## 1 Introduction
The SOS algorithm is rated among the most competitive swarm intelligence-based metaheuristic algorithms for solving optimization algorithms, based on its simplicity and parameter-less attributes. SOS has been used to find the solution to many different real-world problems [10; 11; 12; 13; 14; 15; 16]. [PERSON] et al. [17] introduced a parameter setting of the beneficial factor, based on the normalized value of organisms, to create an adaptive SOS algorithm for structural optimization problems. A discrete version of SOS was designed and implemented by [18] for task scheduling in a cloud computing environment. [PERSON], [PERSON] and [PERSON] [11] introduced another discrete SOS for multiple resources leveling optimization. [PERSON] and [PERSON] [10] introduced multi-objective SOS for handling multi-objective optimization problems. [PERSON] et al. [12] proposed a cloud-based model SOS using cloud-based theory to generate random number operators in the mutualism phase for power system distributed generators. [PERSON] and [PERSON] [19] proposed three variants of SOS to solve the feature selection challenge, and [PERSON], [PERSON], and [PERSON] [14] proposed an SOS optimized neural network-long short-term memory for obtaining hyperparameters of the neural network and long short-term memory for the establishment of a robust hybridization model for cash flow forecasting. SOS has also been employed in solving automatic clustering problems [20; 21; 22; 23; 24; 25]. [PERSON], [PERSON], and [PERSON] [20] proposed a biomedical document clustering solution usingaccelerated symbiotic organisms search, which required no parameter tuning. [PERSON] and [PERSON] [25] proposed a clustering-based solution for high-dimensional optimization problems using SOS with only one control parameter. [PERSON], [PERSON], and [PERSON] proposed an adaptive clustering-based algorithm using SOS for automatic path planning of heterogeneous UAVs [22]. [PERSON] and [PERSON] [23] proposed a novel solution for software module clustering problems using a modified symbiotic organism search with levy flights. The effectiveness of the SOS algorithm in solving automatic clustering problems was demonstrated by [21], where the SOS algorithm was used in clustering different UCI datasets. SOS has been hybridized with other metaheuristic algorithms for performance enhancement in cluster analysis. [PERSON] and [PERSON] [24] combined the SOS algorithm with four different metaheuristic algorithms to solve the automatic clustering problem and compared the clustering performances of each hybrid algorithm. Our earlier work combined the SOS algorithm with K-means to boost the traditional clustering algorithm's performance for automatic clustering [26]. However, SOS exhibits some limitations, such as slow convergence rate and high computational complexity [17; 26; 27; 28]. Modifications have been made to the standard SOS to improve its performance. [PERSON], [PERSON] and [PERSON] [17] introduced adaptive benefit factors to the classical SOS algorithm, proposing three modified variants of SOS for improved efficiency. Adaptive benefit factors and benefit factors were effectively combined to achieve a good exploration-exploitation balance in the search space. [PERSON], [PERSON], and [PERSON] [27] introduced a random weighted reflective parameter, to enhance searchability within the additional predation phase, to the classical SOS algorithm to improve the solving of multiple complex global optimization problems and improve the algorithm's performance. [PERSON] [29] sought to improve the algorithm's capacity for the timely identification of stable and high-quality solutions by introducing new relations for solution updates at the mutualism and commensalism phases. A logistic map-generated chaotic component for finding promising zones was also added for the enhancement of the algorithm's exploration capacity. The removal of the parasitism phase reduced the computational load.