bat which meets the requirement in 7th line in Algorithm 1, once one of the existing solution among the best solutions = + ( − ) , (2) is selected thus new candidate solution are generated by = + – ∗ , (3) random walk = + , (4) = + Ᾱ, (5) where β ϵ [0,1] indicates randomly generated number, x* represents solution of bat which has best fitness value where Ᾱt, is average loudness of all bats, ɛ ϵ [0,1] is random obtained after comparison among all the n bats so far. number and represents direction and intensity of random- In order to increase the diversity of possible solutions, for walk. TABLE III. THE COMPETITIVE PERFORMANCE OF BA AND MBA ON MULTIMODAL FUNCTIONS. Fun Dim Best Worst Mean Median SD Significant 5 BA -3.84e-00 -2.49e-00 -3.15e-00 -3.16e-00 3.30e-01 MBA -4.45e-00 -3.91e-00 -4.20e-00 -4.18e-00 1.26e-01 + 10 BA -5.74e-00 -3.40e-00 -4.54e-00 -4.54e-00 4.58e-01 MBA -6.66e-00 -5.69e-00 -6.05e-00 -5.98e-00 2.65e-01 + f6 30 BA -1.20e+01 -8.46e-00 -9.70e-00 -9.48e-00 9.32e-01 MBA -1.32e+01 -1.00e+01 -1.11e+01 -1.10e+01 5.83e-01 + 60 BA -1.79e+01 -1.45e+01 -1.60e+01 -1.59e+01 8.56e-01 MBA -1.91e+01 -1.58e+01 -1.70e+01 -1.68e+01 7.95e-01 + 5 BA 1.22e-00 8.87e-00 3.84e-00 3.31e-00 1.97e-00 MBA 1.06e-01 1.95e-00 3.54e-01 2.35e-01 3.48e-01 + 10 BA 2.51e-00 2.59e+01 1.58e+01 1.67e+01 5.15e-00 MBA 2.05e-00 2.06e+01 8.12e-00 6.62e-00 5.39e-00 + f7 30 BA 4.84e+01 1.48e+02 9.55e+01 9.21e+01 2.68e+01 MBA 6.36e+01 1.82e+02 1.10e+02 1.01e+02 2.83e+01 . 60 BA 1.03e+02 4.09e+02 2.00e+02 1.80e+02 6.19e+01 MBA 2.16e+02 4.26e+02 3.19e+02 3.21e+02 5.64e+01 . 5 BA 7.24e-00 2.79e+01 1.72e+01 1.72e+01 6.23e-00 MBA 1.66 e-00 4.95 e-00 3.35 e-00 3.46 e-00 7.95e-01 + 10 BA 4.91e+01 8.62e+01 6.64e+01 6.47e+01 9.99e-00 MBA 1.46e+01 3.48e+01 2.49e+01 2.55e+01 4.35e-00 + f8 30 BA 2.11e+02 3.04e+02 2.67e+02 2.67e+02 2.01e+01 MBA 2.72e+01 2.11e+02 1.63e+02 1.77e+02 4.40e+01 + 60 BA 5.33e+02 6.37e+02 5.88e+02 5.87e+02 2.70e+01 MBA 1.85e+02 5.58e+02 3.84e+02 4.00e+02 1.21e+02 + 5 BA 5.84e+02 1.04e+03 8.49e+02 8.21e+02 1.28e+02 MBA 1.40e-02 7.15e+02 2.56e+02 2.42e+02 1.84e+02 + 10 BA 1.50e+03 2.82e+03 2.27e+03 2.32e+03 2.83e+02 MBA 7.01e+02 1.45e+03 1.01e+03 9.78e+02 1.82e+02 + f9 30 BA 6.71e+03 1.01e+04 8.72e+03 8.96e+03 1.12e+03 MBA 3.91e+03 5.71e+03 5.10e+03 5.04e+03 3.83e+02 + 60 BA 1.39e+04 2.16e+04 1.85e+04 1.97e+04 2.86e+03 MBA 1.10e+04 1.35e+04 1.24e+04 1.25e+04 6.77e+02 + 5 BA 4.40e-00 1.17e+01 8.70e-00 9.31e-00 2.08e-00 MBA 3.47e-02 1.53e-01 9.08e-02 8.88e-02 2.39e-02 + 10 BA 8.29e-00 1.71e+01 1.27e+01 1.28e+01 2.11e-00 MBA 3.61e-02 1.79e-00 1.67e-01 6.91e-02 3.60e-01 + f10 30 BA 1.35e+01 1.68e+01 1.51e+01 1.50e+01 7.11e-01 MBA 7.53e-00 1.38e+01 1.11e+01 1.10e+01 1.63e-00 + 60 BA 1.45e+01 1.70e+01 1.57e+01 1.56e+01 6.84e-01 MBA 1.31e+01 1.63e+01 1.45e+01 1.45e+01 8.07e-01 + 5 BA 1.51e-00 3.86e+01 7.57e-00 5.99e-00 6.59e-00 MBA 1.90e-01 2.09e-00 1.13e-00 1.20e-00 4.11e-01 + 10 BA 1.73e+01 1.11e+02 6.36e+01 5.86e+01 2.57e+01 MBA 7.44e-00 1.64e+01 1.03e+01 1.00e+01 1.94e-00 + f11 30 BA 1.94e+02 8.38e+02 4.56e+02 4.48e+02 1.46e+02 MBA 2.52e+01 3.4e+01 2.97e+01 2.98e+01 1.75e-00 + 60 BA 4.34e+02 1.77e+03 1.09e+03 1.09e+03 3.30e+02 MBA 1.69e+02 3.65e+02 2.57e+02 2.40e+02 6.19e+01 + 74 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 20, NO. 2, 2014 D. Updating Loudness and Pulse Emission Rate Update is necessary for the factors loudness Ai and pulse emission rate ri as iteration proceeds. As bats approach to their prey, the pulse emission rate increases while loudness usually decreases (Fig. 1, Fig. 2). Fig. 2. Changes in pulse rate (r) throughout 100 iterations. III. LITERATURE REVIEW Khan and Sahai used BA for training of Proben1 dataset by neural network [21], Gandomi and Yang tested the performance of BA on some constrained engineering problems [22], Komarasamy and Wahi united the BA and Fig. 1. Changes in loudness (A) throughout 100 iterations. K-Medoid (KM) clustering algorithm as a new metaheuristic (KMBA) to fulfil the problem of initialization cluster These factors will be updated when only new solutions centroid of KM [23], are improved, namely bats approach their prey/targets. continuous problems [24], Yilmaz and Kucuksille Loudness Ai and pulse emission rate ri are updated by the proposed some modifications on BA for continuous following equations as iteration proceeds: problems [25], Wang and Guo hybridized BA with = , (6) Harmony Search Algorithm for solving numerical problems = (1 − ), (7) [26], Biswal et. al used BA to find optimal solution on where α and γ are constants. ri0 and Ai are factors which economic load dispatch problem [27], Marichelvam et al., consist of random values and Ai0 can typically be [1], [2], proposed BA on multistage hybrid flow shop scheduling while ri0 can typically be [0, 1]. problem [28]. TABLE IV. THE COMPETITIVE PERFORMANCE OF BA AND MBA ON SHIFTED FUNCTIONS. Fun Dim Best Worst Mean Median SD Significant 5 BA 2.06e+01 1.79e+03 5.17e+02 4.64e+02 3.85e+02 MBA 7.25e-05 1.70e-03 3.84e-04 3.11e-04 3.08e-04 + 10 BA 1.48e+03 8.97e+03 5.05e+03 4.93e+03 1.73e+03 MBA 4.38e-04 8.84e+02 1.52e+02 9.71e+01 1.80e+02 + f12 30 BA 3.38e+04 9.47e+04 6.17e+04 6.33e+04 1.44e+04 MBA 9.60e+03 2.79e+04 1.70e+04 1.59e+04 5.29e+03 + 60 BA 1.18e+05 2.41e+05 1.75e+05 1.67e+05 2.91e+04 MBA 6.51e+04 12.6e+05 9.09e+04 8.93e+04 1.57e+04 + 5 BA 5.44e-00 3.80e+01 1.72e+01 1.67e+01 7.79e-00 MBA 6.86e-01 5.26e-00 2.91e-00 3.07e-00 1.17e-00 + 10 BA 5.45e+01 1.12e+02 8.04e+01 8.45e+01 1.46e+01 MBA 1.31e+01 2.81e+01 2.09e+01 2.05e+01 4.72e-00 + f13 30 BA 3.33e+02 4.86e+02 4.18e+02 4.16e+02 3.57e+01 MBA 3.81e+01 9.13e+01 5.45e+01 5.21e+01 1.15e+01 + 60 BA 8.35e+02 1.24e+03 1.01e+03 9.87e+02 7.91e+01 MBA 1.89e+02 3.24e+02 2.58e+02 2.61e+02 3.57e+01 + 5 BA 3.63e-00 1.48e+01 8.97e-00 8.49e-00 2.53e-00 MBA 3.29e-02 1.21e-01 7.39e-02 7.31e-02 2.20e-02 + 10 BA 1.31e+01 2.05e+01 1.69e+01 1.66e+01 2.02e-00 MBA 2.05e-02 2.34e-00 4.47e-01 7.70e-02 7.50e-00 + f14 30 BA 1.96e+01 2.11e+01 2.07e+01 2.08e+01 3.73e-01 MBA 1.41e+01 2.07e+01 1.68e+01 1.67e+01 1.63e-00 + 60 BA 2.08e+01 2.13e+01 2.10e+01 2.10e+01 1.20e-01 MBA 1.81e+01 1.99e+01 1.92e+01 1.92e+01 3.74e-01 + 5 BA 1.72e-00 1.58e+01 7.14e-00 6.38e-00 4.15e-00 MBA 4.19e-02 1.78e-00 4.58e-01 3.38e-01 4.12e-01 + 10 BA 1.21e+01 9.92e+01 4.95e+01 4.32e+01 2.07e+01 MBA 1.86e-00 1.79e+01 6.51e-00 5.52e-00 3.44e-00 + f15 30 BA 4.23e+02 9.34e+02 6.24e+02 6.21e+02 1.40e+02 MBA 9.75e+01 2.90e+02 2.02e+02 2.00e+02 5.46e+01 + 60 BA 1.17e+03 1.85e+03 1.59e+03 1.62e+03 1.75e+02 MBA 6.30e+02 1.38e+03 9.37e+02 9.34e+02 1.62e+02 + 75 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 20, NO. 2, 2014 Fister et al. hybridized BA with Differential Evaluation B. Proposed Approach Algorithm and tested the algorithm on some unconstrained BA has poor exploration capability therefore the IV. MODIFIED BAT ALGORITHM convergence of obtained solution to the global optimum point is mostly impossible. Exploration mechanism of BA is BA is an optimization method which includes loudness A improved by equalizing the loudness A and pulse emission and pulse emission rate r factors apart from some rate r to the problem dimension. The factors A and r, which parameters of population based algorithm such as population belong to each bat, exist in BA and these factors influence number, search dimension, maximum cycle number. At the all dimensions of the solutions. Such factors are assigned to onward iterations of BA pulse emission rate, r decreases each dimension of the solution separately in this proposed while loudness A increases exponentially (Fig. 1, Fig. 2). approach. Thus each dimension of the solution can perform Thus, According to pseudo code (Algorithm 1), it’s low different capabilities (exploration and exploitation) possibility that the condition (7th row) is ensured by a bat. simultaneously. In BA each solution, which provides the Hereby, algorithm loses exploration capability highly at the rand > ri (7th line in Algorithm 1), approaches around the following iterations. At the beginning of the iterations, best solution with its entire dimension, but in MBA, each exploitation capability is dominant while exploration dimension j of solution i, which provides the randj > rij, capability comes to the forefront at the following iterations. approaches around the dimension j of the best solution and However, an optimization algorithm has to drive forward the rest dimensions of solution i keep on seeking the search exploration capability at the first iterations then exploitation space. The equation, which generates candidate solution capability at the later iterations so as to reach optimum around the best solution (5) for all dimensions in BA, is point. The essence of this study is to create modified Bat adapted for each dimension in MBA as following Algorithm which eliminates mentioned problem. A. Balance Problem between Exploration and Exploitation + ̅ > , of Current Algorithm = (8) ℎ , The generation process of candidate solution around the best solution (5) increases exploitation capability; while the where u indicates a solution selected among best solutions, process of updating solution (2)–(4) increases exploration while Ᾱjt represents average loudness of dimension j of all capability of BA. It is understood that, only if new candidate solutions at time t. solutions are generated by (2)–(4), algorithm will be good at While all dimensions of each candidate solution where exploration but bad at exploitation; on the other hand only if Ai > rand (10th line in algorithm 1) are included to new candidate solutions are generated around a solution population in BA, candidate solution is included to which selected among current best solutions (5), algorithm population where Ᾱi > rand in proposed algorithm. Here Ᾱi will be bad at exploration but good at exploitation. Thus is average loudness of solution i. Update processes of A and algorithm can easily get trapped into local minimum on r of proposed approach (12th line in Algorithm 1) only multimodal functions. Actually, pulse emission rate (r) is a influence dimension j of solution i where (randj > rij). factor which provides a balance between exploration and Therefore, the (6), (7) are updated as following: exploitation. However as seen from Fig. 2 and (7), the increase rate of r is proportional to number of iterations. , > , Thus, the case of rand > ri (7th line in Algorithm 1) is most = (9) , ℎ , likely accepted at the beginning of iterations then new candidate solutions will be around a solution which selected (1 − ), > , = (10) among the best solutions. The possibility of rand > ri , ℎ . decreases as the iteration proceeds. This means that exploitation will be applied at first steps of iterations and Suppose the dimensions j, where randj > rij, are called as exploration will be applied at the following iterations. y. It’s expected from dimensions y of solution i which Figure 1 and (6) demonstrate that the loudness A previously exploit, to search the space through exploration decreases during the iterations. Accordingly the possibility capability as iteration proceeds. Therefore the possibility of of Ai > rand (10th line in Algorithm 1) is higher at the randj > rij is reduced by increasing of pulse emission rate r beginning of iterations but lower at the following iterations. for dimensions y. Similarly, it’s expected from the other Although, as seen in Fig. 2, pulse emission rate r increases dimensions, which previously explore apart from y, to exploration capability, the possibility of Ai > rand weakens upgrade current solutions by exploitation capability at the because of loudness A will decrease as the iteration following iterations. For that reason the possibility of randj proceeds. It means that the inclusion possibility of new > rij is preserved for other dimensions apart from y at the candidate solutions, which generated by exploration at the following iterations. end of the iterations, into the bat population is weak. If the If the second term (ɛᾹt) on the right side of the (5) is algorithm gets trapped into local minimum at the beginning analysed, loudness A decreases as iteration proceeds of iterations, newly generated solutions also accumulate (Fig. 1), (6). Therefore the range, where candidate solution around such local minimum. Due to this reason, the elusion searches to find minimum point around best solution of possibility of algorithm from local region decreases. current population, narrows (Fig. 3). Hence, new candidate 76 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 20, NO. 2, 2014 solutions converge to the best solution as iteration proceeds. As the dimensions of problem to be optimized increase, In proposed approach, search range of best solution is performance of most of the optimization method weakens narrowed for dimensions y by reducing loudness A that quickly. There are two reasons: First, solution space of belongs to these dimensions (9). problem exponentially increases and more effective strategies are needed to seek all promising regions. Second, the characteristic of problem also changes with scale. Increment of dimension of some optimization objective functions causes changes in characteristic of this objective function like in Rosenbrock’s function. In this type of objective functions, the performance of algorithm shows a change depending on the dimension [30]. Due to this reason, as seen in Table III, the performance of both algorithms (BA and MBA) decreases as their dimensions increase. Fig. 3. Local search region around selected best solution during four iterations while A=1.9,α=0.3, ɛ=0.9. The reason why loudness A is not decreased apart from dimension y is to protect the local search range of these dimensions and to prevent restriction of this range. V. COMPUTATIONAL EXPERIMENTS a) b) A. Benchmark Functions In order to verify efficiency of proposed approach (MBA), two algorithms (BA – MBA) are tested on 15 different benchmark functions with different dimensions as seen in Table I. The function numbers, bounds of search space, global minimum values of the functions are shown in Table I respectively. Functions are tested with the dimension d = 5, 10, 30 and 60. f1-f5 are unimodal functions, f6-f11 are c) d) multimodal functions and number of local minima of these functions are proportional to problem size. f12-f15 are shifted functions. f12 is Rosenbrock’s function and it’s unimodal for d = 2,3 while it’s multimodal for more dimensions [16]. f6 is Michalewicz’s function and its global minimum is -4.687,- 9.66 for d = 5 and 10 respectively. f5 is Easom’s function, normally it is 2 dimensional test function but Yang extended this function to n dimensions [29]. e) f) As the number of problem dimension increases on each benchmark functions, function evaluation number (FE) also increases and it is 25.000, 50.000, 150.000 and 300.000 for d = 5, 10, 30 and 60 respectively. The solution number in population is fixed to 50. Algorithms are tested with 30 independent runs for each test function. B. Experimental Results In this section, BA - MBA are compared in terms of g) h) solution quality within negligible CPU time. As a result of Fig. 4. Convergence performances of MBA and BA on different functions: 30 runs, the fitness values of “Best, worst, mean, median, a) f6 function with d=5, b) f12 function with d=5, c) f10 function with d=10, d) f2 function with d=10, e) f14 function with d=30, f) f5 function with d=30, standard deviation” are comparatively shown in Table II– g) f4 function with d=60, h) f13 function with d=60. Table IV. In order to analyse the results of performances of both So as to evaluate the performance of both algorithms, 15 algorithms, the “mean” values in Table II–Table IV are different unimodal multimodal and shifted benchmark considered. The signs “+” and “.” at the rightmost column functions with 4 different dimensions are utilized. It means named “significant” indicate that MBA is better than BA 60 test implementations are used. MBA is better than BA on and MBA is worse than BA respectively. 17 of 20 implementations of unimodal functions (85 % The graphics (Fig. 4), which formed through a run that success rate), 22 of 24 implementations of multimodal randomly selected among 30 runs, exhibits changes of functions (92 % success rate) and all of 16 implementations fitness values of objective function with FE for both of shifted functions (100 % success rate). Totally, MBA is algorithms. better than BA on 55 of 60 implementations of three types 77 ELEKTRONIKA IR ELEKTROTECHNIKA, ISSN 1392-1215, VOL. 20, NO. 2, 2014 of functions (92 %). BA only produces better results than [11] S. I. Birbil, S. C. Fang, “An electromagnetism-like mechanism for global optimization”, Journal of Global Optimization, vol. 25, no. 3, MBA on the functions f3 with d = 10, 30, 60 and f7 with d = pp. 263–282, 2003. [Online]. Available: http://dx.doi.org/ 30, 60. 10.1023/A:1022452626305 As it can be easily seen from the implementation results, [12] F. Glover, M. Laguna, Tabu Search. Kluwer, Norwell, 1997. [13] J. Kennedy, R. C. Eberhart, “Particle swarm optimization”, in Proc. of proposed MBA provided smaller fitness values for most of IEEE Int. Conf. on Neural Networks, vol. 4, pp. 1942–1948, 1995. the unconstrained, continuous benchmark functions which [Online]. Available: http://dx.doi.org/10.1109/ICNN.1995.488968 are in Table I. [14] M. Dorigo, V. Maziezzo, A. Colorni, “The ant system: optimization by a colony of cooperating ants”, IEEE Trans. on Systems, Man and Cybernetics B, vol. 26, no. 1, pp. 29–41, 1996. [Online]. Available: VI. CONCLUSIONS http://dx.doi.org/10.1109/3477.484436 In this study, it’s investigated that whether this applied [15] B. Alatas, “ACROA: artificial chemical reaction optimization algorithm for global optimization”, Expert Systems with Applications, modification is successful or not on unimodal, multimodal vol. 38, no. 10, pp. 13170–13180, 2011. [Online]. Available: and shifted unconstrained, numeric optimization problems http://dx.doi.org/10.1016/j.eswa.2011.04.126 by modifying standard Bat Algorithm. While the factors of [16] W. Gao, S. Liu, “A modified artificial bee colony algorithm ”, pulse emission rate (r) and loudness (A) influence all Computers and Operations Research, vol. 39, 2012, pp. 687–697. [Online]. Available: http://dx.doi.org/10.1016/j.cor.2011.06.007 dimensions of solutions during the search in standard [17] X. S. Yang, “Review of metaheuristics and generalized evolutionary method (BA), solutions influence the dimensions of each walk algorithm”, Int. J. Bio-Inspired Computation, vol. 3, no. 2, pp. solution differently owing to these factors, which belong to 77–84, 2011. [Online]. Available: http://dx.doi.org/10.1504/IJBIC. 2011.039907 each bat, are equalized to number of problem dimension in [18] K. C. Tan, S. C. Chiam, A. A. Mamun, C. K. Goh, “Balancing proposed approach (MBA). Thereby these factors cause exploration and exploitation with adaptive variation for evolutionary exploration on some dimensions of a solution and multi-objective optimization”, European Journal of Operational Research, vol. 197, 2009, pp. 701–713. [Online]. Available: exploitation on rest of the dimensions of a solution. http://dx.doi.org/10.1016/j.ejor.2008.07.025 BA and MBA are compared on 15 different benchmark [19] X. S. Yang, “A new metaheuristic bat-inspired algorithm”, in Proc. test functions and results are comparatively shown in Nature Inspired Cooperative Strategies for Optimization (NISCO 2010), Springer Berlin, vol. 284, 2010, pp. 65–74. Table II–Table IV. The results obtained from the [20] X. S. Yang, “Bat algorithm for multi-objective optimization”, Int. unconstrained benchmark functions reveal that the proposed Journal of Bio-Inspired Computation, vol. 3, no. 5, pp. 267–274, version of BA is better than the standard one. 2011. [21] K. Khan, A. Sahai, “A comparison of BA, GA, PSO, BP and LM for The investigation of the performance of proposed training feed forward neural networks in e-learning context”, Int. algorithm (MBA) on discrete, constrained engineering Journal of Intelligent Systems and Applications, vol. 4, no. 7, 2012, problems and system identification problems is planned in pp. 23–29. [Online]. Available: http://dx.doi.org/10.5815/ijisa.2 the future. 012.07.03 [22] A. H. Gandomi, X. S. Yang, A. H. Alavi, T. Siamak, “Bat algorithm REFERENCES for constrained optimization tasks”, Neural Computing and Applications, vol. 22, no. 6, pp. 1239–1255, 2013. [Online]. [1] C. F. Juang, “A hybrid of genetic algorithm and particle swarm Available: http://dx.doi.org/10.1007/s00521-012-1028-9 optimization for recurrent network design”, IEEE Trans. Systems, [23] G. Komarasamy, A. Wahi, “An optimized K-means clustering Man, and Cybernetics-Part B: Cybernetics, vol. 34, no. 2, April 2004. technique using bat algorithm”, European Journal of Scientific [2] Y. Chen, X. Huang, “An optimization method based on chaotic Research, vol. 84, no. 2, pp. 26–273, 2012. immune evolutionary algorithm advances in natural computation”, [24] I. Fister, D. Fister, X.-S. Yang, “A hybrid bat algorithm”, Springer Berlin Heidelberg, vol. 3611, 2005, pp. 890–894. Elektrotehniski vestnik, vol. 80, no. 1–2, pp. 1–7, 2013. [3] X. S. Yang, “Harmony search as a metaheuristic algorithm”, Music- [25] S. Yilmaz, E. U. Kucuksille, “Improved bat algorithm (IBA) on Inspired Harmony Search Algorithm: Theory and Applications, continuous optimization problems”, Lecture Notes on Software Studies in Computational Intelligence, Springer Berlin, vol. 191, Engineering, vol. 1, no. 3, pp. 279–283, 2013. [Online]. Available: 2009, pp. 1–14. [Online]. Available: http://dx.doi.org/10.1007/978-3- http://dx.doi.org/10.7763/LNSE.2013.V1.61 642-00185-7_1 [26] G. Wang, L. Guo, “A novel hybrid bat algorithm with harmony search [4] X. S. Yang, Nature-inspired Metaheuristic Algorithms. Luniver Press, for global numerical optimization”, Journal of Applied Mathematics, 2008. vol. 2013, no. 1, pp. 1–21, 2013. [Online]. Available: [5] C. Blum, A. Roli, “Metaheuristics in combinatorial optimization: http://dx.doi.org/10.1155/2013/696491 Overview and conceptual comparison”, ACM Comput. Surv., vol. 35, [27] S. Biswal, A. K. Barisal, A. Behera, T. Prakash, “Optimal power 2003, pp. 268–308. [Online]. Available: http://dx.doi.org/10.1145/ dispatch using BAT algorithm”, in Proc. Int. Conf. on Energy 937503.937505 Efficient Technologies for Sustainability (ICEETS 2013), Nagercoil, [6] B. Atalas, S. Akyol, “The Current Swarm Intelligence Optimization 2013, pp. 1018–1023. Algorithms”, Nevsehir University Graduate School of Natural and [28] M. K. Marichelvam, T. Prabaharan, X. S. Yang, M. Geetha, “Solving Applied Sciences Journal, vol. 1, pp. 36–50, 2012. hybrid flow shop scheduling problems using bat algorithm”, Int. [7] B. Alatas, “Development of chaotic maps embedded particle swarm Journal of Logistics Economics and Globalisation, vol. 5, no. 1, pp. optimizatıon algorithms”, Ph.D. dissertation, Firat University 15–29, 2013. [Online]. Available: http://dx.doi.org/10.1504/ Graduate School of Natural and Applied Sciences, 2007. IJLEG.2013.054428 [8] D. E. Goldberg, Genetic algorithms in search, optimization and [29] X. S. Yang, “Test problems in optimization”, Engineering machine learning. Kluwer Academic Publishers, 1989. Optimization: An Introduction with Metaheuristic Applications, John [9] R. Storn, K. Price, “Differential evolution - a simple and efficient Wiley & Sons, 2010. [Online]. Available: http://dx.doi.org/10.1002/ adaptive scheme for global optimization over continuous spaces”, 9780470640425 Technical Report, 1995. [30] K. Tang, X. Li, P. N. Suganthan, Z. Yang, T. Weise, “Benchmark [10] E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, “GSA: a gravitational Functions”, in Special Session and Competition on Large-Scale search algorithm”, Information Sciences, vol. 179, 2009, pp. 2232– Global Optimization. Nature Inspired Computation and Applications 2248. [Online]. Available: http://dx.doi.org/10.1016/j.ins.2009.03.004 Laboratory, CEC’2010, 2010, pp. 1–23. 78

References (30)

  1. C. F. Juang, "A hybrid of genetic algorithm and particle swarm optimization for recurrent network design", IEEE Trans. Systems, Man, and Cybernetics-Part B: Cybernetics, vol. 34, no. 2, April 2004.
  2. Y. Chen, X. Huang, "An optimization method based on chaotic immune evolutionary algorithm advances in natural computation", Springer Berlin Heidelberg, vol. 3611, 2005, pp. 890-894.
  3. X. S. Yang, "Harmony search as a metaheuristic algorithm", Music- Inspired Harmony Search Algorithm: Theory and Applications, Studies in Computational Intelligence, Springer Berlin, vol. 191, 2009, pp. 1-14. [Online]. Available: http://dx.doi.org/10.1007/978-3- 642-00185-7_1
  4. X. S. Yang, Nature-inspired Metaheuristic Algorithms. Luniver Press, 2008.
  5. C. Blum, A. Roli, "Metaheuristics in combinatorial optimization: Overview and conceptual comparison", ACM Comput. Surv., vol. 35, 2003, pp. 268-308. [Online]. Available: http://dx.doi.org/10.1145/ 937503.937505
  6. B. Atalas, S. Akyol, "The Current Swarm Intelligence Optimization Algorithms", Nevsehir University Graduate School of Natural and Applied Sciences Journal, vol. 1, pp. 36-50, 2012.
  7. B. Alatas, "Development of chaotic maps embedded particle swarm optimizatıon algorithms", Ph.D. dissertation, Firat University Graduate School of Natural and Applied Sciences, 2007.
  8. D. E. Goldberg, Genetic algorithms in search, optimization and machine learning. Kluwer Academic Publishers, 1989.
  9. R. Storn, K. Price, "Differential evolution -a simple and efficient adaptive scheme for global optimization over continuous spaces", Technical Report, 1995.
  10. E. Rashedi, H. Nezamabadi-pour, S. Saryazdi, "GSA: a gravitational search algorithm", Information Sciences, vol. 179, 2009, pp. 2232- 2248. [Online]. Available: http://dx.doi.org/10.1016/j.ins.2009.03.004
  11. S. I. Birbil, S. C. Fang, "An electromagnetism-like mechanism for global optimization", Journal of Global Optimization, vol. 25, no. 3, pp. 263-282, 2003. [Online]. Available: http://dx.doi.org/ 10.1023/A:1022452626305
  12. F. Glover, M. Laguna, Tabu Search. Kluwer, Norwell, 1997.
  13. J. Kennedy, R. C. Eberhart, "Particle swarm optimization", in Proc. of IEEE Int. Conf. on Neural Networks, vol. 4, pp. 1942-1948, 1995. [Online]. Available: http://dx.doi.org/10.1109/ICNN.1995.488968
  14. M. Dorigo, V. Maziezzo, A. Colorni, "The ant system: optimization by a colony of cooperating ants", IEEE Trans. on Systems, Man and Cybernetics B, vol. 26, no. 1, pp. 29-41, 1996. [Online]. Available: http://dx.doi.org/10.1109/3477.484436
  15. B. Alatas, "ACROA: artificial chemical reaction optimization algorithm for global optimization", Expert Systems with Applications, vol. 38, no. 10, pp. 13170-13180, 2011. [Online]. Available: http://dx.doi.org/10.1016/j.eswa.2011.04.126
  16. W. Gao, S. Liu, "A modified artificial bee colony algorithm", Computers and Operations Research, vol. 39, 2012, pp. 687-697. [Online]. Available: http://dx.doi.org/10.1016/j.cor.2011.06.007
  17. X. S. Yang, "Review of metaheuristics and generalized evolutionary walk algorithm", Int. J. Bio-Inspired Computation, vol. 3, no. 2, pp. 77-84, 2011. [Online]. Available: http://dx.doi.org/10.1504/IJBIC. 2011.039907
  18. K. C. Tan, S. C. Chiam, A. A. Mamun, C. K. Goh, "Balancing exploration and exploitation with adaptive variation for evolutionary multi-objective optimization", European Journal of Operational Research, vol. 197, 2009, pp. 701-713. [Online]. Available: http://dx.doi.org/10.1016/j.ejor.2008.07.025
  19. X. S. Yang, "A new metaheuristic bat-inspired algorithm", in Proc. Nature Inspired Cooperative Strategies for Optimization (NISCO 2010), Springer Berlin, vol. 284, 2010, pp. 65-74.
  20. X. S. Yang, "Bat algorithm for multi-objective optimization", Int. Journal of Bio-Inspired Computation, vol. 3, no. 5, pp. 267-274, 2011.
  21. K. Khan, A. Sahai, "A comparison of BA, GA, PSO, BP and LM for training feed forward neural networks in e-learning context", Int. Journal of Intelligent Systems and Applications, vol. 4, no. 7, 2012, pp. 23-29. [Online]. Available: http://dx.doi.org/10.5815/ijisa.2 012.07.03
  22. A. H. Gandomi, X. S. Yang, A. H. Alavi, T. Siamak, "Bat algorithm for constrained optimization tasks", Neural Computing and Applications, vol. 22, no. 6, pp. 1239-1255, 2013. [Online]. Available: http://dx.doi.org/10.1007/s00521-012-1028-9
  23. G. Komarasamy, A. Wahi, "An optimized K-means clustering technique using bat algorithm", European Journal of Scientific Research, vol. 84, no. 2, pp. 26-273, 2012.
  24. I. Fister, D. Fister, X.-S. Yang, "A hybrid bat algorithm", Elektrotehniski vestnik, vol. 80, no. 1-2, pp. 1-7, 2013.
  25. S. Yilmaz, E. U. Kucuksille, "Improved bat algorithm (IBA) on continuous optimization problems", Lecture Notes on Software Engineering, vol. 1, no. 3, pp. 279-283, 2013. [Online]. Available: http://dx.doi.org/10.7763/LNSE.2013.V1.61
  26. G. Wang, L. Guo, "A novel hybrid bat algorithm with harmony search for global numerical optimization", Journal of Applied Mathematics, vol. 2013, no. 1, pp. 1-21, 2013. [Online]. Available: http://dx.doi.org/10.1155/2013/696491
  27. S. Biswal, A. K. Barisal, A. Behera, T. Prakash, "Optimal power dispatch using BAT algorithm", in Proc. Int. Conf. on Energy Efficient Technologies for Sustainability (ICEETS 2013), Nagercoil, 2013, pp. 1018-1023.
  28. M. K. Marichelvam, T. Prabaharan, X. S. Yang, M. Geetha, "Solving hybrid flow shop scheduling problems using bat algorithm", Int. Journal of Logistics Economics and Globalisation, vol. 5, no. 1, pp. 15-29, 2013. [Online]. Available: http://dx.doi.org/10.1504/ IJLEG.2013.054428
  29. X. S. Yang, "Test problems in optimization", Engineering Optimization: An Introduction with Metaheuristic Applications, John Wiley & Sons, 2010. [Online]. Available: http://dx.doi.org/10.1002/ 9780470640425
  30. K. Tang, X. Li, P. N. Suganthan, Z. Yang, T. Weise, "Benchmark Functions", in Special Session and Competition on Large-Scale Global Optimization. Nature Inspired Computation and Applications Laboratory, CEC'2010, 2010, pp. 1-23.
About the author
Ecir Ugur Kucuksille
Suleyman Demirel University, Faculty Member
Papers
31
Followers
131
View all papers from Ecir Ugur Kucuksillearrow_forward

Related papers

Studying the Effect of Pulse Rate Loudness and Echo-Location in Bat Algorithm
Nabila atika

2015

Swarm intelligence metaheuristic search algorithms are quite popular methods to solve many complex optimization problems in the real life. Bat algorithm is a recent addition to the family of metaheuristics. Bat uses echo-location behaviour of the bats to search optima convergence point in the search trajectory. Although, it has proven its mettle in finding optimal solutions, there are certain parameters that have not been investigated to improve convergence in Bat. Therefore, this paper explores the variations in parameters such as pulse rate, loudness and echo-location in Bat algorithm. The parameter enhancement is simulated on a set of benchmark functions and compared with other state of the art algorithms such as; particle swarm optimization, wolf search, and artificial bee colony. The simulation results show that Bat algorithm performance high correlates with the parameter adjustment.

View PDFchevron_right
A new modification approach on bat algorithm for solving optimization problems
Ecir Ugur Kucuksille

Applied Soft Computing, 2015

Optimization can be defined as an effort of generating solutions to a problem under bounded circumstances. Optimization methods have arisen from a desire to utilize existing resources in the best possible way. An important class of optimization methods is heuristic algorithms. Heuristic algorithms have generally been proposed by inspiration from the nature. For instance, Particle Swarm Optimization has been inspired by social behavior patterns of fish schooling or bird flocking. Bat algorithm is a heuristic algorithm proposed by Yang in 2010 and has been inspired by a property, named as echolocation, which guides the bats' movements during their flight and hunting even in complete darkness. In this work, local and global search characteristics of bat algorithm have been enhanced through three different methods. To validate the performance of the Enhanced Bat Algorithm (EBA), standard test functions and constrained real-world problems have been employed. The results obtained by these test sets have proven EBA superior to the standard one. Furthermore, the method proposed in this study is compared with recently published studies in the literature on real-world problems and it is proven that this method is more effective than the studies belonging to other literature on this sort of problems.

View PDFchevron_right
Bat algorithm (BA): review, applications and modifications
Jinda Org, Saman M. Almufti

Science Publishing Corporation, 2020

Generally, Metaheuristic algorithms such as ant colony optimization, Elephant herding algorithm, particle swarm optimization, bat algorithms becomes a powerful methods for solving optimization problems. This paper provides a timely review of the bat algorithm and its new variants. Bat algorithm (BA) is a Swarm based metaheuristic algorithm developed in 2010 by Xin-She Yang, BA has been inspired by the foraging behavior of micro bats, algorithm carries out the search process using artificial bats as search agents mimicking the natural pulse loudness and emission rate of real bats. It has become a powerful swarm intelligence method for solving optimization problems over continuous and discrete spaces. Nowadays, it has been successfully applied to solve problems in almost all areas of optimization , and it found to be very efficient. As a result, the literature has expanded significantly, a wide range of diverse applications and case studies has been made base on the bat algorithm.

View PDFchevron_right
A New Metaheuristic Bat-Inspired Algorithm
Xin-She Yang

Metaheuristic algorithms such as particle swarm optimization, firefly algorithm and harmony search are now becoming powerful methods for solving many tough optimization problems. In this paper, we propose a new metaheuristic method, the Bat Algorithm, based on the echolocation behaviour of bats. We also intend to combine the advantages of existing algorithms into the new bat algorithm. After a detailed formulation and explanation of its implementation, we will then compare the proposed algorithm with other existing algorithms, including genetic algorithms and particle swarm optimization. Simulations show that the proposed algorithm seems much superior to other algorithms, and further studies are also discussed.

View PDFchevron_right
An Improved Approach for Bat Algorithm
Eman Oun

International Journal of Advanced Research in Computer Science and Software Engineering, 2017

This paper introduces an alternative bat algorithm based on modifying the rules of the standard Bat Algorithm. The proposed algorithm gives better results compared with other known algorithms in the literature. The study considers five of the well known unconstrained benchmarking problems. The results of the proposed modification, standard Bat Algorithm, and other well-known algorithms are compared. Results indicate that proposed version is the best in terms of solution quality. Keywords-Metaheuristics, Bat algorithm, Real-world problems and Unconstrained problems. I. INTRODUCTION The ongoing research in solving optimization problems has developed new optimization approaches that achieved advantages over more traditional techniques. The need for getting new optimization techniques stemmed from the fact that the traditional techniques such as mathematical programming approaches have become inefficient for solving real-life applications. The large scale of systems, numerous design variables and practical requirements of designs in actual applications make the present day problems difficult to be handled using traditional optimization methods [1]. Recently, metaheuristic techniques are used to get a robust solution in solving complex problems. These algorithms tend to produce different solutions even when their initial conditions remain constant at each run because of their random nature. They are preferred for these functions which have several local optima as they can escape from local minima easily in spite of their slow convergence speed [2]. The basic idea behind these techniques is to simulate biological and physical systems in nature, such as natural evolution, immune system, swarm intelligence, annealing process, etc., in a numerical algorithm. These algorithms differ in the way the moves in the search space based on an associated nature-inspired strategy [3]. One of the promising metaheuristic methods, namely, the Bat Algorithm (BA), depends on simulating the echolocation behavior of bats. The capability of echolocation of micro bats is fascinating as these bats can find their prey and discriminate different types of insects even in complete darkness. They achieve this by emitting calls out to the environment and listening to the echoes that bounce back from them. They can identify the location of other objects and instinctively measure how far they are away from them by following delay of the returning sound [4]. From a quick literature review, it is found a set of researches that make a set of modifications or hybridizations on the standard BA to enhance its performance. Iztok F. made hybridization between the differential evolution strategies and the standard BA and named it as a hybrid bat algorithm. It has shown that this algorithm improves significantly the original version of BA [5]. Yilmaz S enhanced exploration and exploitation mechanisms of BA by three modifications, the first one it analyzed the structure of velocity with the inertia weighted update process. The second one it takes into consideration the difference between the solution and the global best solution to get the closest and the farthest dimension of the solution. The third modification is making hybridization between Artificial Bee Colony and BA to improve the exploration capability of BA [6]. Chen Z. removed the velocity parameter and added the inertia weight of location in BA which is determined using normal distribution and then the frequency of the micro bats emitted pulses adjust to the change of random position and optimal position of the micro bats [7]. Amir H. introduced chaos into BA to increase global search mobility for robust global optimization. This method uses chaotic maps to replace random variables which make enhancement when replaced for some random variables of standard BA [8]. Yilmaz S. improved the exploration mechanism by equalizing the loudness and pulse emission rate to the problem dimension by assigning them to each dimension of the solution separately which can perform different capabilities of exploration and exploitation simultaneously [9]. Wasi M. presented an improved self-adaptive BA for the problem of global numerical optimization over continuous domains. It has introduced two improved solution search equations. It has also used a selection probability to control the frequency of employing which leads to a new self-adaptive search mechanism for the Bat algorithm [10]. Ali A. accelerated the search process by invoking the Nelder-Mead method as a local search method in order to refine the best-obtained solution at each iteration [11].

View PDFchevron_right

Related topics

  • Electrical and Electronic Engine...
  • Electrical and Electronics Engin...

    • Cited by

    Improved Directional Bat Algorithm Based Electric Power Dispatch
    Diljinder Singh

    Electric Power Components and Systems, 2021

    Abstract No single metaheuristic search algorithm can be adjudged universally best general-purpose optimizer. The performance of search algorithms mainly depends upon the weightage assigned to global and local search strategies. This paper proposed an improved directional bat optimizer to minimize the operating cost of the electric power dispatch (EPD) problem that establishes a balance between global and local search strategies. Improved directional bat algorithm exploits directional echolocation bat behavior, directional exploration, neighborhood search and opposition based learning for generation jumping. The directional bat algorithm acts as a global search tool whereas exploration in each direction and neighborhood search performs local search. Opposition learning improves convergence with diversity. An effect of valve-point loading introduces a discontinuity in cost characteristics. The EPD problem addresses energy balance, generator capacity, ramp-rate limits and prohibited operating zones (POZ) avoidance constraints. An iterative technique handles energy balance constraint. The generation is adjusted to avoid the violation of generation capacity, ramp-rate limit and POZ constraints. The proposed algorithm is verified on various electric power systems. The results verify that the proposed algorithm is a potential algorithm to solve EPD problems as it competes with recent existing algorithms undertaken for comparison

    View PDFchevron_right
    A Comparative Study on Recently-Introduced Nature-Based Global Optimization Methods in Complex Mechanical System Design
    Zuomin Dong

    Algorithms

    Advanced global optimization algorithms have been continuously introduced and improved to solve various complex design optimization problems for which the objective and constraint functions can only be evaluated through computation intensive numerical analyses or simulations with a large number of design variables. The often implicit, multimodal, and ill-shaped objective and constraint functions in high-dimensional and "black-box" forms demand the search to be carried out using low number of function evaluations with high search efficiency and good robustness. This work investigates the performance of six recently introduced, nature-inspired global optimization methods: Artificial Bee Colony (ABC), Firefly Algorithm (FFA), Cuckoo Search (CS), Bat Algorithm (BA), Flower Pollination Algorithm (FPA) and Grey Wolf Optimizer (GWO). These approaches are compared in terms of search efficiency and robustness in solving a set of representative benchmark problems in smooth-unimodal, non-smooth unimodal, smooth multimodal, and non-smooth multimodal function forms. In addition, four classic engineering optimization examples and a real-life complex mechanical system design optimization problem, floating offshore wind turbines design optimization, are used as additional test cases representing computationally-expensive black-box global optimization problems. Results from this comparative study show that the ability of these global optimization methods to obtain a good solution diminishes as the dimension of the problem, or number of design variables increases. Although none of these methods is universally capable, the study finds that GWO and ABC are more efficient on average than the other four in obtaining high quality solutions efficiently and consistently, solving 86% and 80% of the tested benchmark problems, respectively. The research contributes to future improvements of global optimization methods.

    View PDFchevron_right
    An Improved BAT Algorithm for Solving Job Scheduling Problems in Hotels and Restaurants
    mokhtar mohammadi

    Artificial Intelligence: Theory and Applications, 2021

    One popular example of metaheuristic algorithms from the swarm intelligence family is the Bat algorithm (BA). The algorithm was first presented in 2010 by Yang and quickly demonstrated its efficiency in comparison with other common algorithms. The BA is based on echolocation in bats. The BA uses automatic zooming to strike a balance between exploration and exploitation by imitating the deviations of the bat's pulse emission rate and loudness as it searches for prey. The BA maintains solution diversity using the frequency-tuning technique. In this way, the BA can quickly and efficiently switch from exploration to exploitation. Therefore, it becomes an efficient optimizer for any application when a quick solution is needed. In this

    View PDFchevron_right
    Gaussian Quantum Bat Algorithm with Direction of Mean Best Position for Numerical Function Optimization
    xingwang huang

    Computational Intelligence and Neuroscience, 2019

    Quantum-behaved bat algorithm with mean best position directed (QMBA) is a novel variant of bat algorithm (BA) with good performance. However, the QMBA algorithm generates all stochastic coefficients with uniform probability distribution, which can only provide a relatively small search range, so it still faces a certain degree of premature convergence. In order to help bats escape from the local optimum, this article proposes a novel Gaussian quantum bat algorithm with mean best position directed (GQMBA), which applies Gaussian probability distribution to generate random number sequences. Applying Gaussian distribution instead of uniform distribution to generate random coefficients in GQMBA is an effective technique to promote the performance in avoiding premature convergence. In this article, the combination of QMBA and Gaussian probability distribution is applied to solve the numerical function optimization problem. Nineteen benchmark functions are employed and compared with othe...

    View PDFchevron_right
    A dynamically adapted and weighted Bat algorithm in image enhancement domain
    Krishna Gopal Dhal

    Evolving Systems, 2018

    This paper proposed one improved Bat algorithm (BA) by incorporating one novel dynamic inertia weight and proposed selfadaptive strategies over algorithm's parameters. Chaotic sequence and developed population diversity metric are employed over BA to perform the local search and generate one improved initial population respectively. The efficacy of the proposed BA is verified by applying it to set the parameters properly of the proposed histogram equalization (HE) variant; called weighted and thresholded Bi-HE (WTBHE). The proper setting of these parameters is time consuming but crucially effects WTBHE's image enhancement ability. One novel co-occurrence matrix based objective function has been also formulated which facilitates the proposed BA for finding the optimal parameters of WBTHE which produces original brightness preserved enhanced images. Experimental results prove that the proposed BA is superior to simple BA in terms of convergence speed, robustness and maximization of objective function and WBTHE is better than some existing well-known HE variants in brightness preserving image enhancement field.

    View PDFchevron_right
    580 California St., Suite 400
    San Francisco, CA, 94104
    © 2026 Academia. All rights reserved