## 2 Literature Review
The specific PRNG used in this new hybrid algorithm is not specified. There are also a large number of hybrid algorithms in the literature that combine a nature-inspired algorithm with a deterministic method, as in [60; 61; 62; 63]. As mentioned earlier, we restrict ourselves here to reviewing the literature that contains hybrid solutions that combine two nature-inspired metaheuristic algorithms. To summarize the hybrid nature-inspired metaheuristics found in the literature, we note that all hybrid solutions adhere to predefined rules within the optimization process. In particular, the third version of the hybrid algorithm described in [14] introduces an adaptive switch between algorithms during optimization. This switch allows to select the algorithm that gives the best results for the given optimization problem, thus improving the overall optimization process. In this work, we follow a similar approach by evaluating the number of improved solutions in the current iteration compared to the previous one. In addition, our approach includes an evaluation of the overall quality of the current population compared to the previous population and whether the current population successfully found the best global solution. It is important to note that the adaptive switch in our approach is not activated immediately; instead, the currently selected algorithm in the hybrid model is assigned a certain number of iterations to explore and possibly discover better solutions. In none of the hybrid nature-inspired algorithms described so far do the authors mention the specific pseudorandom number generators (PRNGs) used during the randomization phase of the optimization process. Therefore, it can be assumed that standard PRNGs already implemented in the programming languages, such as rand() [64] or random() [64], were used. However, it is important to note that the choice of PRNG can significantly affect the quality of the optimization results of a metaheuristic algorithm, as confirmed in the study [20]. The above study provides a detailed analysis of the optimization results of five metaheuristic nature-inspired algorithms (Salp Swarm algorithm [65], Regenerate Genetic Algorithm [66], Particle swarm optimization [67], Artificial Bee Colony [39], and Backtracking Search Optimization [68]) for specific test sets. In particular, the study focused on the use of different PRNGs to define the initial population in each algorithm. The performance of the algorithms was evaluated by testing them on two different numerical benchmark sets and by applying them to nine real-world problems. The results of the study show that the use of different PRNGs indeed affects the results of the optimization process of each of the five selected algorithms. Thus, the quality of the PRNGs themselves is very important for the randomization phase. This was also proven in [19], where an extensive analysis of 29 existing PRNGs was performed to determine the quality of each PRNG. These include PRNGs from all three classifications into which PRNGs are divided: linear congruential generator, linear feedback shift register, and cellular automation. Empirical tests for PRNGs attempt to demonstrate the non-randomness of the particular PRNG. Both types of empirical tests used to test PRNGs are included in this analysis: blind tests and graphical tests. Of the blind or statistical tests, the well-known tests Diehard [69], TestU01 [70], and NIST [71] were used in this analysis. Of the graphical tests, the Lattice test and the space-time diagram [72] were selected. The 64-bit and 32-bit versions of the SFMT pseudorandom number generator (hereafter referred to as SFMT-64 and SFMT-32) were found to be the best PRNGs. These PRNGs are used in our hybrid algorithm for all stages of randomization within the optimization process. In addition, the standard PRNGs commonly used when writing program code in a particular programming language, rand() and random(), ranked 23 rd and 24 th, respectively, out of 29 PRNGs tested.