# BOA-Based FS Process

In this section, the BOAFS algorithm gets executed to select the useful set of features. Nature-based metaheuristic approach has attained maximum attention from diverse applications in last decades. Butterfly optimization algorithm comes under the class of bioinspired model that is defined as a subclass of nature-based metaheuristic method. Basically, BOA is evolved from the food foraging nature of butterflies, and it is applied as searching agents that carry out the optimization in BOA. By default, butterflies comprise sense receptors that are used for sensing the smell of food or flowers. The sense receptors are named as chemoreceptors that have been distributed in butterfly’s overall body.

Additionally, the butterfly can generate smell with some power. It is associated with the fitness of a butterfly determined under the application of objective function of a problem. It represents that if a butterfly shifts from one place to another in a search space, then the fitness will be changed.

The smell that is generated by a butterfly can be sensed by various other butterflies in the surroundings and aggregate social learning mechanism is followed. If the butterfly smells a fragrance from optimal butterfly in search space, then it develops a stride to good butterfly, which is termed as global search phase of BOA. Second, if a butterfly is unable to predict the fragrance of another butterfly in search space, which can develop arbitrary strides, it is termed as local search phase. In BOA, the scent is referred to as a function of external intensity of stimulus in the following:

where *pf,* implies the received magnitude of scent, which determines the intensity of a fragrance of ith butterfly that is perceived by alternate butterflies, *c* depicts the sensory modality, *I* represents the stimulus intensity, and *a* shows the power exponent on the basis of modality, which consumes for different degree of absorption. In BOA, the artificial butterfly contains a position vector that is extended at the time of optimization process with the help of

where *xj* denotes the solution vector x, for ith butterfly with iteration value *t* and *F,* showcases the scent applied by x,th butterfly to upgrade the location at the time of iterations. Moreover, there are two major phases: global search phase and local search phase. Initially, a butterfly moves forward in a direction toward fittest butterfly or solution *g‘* that is represented by

Here *g’* implies the recent best solution that is identified in new iteration. The obtained fragrance of ith butterfly is demonstrated by *pf* and r illustrates an arbitrary value from [0,1]. Local search phase is defined as follows:

where xj and *x[* are jth and *kth* butterflies from a solution space. When xj and *x[* come under similar population and r denotes a uniform random value from [0,1] then equation (3.4) is referred to as a local random walk. A switch probability *p* has been applied in BOA to switch between common global search and intensive local search.

# GBT-Based Classification

Breiman developed the bagging mechanism, which refers to the random sampling model for the purpose of training classification models. The classifiers are organized into a single group and provide maximum accuracy. In contrast to bagging with respect to sampling, boosting offers a weight for observation and alters the weight once the classifier training is completed. The weight of inaccurate classification has been improved, and the weight that is correctly classified observation is limited. The observations with changed weights are applied for training the upcoming classifier. Consequently, various classifiers undergo amalgamation uniformly. Friedman presented the GB approach. It is defined as a step-by-step model that concentrates on gradient reduction of loss function in predefined approaches.

The loss function is interpreted as a degree of error by newly developed approach. In general, if the loss function is maximum, then the method is more effective. The main objective is to reduce the loss function and erroneous rate, the optimal method is to reduce the loss function in gradient direction. Equation (3.5) shows the GB method in the following:

The *F(x;P)* implies the *%* function with *p* parameters and prediction function. Boosting is required for stacking several approaches. Then, *(5* represents the node’s weight and *a *is a parameter. It is feasible to enhance the prediction function *F* by optimizing {)*3*, *a}. P* implies the parameter of a method, and

P. Equation (3.6) represents the loss function *F(xP).*

When *m —* 1, a number of methods are retrieved, the development of mth model could be accomplished with initial derivative to find the direction for loss function, where g_{m} is presented in equation (3.7):

Then, it is the deployment of gradient direction for likelihood function *P* for the proposed approach. Here, *p _{m}* showcases the distance of gradients as expressed in equation (3.8):

At last, *f _{m}(x)* function for mth model is retrieved, as shown in equation (3.9):