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This article mainly shows you "what is the butterfly optimization algorithm in the Internet". The content is simple and clear. I hope it can help you solve your doubts. Let me lead you to study and learn this article "what is the butterfly optimization algorithm in the Internet?"

Brief introduction of algorithm

Butterfly optimization algorithm (butterfly optimization algorithm, BOA) is a meta-heuristic intelligent algorithm proposed by Arora et al in 2019. The algorithm is inspired by butterflies' foraging and mating behavior. Butterflies receive / perceive and analyze odors in the air to determine the potential direction of food sources / mating partners.

Butterflies use their senses of smell, sight, taste, touch and hearing to find food and mates, which also help them migrate from one place to another, escape predators and lay eggs in the right places. Of all the senses, smell is the most important, helping butterflies find food (usually nectar). The butterfly's olfactory receptors are scattered in the butterfly's body parts, such as antennae, legs, tentacles and so on. These receptors are actually nerve cells on the surface of butterflies, called chemosensors. It guides butterflies to find the best mate to inherit powerful genes. Male butterflies can identify female butterflies by pheromones, which are odor secretions emitted by female butterflies that cause specific reactions.

Through observation, it is found that butterflies have a very accurate judgment on the location of these sources. In addition, they can identify different fragrances and sense their intensity. Butterflies produce a certain intensity of fragrance related to their fitness, that is, when the butterfly moves from one position to another, its fitness changes accordingly. When the butterfly senses that another butterfly is emitting more fragrance in this area, it approaches. This stage is called global search. In another case, when a butterfly cannot perceive a fragrance larger than its own, it moves randomly, a stage called local search.

Fragrance; fragrance

In order to understand how fragrance in BOA is calculated, we first need to understand how modes such as smell, sound, light, temperature, and so on are calculated. To perceive and deal with these modes, we need to know three important terms: sensory mode C, stimulus intensity I and power index a. In sensory mode, feeling means measuring the form of energy and processing it in a similar manner, while mode refers to the original input used by the sensor. Different forms can be smell, sound, light, temperature, in BOA, the mode is fragrance. I is the size of the physical stimulus. In BOA, I is related to the fitness of butterflies / solutions. This means that when a butterfly emits more fragrance, other butterflies around it can feel and be attracted. The power is the index of the increase in strength. Parameter an allows regular expressions, linear responses, and response compression. The response expansion is that when I increases, fragrance (f) grows faster than I. Response compression is that when I increases, f grows more slowly than I. The linear response is that when I increases, f increases proportionally. It has been proved by experiments that sometimes with the enhancement of stimulation, the sensitivity of insects to stimulus changes becomes lower and lower. So in BOA, to estimate the size of I, response compression is used.

The natural phenomena of    butterflies are based on two important problems: the change of I and the representation of f. To put it simply, the I of the butterfly is associated with the encoded objective function. However, f is relative, that is, it should be perceived by other butterflies. In Stevens' power law, in order to distinguish smell from other forms, C is used. Now, when butterflies with less I move to butterflies with more I, f increases faster than I. Therefore, we should allow f to vary with the degree of absorption realized by the power parameter a. In BOA, fragrance is expressed as a function of the physical strength of the stimulus, as follows:

Where f is the size of the fragrance, that is, the fragrance intensity perceived by other butterflies, c is the sensory mode, which is taken between [0meme1], I is the stimulus intensity, and an is the power index, which takes the value between [0memen1]. At one extreme, axi1 means that the amount of aroma emitted by a particular butterfly is sensed by other butterflies with the same ability, which is equivalent to saying that the fragrance is transmitted in an idealized environment. A scented butterfly can be felt anywhere in this area. Therefore, a single (usually global) optimal value can be easily achieved. On the other hand, if a butterfly is zero, it means that the scent emitted by any butterfly will not be felt by other butterflies. Therefore, parameter a controls the behavior of the algorithm. Another important parameter is c, which is also the key parameter that determines the convergence speed and performance of BOA algorithm. Theoretically, c ∈ [0, ∞], but in practice it is determined by the characteristics of the system to be optimized. The values of An and c have an important influence on the convergence speed of the algorithm. In the maximization problem, the intensity can be proportional to the objective function.

Specific algorithm

In order to demonstrate the above discussion with a search algorithm, the above characteristics of butterflies are idealized as follows:

1. All butterflies can smell, which attracts butterflies to each other.

two。 Each butterfly moves randomly or toward the best butterfly, giving off more fragrance.

3. The stimulation intensity of butterflies is affected or determined by the landscape of the objective function.

The algorithm is divided into three stages: (1) initialization phase, (2) iteration phase and (3) end phase.

In each run of BOA, the initialization phase is performed first, then the iterative search is carried out, and finally the algorithm is terminated when the optimal solution is found. The parameter values used in BOA are also assigned, and after setting these values, the algorithm continues to create the initial butterfly population for optimization. Since the total number of butterflies remains constant during the simulation of BOA, a fixed size of memory is allocated to store information. The position of butterflies is randomly generated in the search space, and their fragrance and fitness values are calculated and stored. This completes the initialization phase, and the algorithm begins the iterative phase, which uses the created artificial butterfly to perform the search. The second stage of the algorithm, that is, the iterative phase, is performed by the algorithm for many iterations. In each iteration, all butterflies in the solution space are moved to a new location, and then their adaptability values are re-evaluated. Firstly, the fitness values of all butterflies in different positions in the solution space are calculated. Then these butterflies will use formula 1 to produce fragrance in their place. The algorithm has two key steps, namely the global search phase and the local search phase. In the global search phase, the butterfly takes a step towards the most suitable butterfly / solution g ∗, which can be expressed by formula (2).

Here, g ∗ denotes the current best solution found in all the solutions of the current iteration; fi denotes the scent of the first butterfly, and r is a random number in [0Power1]. The local search phase can be expressed as

Among them, xjt and xkt are the j and k butterflies in the solution space.

Butterflies looking for food and mating partners can occur locally and globally. Taking into account geographical proximity and various other factors, such as rain and wind, searching for food may account for a large proportion of the whole foraging activities of mating partners or butterflies. Therefore, the handover probability p is used in BOA to switch between a normal global search and a dense local search.

Iterate until the stop criteria are met. There can be multiple criteria for the end of an iteration, such as the maximum CPU time used, the maximum number of iterations reached, the maximum number of iterations without improvement, the specific value of the error rate reached, or any other appropriate criteria. At the end of the iterative phase, the algorithm outputs the optimal solution with the best fitness.

The above is all the content of this article "what is the Butterfly Optimization algorithm in the Internet?" Thank you for reading! I believe we all have a certain understanding, hope to share the content to help you, if you want to learn more knowledge, welcome to follow the industry information channel!

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