## 1 Introduction
The findings revealed that the maximum thermohydraulic performance parameter value was attained with a value of 1.77 in the design, incorporating a Reynolds number of 18,000 and a semicircular section absorber plate. Furthermore, the data obtained at the conclusion of the study were modeled with machine learning algorithms [9]. [PERSON] et al. sought to ascertain the impact of the slope of the rib roughness element on the heat transfer properties of the solar air heater. The present study investigates the effects of rib height and inclination on the heat transfer properties for a moderate Reynolds number range. The Nusselt number exhibiting the greatest improvement was identified. The objective is to develop a new heat transfer correlation for rough-rib solar air heaters. The data were reduced to a correlation using the linear regression method. It is emphasized that all Nusselt number data are accurately predicted with the correlation calculated with a relative absolute deviation of \(\pm\)6% [10]. Some SAH designs use jet impingement onto corrugated plates to further enhance heat transfer. Research has shown that using multi-jet impingement on trapezoidal or sinusoidal corrugated plates can optimize the Nusselt number by creating localized high-turbulence zones. Studies using CFD and experimental methods have confirmed these significant improvements, with configurations like \(3\times 3\) jet arrays achieving optimal Nusselt numbers under specific flow and spacing conditions [11]. To optimize SAH designs, researchers use statistical or optimization techniques like the Taguchi method [12], or genetic algorithms (GA) [13], integrating these with experimental correlations to find optimal configurations that maximize the Nusselt number. For example, studies have shown that adjusting parameters like flow rate and corrugation geometry through optimization can achieve an optimal thermal performance under the given environmental conditions. Additionally, combined methods like GA with Taguchi or Grey-Taguchi [14] analyses have provided practical approaches to maximize efficiency and reduce experimental needs. Optimization is a technique for searching (near) optimal solutions in a solution space. The solution space generally includes an infinite number of solutions for numerical optimization problems where the dimensions are subject to the continuity of real values. Thus, finding the best solution becomes a problem of NP (non-polynomial time) hard complexity. Numerical function optimization is the major category of the optimization field, which has applications in many areas of science and engineering to solve complex problems [15; 16; 17]. For many real life problems, finding the near optimum solution is as important as finding the optimum solution, which is hard to obtain. Algorithms that are used to find the near optimum solution in a randomized behavior are called metaheuristic algorithms, which are non-deterministic and naturally involve randomization in their searching stages. A large body of metaheuristic algorithms is modeled by imitating simple concepts in nature, such as human behavior [18], biological processes [19], and so on. Metaheuristic algorithms can be roughly separated into four categories: algorithms inspired by humans [20; 21], swarm intelligence [22; 23; 24], physics-based algorithms [25; 26], and evolutionary algorithms [27; 28]. Recently, swarm-based optimizations have been on the rise in the literature. A possible reason is that there are many swarms not yet introduced to the literature and researchers are motivated to study those swarms. Among the swarm-based algorithms, the differential search algorithm (DSA) [29], inspired by the migration and foraging behavior of birds; the artificial bee colony algorithm (ABC) [30], stimulated by the behavior of bees collecting nectar from sources; and the gray wolf optimizer (GWO) [31], inspired by the hunting behaviors of alpha and other wolves can be given as examples.