## 1 Introduction  
Many real-world problems are of NP-complete (nondeterministic polynomial) class. In contrast, systematic approaches (based on explicit rules) require exponential time rather than a polynomial-time to reach a solution. A problem is NP-complete if there is an NP (\(np\)) problem, and all NP problems are reduced to (\(np\)) in polynomial time. Therefore, NP-complete problems are of great interest in computer science because finding an algorithm that could solve any NP-complete problem implies that there is a general-purpose algorithm that could solve all NP-complete problems of the same class. Metaheuristics methods are widely employed to handle NP-complete problems with attributes such as uncertainty and vast search spaces. The metaheuristic approach's main idea is to find a solution with an acceptable quality rather than finding an optimal one. Another characteristic of metaheuristics methods is that they are incomplete such that they do not guarantee to find a solution if one exists. In literature, the metaheuristics methods are classified into global-based approaches (also known as population-based approaches) and local-based approaches. Nature designs generally inspire the global-based metaheuristics to solve optimization problems [1; 2; 3], such as the Ant Colony Optimization [4], which was mainly inspired by ants' actions and behaviors searching for food. Moreover, the Genetic algorithms (GA metaheuristics) [5] are other examples that were primarily derived from the natural selection process that is based on past knowledge that is stored in many chromosomes (mainly derived from [PERSON] theory [6]) and used to make future decisions on the selection process. In recent years, Swarm Intelligence (SI) global-based metaheuristics have shown significant improvements in the overall process of handling optimization problems, mainly when applied for solving real-world industrial optimization problems such as scheduling [7; 8], vehicle routing [9]. The underlying general framework in swarm intelligence depends on a decision-making process involving a broad range of information gathered from multiple dimensions and sub-domains of the search space. For instance, when searching for a solution using a SI technique, two factors are considered to evaluate the current search stage progress: (1) the improvement of the current search stage cost and (2) the impact of the current search stage on the overall improvement of the objective cost function of the search process. The other metaheuristic category proposed almost four decades ago and received a high level of researcher's attention is local search-based metaheuristics (LS). LS techniques share most of the characteristics of the global-based metaheuristics such as incompleteness, and the ability to handle NP-complete optimization problems when covering all possible solution within the search space is not feasible due to a limitation in computational resources. Our focus on this research is local search metaheuristics, specifically the general-purpose weighting dynamic local search techniques for SAT. In 1971, the Boolean satisfiability problem (SAT) (also known as propositional satisfiability problem, or SAT for short) was proven to be an NP-complete as in Reference [10], which motivated researchers around the world to come up with general mechanisms for solving SAT. However, no such mechanisms exist and engineering a general mechanism to tackle the SAT problem still an open area for research and experimentation. Stochastic local search (SLS) techniques efficiently handle problems encoded into SAT. Therefore, researchers over the decades are motivated to enhance the performance of SLS techniques. SAT problems are of great interest to researchers as a wide range of real-world problems are encoded into SAT in areas like artificial intelligence such as planning, scheduling, and other areas such as cryptography or bioinformatics, computer theory, engineering, operation research, physics, to mention a few.