# Efficient Feature Selection Using Weighted Superposition Attraction Optimization Algorithm
## 2 Methodology
### Metaheuristics
#### 2.3.5. Symbiotic Organism's Search  
The SOS is used to simulate the interaction of living things in an ecosystem. Organisms do not live in isolation but depend on each other for survival and sustenance [46]. This reliance on each other for survival is called symbiosis. There are three major dependenciesin nature, i.e., mutualism, commensalism and parasitism [47]. The SOS algorithm starts with a population in which a group of individuals is generated by random chance in the search area. Each organism is associated with a fitness value reflecting a degree of adaptation to the optimization objective [48]. In mutualism, two different species depend on each other such that both are benefited, for example, an oxpecker and a cow; the oxpecker benefits from feeding on ticks on the cow, while the cow benefits from the removal of the parasites [47]. In SOS, \(X_{i}\) is the \(i\)th member in the ecosystem, while \(X_{j}\) is a randomly selected member in the ecosystem that interacts with \(X_{i}\). The mutual interaction aims to increase the survival ability of both the organisms. The equations to simulate the interactions are stated as below:  
\[X_{i\ new} =X_{i}+rand(0,1)\times(X_{best}-MV\times BF_{1}) \tag{9}\] \[X_{j\ new} =X_{j}+rand(0,1)\times(X_{best}-MV\times BF_{2}) \tag{10}\]  
where \(MV=\left(X_{i}+X_{j}\right)/2\), \(rand(0,1)\) is a vector of random numbers, \(MV\) is a mutual vector, and \(BF_{1}\) and \(BF_{2}\) are the benefit factors. These factors state the benefit achieved by each organism, i.e., whether an organism partially or fully benefits from the interaction.  
In commensalism, one organism benefits while the other is neutral or unaffected. In SOS, \(X_{j}\) is randomly selected to interact with \(X_{i}\). In this case, \(X_{i}\) tries to benefit from \(X_{j}\), but \(X_{j}\) does not benefit from \(X_{i}\). The interaction is modeled as shown in the equation below; the organism xi's optimal solution is only updated if its new fitness is better than the pre-interaction fitness.  
\[X_{i\ new}=X_{i}+rand(-1,\ 1)\times\left(X_{best}-X_{j}\right) \tag{11}\]  
The \(\left(X_{best}-X_{j}\right)\)part of the equation reflects the beneficial advantage, where \(X_{j}\) helps \(X_{i}\) to increase its survival ability to a higher degree.  
In parasitism, one of the individuals benefits while the other is harmed. Such a parasitic relationship is noticed in worms inside the gastrointestinal tract of human beings or any other animal; the host is severely affected while the parasite benefits. In the parasitism phase, there is a fight for existence between the parasite and the host. If the host can develop immunity against the parasite, the parasite will not be able to live in the ecosystem; if the parasite has a better fitness value, it will kill the host [47]. Assuming \(X_{i}\) is the parasite vector while \(X_{j}\) is the host vector and both are randomly selected, both would try to outdo each other so that the resilient vector survives in the ecosystem. The procedure for the SOS algorithm is highlighted in Algorithm 6.  
```
Objective function \(f(x),\ x=\left(x_{1},\ x_{2},\ldots,x_{d}\right)\) Initialize population FOR \(t=1:\ max\ generation\) Mutual interaction phase Commensalism interaction phase Parasitic interaction phase current best solution END
```  
**Algorithm 6**Symbiotic organisms search