## 1 Introduction  
Variable Neighborhood Search (VNS) is a metaheuristic approach proposed by [PERSON] and [PERSON] to solve combinatorial and global optimization problems [1; 2]. This framework is primarily designed to systematically modify the neighborhood structure, to reach an optimal (or near-optimal) solution [3]. VNS and its extensions have demonstrated their effectiveness in solving many problems in the combinatorial and global optimization field [4; 5]. Each VNS heuristic consists of three parts. The first is a process of shaking (phase of diversification) used to escape from local optimal solutions. The next one is changing the neighborhood, where the next neighborhood structure to be searched will be determined; an approval or rejection criterion will also be applied to the last solution found during this part. The third part is the phase of improvement (intensification) achieved by exploring neighborhood structures by applying various local search moves. This exploration is carried out primarily through one of the following steps to change the neighborhood:  
* Cyclic neighborhood change step: Whether there is an improvement in some neighborhood or not, the search continues in the next neighborhood structure in the list. * Pipe neighborhood change step: If the current solution is improved in some neighborhood, exploration in that neighborhood will continue. * Skewed neighborhood change step: Accept as new incumbent alternatives that not only improve solutions, but also some that are worse than the current incumbent solution. Such a neighborhood change step is intended to allow valley exploration away from the incumbent solution. A trial solution is evaluated taking into consideration not only the trial's objective values and the incumbent solution, but also their distance. **Variable neighborhood search variants. ** Many VNS variants have already been developed and used to solve hard optimization problems [6; 7]. The most commonly used variants are the Basic VNS (BVNS), the Variable Neighborhood Descent (VND), and the General VNS (GVNS) and the Reduced VNS (RVNS). In the BVNS a method of diversification is alternated with a local search operator. VND consists of an improvement procedure in which neighborhood structures are systematically explored and a neighborhood change step. According to their neighborhood change step, there are different variants of VND. The pipe-VND, which uses the pipe neighborhood change step, appears to be the most efficient way to solve computational problems [6]. General Variable Neighborhood Search (GVNS) is a VNS variant that uses a VND method to improve. In many applications, GVNS has been successfully tested, as several recent works have shown [8; 9]. The efficiency of metaheuristics depends on the efficiency of their components. Performance studies are a prerequisite for evaluating different metaheuristics [10] or different components of a metaheuristic algorithm [11]. In this direction and based on the VNS, [PERSON] and [PERSON] (2017) [12] examined the impact of different order of local search operators in the improvement component of a VNS algorithm. There are similar studies for the impact of the initial solution [13] or the use of different neighborhood change strategies [2] to the overall performance of a VNS algorithm. However, there is a lack of contributions on studying the impact of the shaking components to the overall performance of a VNS algorithm. [PERSON] et al. (2019) [14] attempted an initial study on the impact of diversification methods on the performance of GVNS by focusing on asymmetric TSP instances. This work is a substantial extension of our recent conference paper [14] in which we investigated the impact of three shaking methods on a GVNS metaheuristic, applied on asymmetric Traveling Salesman Problem (TSP) instances from the TSPLib.