## 2 Related Work
### SOS Algorithm  
[PERSON] and [PERSON] [8] proposed the concept of SOS simulating the interactive relationships between organisms in an ecosystem. In an ecosystem, most organisms do not live in isolation because they need to interact with other organisms for their survival. These relationships between organisms, known as symbiotic relationships, are, thus, defined using three possible major interactions: mutualism, commensalism, and parasitism. Mutualism represents a symbiotic relationship where the participating organisms benefit from each other. For instance, an expocker feeds on the parasites living on the body of a zebra or rhinoceros, while the symbiont, in turn, enjoys the benefit of pest control. Commensalism describes a relationship where only one of the participating organisms benefits from the association while the other organism does not benefit from the relationship, although it is not negatively affected either. An example of this is orchids, which grow on branches and trunks of trees to access sunlight and obtain nutrients from the branches. As a slim, tender plant, their existence does not harm the tree on which they grow. The relationship between humans and mosquitos provides a perfect scenario of the parasitism symbiotic relationship, in which one of the organisms (mosquito) benefits from the association while simultaneously causing harm to the symbiont (human). These three relationships are captured in the SOS algorithm [8]. In most cases, the type of relationship increases the fitness of benefiting organisms, giving them a long-term survival advantage. In the SOS algorithm, the three-symbiosis relationship is simulated as the three phases of the algorithm. At the initial stage, a population of candidate solutions are randomly generated to the search space for solution representations for optimal global solution search. This set of solutions forms the initial ecosystem. where each individual candidate solution represents an organism in the ecosystem. A fitness value is associated with each organism to determine the measure of its adaptation capability with respect to the desired objective. Subsequently, each candidate solution is further updated using the three simulated symbiotic relationship phases to generate a new solution. For each phase, a new solution is only accepted if its fitness value is better than the previous one. Otherwise, the initial solution is retained. This iterative optimization process is performed until the termination criteria are met. The three simulated symbiotic relationship phases of the SOS algorithm are described below. Given two organisms \(x_{i}\) and \(x_{j}\) co-existing in an ecosystem such that \(i\) and \(j\) represent the iterative values of the optimization, ranging from 1 to \(d\), where \(d\) is the problem dimension and \(i\
eq j\), an organism, \(x_{j}\), is randomly selected during the mutualism phase to participate in a mutual relationship with \(x_{i}\) such that the two organisms enjoy a common benefit from their interaction for survival. Their interaction yields new solutions \(x_{inew}\) and \(x_{jnew}\) based on Equations (7) and (8), respectively, with Equation (9) representing the mutual benefit \(x_{mutual}\) enjoyed by both organisms. \[x_{inew}=x_{i}+rand(0,1)\times(x_{best}-x_{mutual}\times BF_{1}) \tag{7}\]  
\[x_{jnew}=x_{j}+rand(0,1)\times(x_{best}-x_{mutual}\times BF_{2}) \tag{8}\]  
\[x_{mutual}=\frac{x_{i}+x_{j}}{2} \tag{9}\]  
The expression (\(x_{best}-x_{mutual}\times BF_{1}\)) as shown in Equations (7) and (8), represents the mutual survival efforts exhibited by each organism to remain in the ecosystem. The highest degree of adaptation achieved in the ecosystem is represented by the \(x_{best}\) which acts as the target point for increasing the fitness of the two interacting organisms. Each organism's benefit level of value 1 or 2 is randomly determined to indicate the organism's benefit from the relationship, which can either be full or partial. This benefit level is denoted as \(BF\) (benefit factor) in the equations.