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Firefly Algorithm (FA): A Novel method motivated from the behavior of Fireflies for Optimal Solution – Transpire Online
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Firefly Algorithm (FA): A Novel method motivated
from the behavior of Fireflies for Optimal Solution
1. Introduction
Firefly algorithm (FA) was first developed by Yang in 2007 (Yang, 2008, 2009) which was based on the flashing pa erns and
behavior of fireflies. Firefly algorithm is classified as swarm intelligent, metaheuristic and nature-inspired, and it is developed by
Yang in 2008 by animating the characteristic behaviors of fireflies [1]. In fact, the population of fireflies show characteristic
luminary flashing activities to function as a racting the partners, communication, and risk warning for predators. As inspiring
from those activities, Yang formulated this method under the assumptions of all fireflies are unisexual such that all fireflies has
a racting potential for each other and the a ractiveness is directly proportionate to the brightness level of individuals. Hence, the
brighter fireflies a ract to the less brighter ones to move toward to them, besides that in the case of no fireflies brighter than a
certain firefly then it moves randomly [2]. In the formulation of firefly algorithm, the objective function is associated with flashing
light characteristics of the firefly population. Considering the physical principle of the light intensity, it is inversely quadratic
proportional to the square of the area, so that this principle enables to define fi ing function for the distance between any two
fireflies. For the optimization of fi ing function, the individuals are forced to systematic or random moves in the population. In
this way, it is ensured that all the fireflies move toward to more a ractive ones which have brighter flashing until the population
converge to brightest one. Within this procedure, firefly algorithm is executed by three parameters which are a ractiveness,
randomization, and absorption [3].
2. Life cycle of Firefly Algorithm
Fig1: Life circle of Firefly Algoritm
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Fig1 shows the Life cycle of Firefly Algorithm. The Adult Firefly is the one we know and love. They only in this for a few
weeks. Their only mission now is to mate. Female Fireflies lay about 100 eggs in the grass or on the ground. Most of the Firefly is in
this Larva stage [4]. They lives like this for 1-3 years spending winter underground or beneath the bark of a tree. Larva forms a
peotective covering as it changes into an awasome firefly. This process takes about 2 and a half weeks either underground or on a
tree branch [5].
3. Firefly Algorithm
Fireflies are unisexual, so one firefly will be a racted to other fireflies regardless of their sex. Their a ractiveness is
proportional to their brightness, and both decrease as their distance increases. Thus, for any two flashing fireflies, the less brighter
one will move toward the brighter one. If a particular firefly does not find a brighter one, it will move randomly. The brightness of
a firefly is determined by the landscape of the objective function [6]. The “firefly algorithm” (FFA) is a modern metaheuristic
algorithm, inspired by the behavior of fireflies. This algorithm and its variants have been successfully applied to many continuous
optimization problems. This work analyzes the performance of the FFA when solving combinatorial optimization problems. In
order to improve the results, the original FFA is extended and improved for self-adaptation of control parameters, and thus more
directly balancing between exploration and exploitation in the search process of fireflies [7]. We use a new population model to
increase the selection pressure, and the next generation selects only the fi est between a parent and an offspring population. The
brightness of a firefly is affected or determinedby the landscape of the objective function. For a maximization problem,
thebrightness can simply be proportional to the value of the objective function.Other forms of brightness can be defined in a
similar way to the fitness functionin genetic algorithms [8].
Fig2: Firefly Algorithm
3.1. A ractiveness and distance
The primary parameter which determines the efficiency of the FA is the variation of light intensity, i.e., a ractiveness between
neighboring fireflies. In FA, there are two important issues: formulation of a ractiveness and variation of light intensity [9]. For
simplicity, it is assumed that the a ractiveness of a firefly is determined by its brightness which is always encoded with the
objective function [10].
4. Steps for Firefly Algorithm
Initialization
A aractiveness and Distance
Generate the next generation
Iterative computing
Termination
4.1. Initialization
The main steps of the FA start from initializing a swarm of fireflies, each of which is determined the flashing light intensity.
During the loop of pair wise comparison of light intensity, the firefly with lower light intensity will move toward the higher one
[11]. The moving distance depends on the a ractiveness. After moving, the new firefly is evaluated and updated for the light
intensity.
4.2. A ractiveness and Distance
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Firefly algorithm is based on two important factors: variation of light intensity and formulation of the a ractiveness. An
assumption is made that a ractiveness of a firefly is calculated according its brightness which is associated further with the
encoded objective function [12].
4.3. Generate the next generation
The firefly is re-initialized with a new random position in the search space, if its status is inactive. In the FA, as per our
objective, we recast the algorithm and employed it to reposition the random firefly. In this, we reduce the TEST phase as per the
requirement for the random firefly and assume the random firely as an inactive agent [13]. Now, for the randomly selected
firefly, another firefly is selected from the swarm. If the firefly has more brightness than the random selected firefly then the
random firefly initializes itself to a new position in the neighboring region of the firefly, otherwise the selected firefly re-initialize
itself randomly in the search space [14].
4.4. Iterative computing
In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a
sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the
previous ones [15].
4.5. Termination
The Firefly Algorithm (FA) is a nature – inspired algorithm which is based on the social flashing behavior of fireflies.
A ractiveness is proportional to their flashing brightness which decreases as the distance from the other firefly increases due to the
fact that the air absorbs light [16].
4.6. Flow Chart
Fig3: Flowchart of FA
5. Numerical Expression for FA
The main steps of the FA start from initializing a swarm of fireflies, each of which is determined the flashing light intensity.
During the loop of pair wise comparison of light intensity, the firefly with lower light intensity will move toward the higher one
[17]. The moving distance depends on the a ractiveness. After moving, the new firefly is evaluated and updated for the light
intensity [18].
In this work, the evaluation on the goodness of schedules is measured by the makespan, which can be calculated using this
equation , where Ck is completed time of job k.
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Firefly Algorithm (FA): A Novel method motivated from the behavior of Fireflies for Optimal Solution – Transpire Online
Speed
sequence
Distance
(rij)
A ractiveness
βr)
(
Movement
(Xi)
Sequence for
generation
Next
Makespan
23514
0.6
0.55
0.9986
23514
48
32514
0.7
0.497
1.6388
32514
48
24351
0.4
0.6703
0.6703
24351
45
15234
1.2
0.3012
2.2943
12534
45
6. Applications of Firefly Algorithm
For solving Travelling Salesman problem[19]
Digital image compression and image processing
Feature selection and fault processing
Antenna design
Structural design[20]
Scheduling
Chemical phase equlibrium[21]
Dynamic problems
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Firefly Algorithm (FA): A Novel method motivated from the behavior of Fireflies for Optimal Solution – Transpire Online
Fig4: Applications of FA
7. Advantages of Firefly Algorithm
Firefly can be accessed anywhere with a web browser and an internet connection. This makes it a potentially more convenient
and portable tool than Kurzweil [22].
The reading voices in Firefly are, as a whole, superior to those in the Mac version of Kurzweil.
Firefly is comparable to Kurzweil (both Windows and Mac versions) in its ability to translate text. Unlike Mac Kurzweil,
Firefly can also intelligibly read text in Spanish [23].
FA can deal with highly non- linear, multimodel optimization problems naturally and effictively.
FA does not use velocities, and there is no problem as that associated with velocity in PSO [24].
The speed of convergence of FA is very high in probability of finding the global optimized answer.
It has the flexibility of integration with other optimization techniques to form hybrid tools.
It does not require a good initial solution to start its iteration process.
Reference
[1] Li, J. (2014). The Shortest Path Optimization Based on Mutation Firefly Optimization Algorithm. Advanced Materials Research,
1049-1050, pp.1690-1693.
[2] Arora, S. and Kaur, R. (2018). An escalated convergent firefly algorithm. Journal of King Saud University – Computer and
Information Sciences.
[3] Weber, P. and Pepłowski, P. (2014). Gaussian Motion Competing with L\’evy Flights. Acta Physica Polonica B, 45(11), p.2067.
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Firefly Algorithm (FA): A Novel method motivated from the behavior of Fireflies for Optimal Solution – Transpire Online
[4] Fister, I., Perc, M., Kamal, S. and Fister, I. (2015). A review of chaos-based firefly algorithms: Perspectives and research
challenges. Applied Mathematics and Computation, 252, pp.155-165.
[5] Johari, N., Zain, A., Noorfa, M. and Udin, A. (2013). Firefly Algorithm for Optimization Problem. Applied Mechanics and
Materials, 421, pp.512-517.
[6] Mishra, A., Agarwal, C., Sharma, A. and Bedi, P. (2014). Optimized gray-scale image watermarking using DWT–SVD and
Firefly Algorithm. Expert Systems with Applications, 41(17), pp.7858-7867.
[7] Tighzert, L., Fonlupt, C. and Mendil, B. (2018). A set of new compact firefly algorithms. Swarm and Evolutionary Computation,
40, pp.92-115.
[8] Kopciewicz, P. and Łukasik, S. (2019). Exploiting flower constancy in flower pollination algorithm: improved biotic flower
pollination algorithm and its experimental evaluation. Neural Computing and Applications.
[9] Liu, F., Li, F. and Jing, X. (2019). Navigability Analysis of Local Gravity Map With Projection Pursuit-Based Selection Method
by Using Gravitation Field Algorithm. IEEE Access, 7, pp.75873-75889.
[10] Teng, L. and Li, H. (2018). Modified Discrete Firefly Algorithm Combining Genetic Algorithm for Traveling Salesman
Problem. TELKOMNIKA (Telecommunication Computing Electronics and Control), 16(1), p.424.
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Firefly Algorithm (FA): A Novel method motivated from the behavior of Fireflies for Optimal Solution – Transpire Online
[11] Rajinikanth, V. and Couceiro, M. (2015). RGB Histogram Based Color Image Segmentation Using Firefly Algorithm. Procedia
Computer Science, 46, pp.1449-1457.
[12] Wang, J. (2017). Firefly algorithm with dynamic a ractiveness model and its application on wireless sensor networks.
International Journal of Wireless and Mobile Computing, 13(3), p.223.
[13] Jagatheesan, K., Anand, B., Samanta, S., Dey, N., Ashour, A. and Balas, V. (2019). Design of a proportional-integral-derivative
controller for an automatic generation control of multi-area power thermal systems using firefly algorithm. IEEE/CAA Journal of
Automatica Sinica, 6(2), pp.503-515.
[14] Bojic, I., Podobnik, V., Ljubi, I., Jezic, G. and Kusek, M. (2012). A self-optimizing mobile network: Auto-tuning the network
with firefly-synchronized agents. Information Sciences, 182(1), pp.77-92.
[15] Brajević, I. and Stanimirović, P. (2018). An improved chaotic firefly algorithm for global numerical optimization. International
Journal of Computational Intelligence Systems, 12(1), p.131.
[16] Miguel, L., Lopez, R. and Miguel, L. (2013). Multimodal size, shape, and topology optimisation of truss structures using the
Firefly algorithm. Advances in Engineering Software, 56, pp.23-37.
[17] Baykasoğlu, A. and Ozsoydan, F. (2014). An improved firefly algorithm for solving dynamic multidimensional knapsack
problems. Expert Systems with Applications, 41(8), pp.3712-3725.
[18] Baykasoğlu, A. and Ozsoydan, F. (2014). An improved firefly algorithm for solving dynamic multidimensional knapsack
problems. Expert Systems with Applications, 41(8), pp.3712-3725.
[19] Coelho, L. and Mariani, V. (2013). Improved firefly algorithm approach applied to chiller loading for energy conservation.
Energy and Buildings, 59, pp.273-278.
[20] ZHENG, H., LIU, H. and ZHENG, X. (2013). Group path planning method based on improved group search optimization
algorithm. Journal of Computer Applications, 32(8), pp.2223-2226.
[21] Wang, D., Luo, H., Grunder, O., Lin, Y. and Guo, H. (2017). Multi-step ahead electricity price forecasting using a hybrid model
based on two-layer decomposition technique and BP neural network optimized by firefly algorithm. Applied Energy, 190, pp.390407.
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Firefly Algorithm (FA): A Novel method motivated from the behavior of Fireflies for Optimal Solution – Transpire Online
[22] Singh, D., Singh, D. and Verma, K. (2008). GA based energy loss minimization approach for optimal sizing & placement of
distributed generation. International Journal of Knowledge-based and Intelligent Engineering Systems, 12(2), pp.147-156.
[23] Gholizadeh, S. (2015). Performance-based optimum seismic design of steel structures by a modified firefly algorithm and a
new neural network. Advances in Engineering Software, 81, pp.50-65. [24] Tawhid, M. and Ali, A. (2016). Direct Search Firefly
Algorithm for Solving Global Optimization Problems. Applied Mathematics & Information Sciences, 10(3), pp.841-860.
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Decoderz
July 23, 2019
AI techniques
Advantages of Firefly Algorithm, AI, applications, Artificial Intelligence, computer science, crossover, engineering, inspiring, phd, research
7 thoughts on “Firefly Algorithm (FA): A Novel method motivated from
the behavior of Fireflies for Optimal Solution”
ajithkumarsv
July 23, 2019 at 3:02 pm
great explanation…
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seaashyin
July 23, 2019 at 3:09 pm
We appreciate your innovative thinking.
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July 23, 2019 at 3:22 pm
Fantastic presentation
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good presentation
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It was Excellent and generous work
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