## 2 Literature Review  
It has been proved that VRP is one of the nondeterministic polynomial hard (NP-hard) problems by [PERSON] and [PERSON] [5]. Therefore, the early VRP models assumed that only one vehicle is assigned for each route, starting from a single depot and returning to the same depot. [PERSON] et al. [6] and [PERSON] et al. [7] classified various VRP models according to the nature of the problems. VRP models can be classified into the capacitated VRP (CVRP), VRP with time windows (VRPTW), the multi-depot VRP (MDVRP), and the VRP with delivery and pick-up (VRPDP). This study focused on VRPTW and VRP with simultaneous delivery and pick-up, as described in Section 1. In contrast to other groups of VRP, in VRPTW it is assumed that the vehicles have to visit customers within the predefined time schedule (time windows). The objective of VRPTW is to find a set of routes for the vehicle without violating the capacity and time constraints of the vehicle [8]. VRPTW models can be characterized based on how relaxed the time window constraints are [9]. If it is allowed to violate the time windows constraints by paying the penalty, this model has soft time windows. Otherwise, the model has hard time window constraints. Several previous studies have presented derived models considering different conditions. [PERSON] et al. [10] studied the vehicle routing problem with backhaul (VRPB) service after servicing linehaul customers. They applied the Restricted Intersection Neighborhood Search (R-INS) heuristic algorithm to collect the vehicle's capacity-based linehaul customer service in the middle of the service. [PERSON] et al. [11] presented a step-by-step approach heuristic method to address the periodic vehicle routing problem involving reusable waste in Colombia. In this method the first step is to separate each area into zones, the second step is to set the type of waste to collect and the area to visit, and the last step is to determine the route. [PERSON] et al. [12] studied VRPTW under the time constraints for actual garbage collection, taking into account the compactness and workload balancing They presented a solution using first clustering and an extended insertion algorithm. [PERSON] et al. [13] studied the problem of optimizing the route of the waste collection vehicle considering the rest and lunch time of the vehicle drivers and proposed an Adaptive Large Neighborhood Search (ALNS) algorithm using clustering and actual data from the waste collection company. [PERSON] et al. [14] presented a hybrid method of a metaheuristic using large neighborhood search (LNS) and iterated local search (ILS) for VRP with time windows and multi delivery service providers (VRPTWMD). It showed better performance than the branch-price-and-cut method. [PERSON] et al. [15] studied a delivery and pick-up inventory-routing problem within time windows (PDIRTW) in situations where each partner shares returnable transport items (RTIs) in an integrated supply chain network due to environmental impact and corporate regulation. They developed a cluster first-route second metaheuristic and then it produced a good solution for realistic instance. [PERSON] et al. [16] conducted a study on the open VRP with soft time window and pattern rate (OVRPSTWSR) that increase customer satisfaction in OVRP situations. They proposed the Improved Tabu Search algorithm (ITSA), which showed the better result than traditional heuristics. [PERSON] et al. [17] has developed a cross-exchange method for Tabu Search among metaheuristics to improve the performance of VRP with soft time windows (VRPTW). [PERSON] et al. [18] studied the vehicle routing problem of Tele Atlas, a company that makes digital maps. This paper aimed to minimize the number of days required to travel, and soft time windows were considered to avoid taking pictures in the solar direction. The first step was to minimize the visit time of VRPTW, and the second step was to utilize the hybrid metaheuristic method, which minimizes time violation. [PERSON] et al.