Butterfly Optimization Algorithm(BOA) : To Solve Engineering Problems


Butterfly optimization algorithm(BOA) is a population based natural inspired algorithm. BOA algorithm is first introduced by Aroa and Sing in 2019[1]. The real-world biological or physical phenomena of the food/flowersare solved using BOA optimization problems. The butterflies food searching capability is the main inspiration of this algorithm. Butterflies have a several senses such as hearing, smelling, and taste to help them to find the suitable nectar, partner mating, and laying the eggs in a suitable place and also to escape from the hunters. Butterflies have a most principle of smelling sense to find a food from long distances and to separate different fragrances within good precise location[2]. Butterflies foraging is the main strategy of BOA optimization algorithm, which utilize their sense of smell to determine the location of food. In BOA, an assumption is made about butterflies that they produce fragrance with some intensity.BOA is high efficient to low computational complexity and good solving convergence.

2.Inspirations of BOA

In all over the world the butterflies are found in all types of environments: such as,  hot and cold, dry and moist, at sea level and high in the mountains. Most butterfly species  are found in tropical areas, especially tropical rainforests. Butterflies sensory system helps them to find food and mates. That sensory system is said to be a chemoreceptor. Chemoreceptor is a nerve cell and a sense receptor that is employed for smelling and distributing fragrance in all over butterfly’s body parts[3].

Chemoreceptor also assists to butterfly to find the best mating partner. BOA is also said to be a swarm optimization algorithm in which each agent share its experiences by the other butterflies based on distributing the fragrance over the distance. Butterflies moves along with considering the phase as global search point by sensing the fragrance from the other one.The local search of the optimization is also considered as another movement of the butterfly. This local search and global search is performed by random generating. The method of BOA is based on a trade-off between fragrance and smell senses[4].

Fig 1: Inspiration of BOA

3.Life Cycle Of BOA

Four steps present in the lifecycle of BOA.They are

  • Egg
  • Caterpillar
  • Chrysalis
  • Butterfly

Fig 2: Lifecycle of BOA

3.1 Egg

The very small oval, round, or cylindrical egg is a first stage of butterflies life and their colors can be yellow, white, green or other shades, depending on the species of butterfly. The butterfly eggs are very thin and it havetough shell with raised ribs or pits reticulation. The adult female butterfly lay eggs on plants. After three to eight days the eggs are hatched and the caterpillars are comes out. And these caterpillars eat parts of the plant that the eggs were laid on. The butterfly lay eggs from spring, summer or fall season depend on the species of butterfly. Female butterflies lay lot of eggs at once and they also take special care of their eggs and keep warm but some of the eggs are survive.

Fig 3 : Butterfly Egg

3.2  Caterpillar

The larva or caterpillar emerges during the egg hatches. The caterpillar’s one and only job was to eat. The caterpillar splits its skin and sheds about 4 or 5 times when it grows up. And they store the eaten food at this time and used later as an adult. During this stage of  the caterpillars are grow hundreds of times their size. And they grow upto 2 inches longer in several weeks.

Fig 4 : Butterfly Caterpillar

3.3 Chrysalis

The pupa of butterflies is also called a chrysalis. When the pupa or chrysalis stops eating and it considered to be a fully grown caterpillar. The pupa of many moths is protected inside a coccoon of silk. The larva is now growing rapidly with a presents of special cells. Then the larva’s special cell become as legs, wings, eyes and other parts of the adult butterfly. These growing adult cell provide energy from the orginal larva cell

Fig 5: Butterfly Chrysalis

3.4  Butterfly

The chrysalis is grown and the adult butterfly emerges with its soft wings folded about its body. The blood vessels pumps into butterfly wings and its begin to fly  after resting period. The adult butterfly have a large and bright different coloured wings. The species of some butterflies hibernate during the winter and live several months. But most adult butterflies live one or two weeks.

Fig 6: Butterfly

4.Butterfly Optimization Algorithm(BOA):

BOA  mimics the food foraging behavior of butterflies. To understand this algorithm some biological facts and how to model them in BOA are discussed in following subsections[5].

There are three phases in BOA:

(1) Initialization phase,

(2) Iteration phase

 (3) Final phase. In each run of BOA,

First initialization phase, the algorithm defines the objective function and its solution space. The values for the parameters used in BOA are also assigned. After setting the values, the algorithm proceeds to create an initial population of butterflies for optimization. As the total number of butterflies remains unchanged during the simulation of BOA, a fixed size memory is allocated to store their information. The positions of butterflies are randomly generated in the search space, with their fragrance and fitness values calculated and stored. This finishes the initialization phase and the algorithm starts the iteration phase, which performs the search with the artificial butterflies created.the initialization phase is executed, then searching is performed in an iterative manner and in the last phase, the algorithm is terminated finally when the best solution is found.

3.1 Butterfly

In the Linnaean system of Animal Kingdom, butterflies lie in the class of Lepidoptera. There are more than 18,000 species of butterflies across the world. Butterflies use their sense of smell, sight, taste, touch and hearing to find food and mating partner. These senses are also helpful in migrating from one place to another, escaping from predator and laying eggs in appropriate places. Among all these senses, smell is the most important sense which helps butterfly to find food, usually nectar, even from long distances. Body parts like antennae, legs, palps are actually nerve cells on butterfly’s body surface and are called chemoreceptors and These chemoreceptors guide the butterfly to find the best mating partner in order to continue a strong genetic line[6][7].

 A male butterfly is able to identify the female through her pheromone which are scent secretions emitted by the female butterfly to cause specific reactions. Based on scientific observations, it is found that butterflies have a very accurate sense of locating the source of fragrance. A butterfly will generate fragrance with some intensity which is correlated with its fitness, i.e., as a butterfly moves from one location to another, its fitness will vary accordingly. The fragrance will propagate over distance and other butterflies can sense it and this is how the butterflies can share its personal information with other butterflies and form a collective social knowledge network. When a butterfly is able to sense fragrance from any other butterfly, it will move toward it and this phase is termed as global search in the algorithm. In another scenario, when a butterfly is not able to sense fragrance from the surrounding, then it will move randomly and this phase is termed as local search in the algorithm.

3.2 Fragrance

In BOA, each fragrance has its own unique scent and personal touch. The whole concept of sensing and processing the modality is based on three important terms viz. sensory modality (c), stimulus intensity (I) and power exponent (a).

In sensory modality, sensory means to measure the form of energy and process it in similar ways and modality refers to the raw input used by the sensors. Now different modalities can be smell, sound, light, temperature and in BOA, modality is fragrance[8].

I is the magnitude of the physical/actual stimulus. In BOA, I is correlated with the fitness of the butterfly/solution. This means that when a butterfly is emitting a greater amount of fragrance, the other butterflies in that surrounding can sense it and gets attracted toward it[9].

 Power is the exponent to which intensity is raised. The parameter a allows for regular expression, linear response and response compression. Response expansion is when I increases,the fragrance ( f ) increases more quickly than I. Response compression is when I increases, f increases more slowly than I.

The fragrance of the butterflies are calculated as

Pfj = cIa                                                                                                                                        (1)

Where , Pfj is denoted as  perceivedmagnitude of fragrance for jth butterfly.

3.3 Movement of butterflies

For movement of butterflies the three steps are used..

1. All butterflies are supposed to emit some fragrance which enables the butterflies to attract each other.

2. Every butterfly will move randomly or toward the best butterfly emitting more fragrance.

3. The stimulus intensity of a butterfly is affected or determined by the landscape of the objective function.

The algorithm consists of two main stages; Global and local search phases.

The global search phase is given by

BFjk+1  =  BFjk  + (r2*BestBF BFjk )fj                                                                              (2)

Where  is the vector which represent the butterfly solution at iteration k.BestBF is the best butterfly solution.fj is the fragrance of ith butterfly.r is the random number.

The local search phase is given by

           BFjk+1  =  BFjk  + (r2*BFmk BFnk )fj                                                                                  (3)

BFmk and BFnk are the two different vectors which represent the butterfly solution at iteration k.

Until the stop criteria are satisfied the iteration process continues

5. Flowchart

Fig 7: Flowchart of BOA

6. Pseudecode

Fig 8: Pseudecode of BOA

7.Advantages & Disadvantages:

The advantages and disadvantages[10][11] are given below

Fig 9: Advantages & Disadvantages of BOA


The applications of BOA[12] are given below

Fig 10: Applications of BOA


1.Arora, S. and Singh, S., 2017. An Effective Hybrid Butterfly Optimization Algorithm with Artificial Bee Colony for Numerical Optimization. International Journal of Interactive Multimedia and Artificial Intelligence, 4(4), p.14.

2.Arora, S. and Singh, S., 2018. Butterfly optimization algorithm: a novel approach for global optimization. Soft Computing, 23(3), pp.715-734.

3.Arora, S. and Singh, S., 2017. An improved butterfly optimization algorithm with chaos. Journal of Intelligent & Fuzzy Systems, 32(1), pp.1079-1088.

4.Arora, S. and Singh, S., 2017. Node Localization in Wireless Sensor Networks Using Butterfly Optimization Algorithm. Arabian Journal for Science and Engineering, 42(8), pp.3325-3335.

5.Arora, S. and Singh, S., 2016. An Improved Butterfly Optimization Algorithm for Global Optimization. Advanced Science, Engineering and Medicine, 8(9), pp.711-717.

6.Arora, S., Singh, S. and Yetilmezsoy, K., 2018. A modified butterfly optimization algorithm for mechanical design optimization problems. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40(1).

7.Arora, S. and Singh, S., 2018. Butterfly optimization algorithm: a novel approach for global optimization. Soft Computing, 23(3), pp.715-734.

8.Khasnabish, J., Mithani, M. and Rao, S., 2017. Tier-Centric Resource Allocation in Multi-Tier Cloud Systems. IEEE Transactions on Cloud Computing, 5(3), pp.576-589.

9.Arora, S. and Singh, S., 2018. Butterfly optimization algorithm: a novel approach for global optimization. Soft Computing, 23(3), pp.715-734.

10.Shukla, A. and Goyal, V., 2019. Formation of Artificial Bee Colony with Monarch Butterfly Optimization and Cluster Head Load Distribution for Energy Saving in MANET. Journal of Advanced Research in Dynamical and Control Systems, 11(10-SPECIAL ISSUE), pp.647-654.

11.Sharma, S. and Saha, A., 2019. m-MBOA: a novel butterfly optimization algorithm enhanced with mutualism scheme. Soft Computing, 24(7), pp.4809-4827.

12.Zhi, Y., Weiqing, W., Haiyun, W. and Khodaei, H., 2020. Improved butterfly optimization algorithm for CCHP driven by PEMFC. Applied Thermal Engineering, 173, p.114766.

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