1. Introduction
Bio-inspired computing refers to a class of optimization algorithms which apply the intelligence of the nature and one of their main applications is the solving of the complex engineering optimization problems [1]. A novel algorithm inspired from the hierarchical organization of the horse herds obtained a Horse Optimization Algorithm (HOA). The modified version of HOA, namely Discrete Binary Horse Optimization Algorithm (DBHOA) [2], was applied in features selection for high dimensional datasets with a case study on smart grid stability classification. The primary objective of this research article is to introduce an algorithm which approaches both the exploration and the exploitation of the search space, is simple to implement.
Some bio-inspired algorithms are better in the exploration of the search space while others are better in the exploitation of the search space. The optimal and one in which the mechanism applied in the changing of the positions of the objects is modified considering the value of the parameter seeking range of the selected dimension [3]. The optimal combination of features maximizing the performance of the classification while minimizing the number of the selected features. However, that approach considers the K-Nearest Neighbor (K-NN) classifier in the definition of the fitness function while in this article the Random Forest (RF) classifier is considered because even if K-NN works very well with multi class datasets, the dataset considered in this article has only two classes and RF is extremely flexible, characterized by high accuracy and deals very well with over fitting. Moreover, The HOA presents the adaptation of the newly introduced algorithm in features selection for high dimensional datasets.
2. General Biology of Horses
In this section the diagrammatic representation below mentioning the main characteristics of the horses which are considered in the development of Horse optimization Algorithm (HOA)
3. Inspiration of HOA
The main inspiration of Horse Optimization Algorithm is the hierarchical organization of the horse herds. Horses have evolved to live in herds. As with many animals that live in large groups, establishment of a stable hierarchical system or “pecking order” is important to reduce aggression and increase group cohesion [4]. This is often, but not always, a linear system. In non-linear hierarchies horse A may be dominant over horse B, who is dominant over horse C, yet horse C may be dominant over horse A. Dominance can depend on a variety of factors, including an individual’s need for a particular resource at a given time. It can therefore be variable throughout the lifetime of the herd or individual animal. Some horses may be dominant over all resources and others may be submissive for all resources. It is important to note, that this is not part of natural horse behavior. It is forced by humans forcing horses to live together in limited space with limited resources [5]. So called “dominant horses” are often horses with dysfunctional social abilities horses. When horses are in a herd, their behavior is hierarchical; the higher-ranked animals in the herd eat and drink first. Low-status animals, that eat last, may not get enough food, and if there is little available feed, higher-ranking horses may keep lower-ranking ones from eating at all [6].
5. Numerical Expression of HOA
A horse herd has a dominant stallion or mare and the hierarchical order of the horses in a herd specifies the priority access to resources [7]. The hierarchy of the horses in a herd is computed in the initial phase of the algorithm considering the fitness values of the horses from that herd. Let as assume herd of k horses and P is a function
6. Advantages of HOA
The advantages of HOA must be adapted to discrete optimization problems prior to its application in features selection for high dimensional data [10].
7. Flowchart of HOA
The below figure represent the flowchart of HOA;
8. Pseudo Code of HOA
The pseudo-code of HOA is presented in figure representation as below;
9. Application of HOA
The application of HOA in a representative engineering problem, namely the classification of the smart grid stability [11]. Even though the analysis of the stability of the smart grids was approached in literature before from different perspectives such as the proposal of a novel delay-adaptive control strategy which enhances the transient stability of the system and the development of a quantitative framework applied in the assessment of the voltage stability in the case of smart power networks, there are relatively few studies which consider the classification of the smart grid stability [12]. However, the prediction of the smart grid stability was approached in where the authors propose a new real-time model order reduction technique for predicting the stability of the smart grid [13]. That method is capable of predicting the limit of the stability, the transient stability and unstable machines [14]. That method was tested on three test systems and the results show that it is practical for large scale power systems [15]. A drawback of that method is that it should be adapted in power networks that are characterized by high penetration of Renewable Energy Sources (RES) and therefore there are still major issues which require further investigation [16].
10. HOA Based Methodology for Smart Grid Stability Classification
The machine learning methodology applied in the classification of the stability of the smart grid is represented in the figure below [17]. The methodology consists of three main steps such as the extraction of the features using the Feature Extraction on basis of Scalable Hypothesis tests (FRESH) algorithm [18], the selection of the features using the discrete binary version of HOA, namely Discrete Binary Horse Optimization Algorithm (DBHOA) [19] and the classification of the stability of the smart grid using an approach based on Random Forest (RF) [20].
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