## 1 Introduction  
Distribution systems involving autonomous vehicles, such as automated guided vehicles (AGV), are an interesting research topic that continuously grows in the operational research area. Routing and scheduling have been dominating issues to explore. Particularly, in applications involving multiple vehicles, vehicle routing problem (VRP) and its variants are well-known approach to solve client services. Such problems are usually generalized by the traveling salesman problem (TSP) [1; 2; 3; 4; 5]. Many approaches to solve complexity in TSP are explored, such as min-k-SCCP [6; 7; 8; 9]. In general, many scholars are focused on the minimization of cost, especially with regard to the required processing time [1; 10; 11; 12; 13; 14; 15]. However, in the modern distribution systems, other issues, such as collision, appear [11; 14]. Particularly, for instance, in warehouses, cross-sections always exist in their layout. This condition leads to an unsafe situation caused by the high possibility of collision. Numerous researches have been reported, such as conflict-free routing for material handling vehicles [10; 11; 12; 13; 14] and distribution system [15; 16; 17; 18]. Thus, this issue emerges in studies on avoiding collision scheduling. Mostly, artificial intelligence (AI)-based methods were proposed to solve the problem [1; 14; 15; 16; 17; 18]. Based on our investigation, less of the publications address a problem of asymmetric TSP (ATSP). In this problem, an individual (vehicle, human, etc.) is required to travel from node-to-node on a not-fully connected graph, where each node can be visited only once by minimizing a given cost function. This type of problem was initially analyzed by a simple problem such as TSP, which has been explored for decades [15; 16; 18; 19; 20; 21; 22; 23; 24]. At the first appearance, this problem was overcome by simple computational techniques, such as the ascent method [19] or taboo parallel search method [20]. However, as more variations of TSP appeared, the use of these computational techniques is inadequate, especially because of great computational efforts. A particular complex variant of TSP is Multiple TSP (MTSP), which is proven as NP-hard [25; 26; 10; 27]. In the MTSP, each node is allowed to be visited only once. Furthermore, the order of the routes of each agent is free of constraint. Consequently, this scenario leads to split routes, i.e., there is no intercepted route among agents. Several methods were proposed, i.e., Ant Colony Optimization (ACO) [17; 27; 28], Bee Colony Optimization (BCO) [18], neural network [21], branch-and-bound algorithm [13], and so forth. We introduce a variant of MTSP called Collision-Free Multiple Traveling Salesman Problem (CFMMSP). Unlike the typical MTSP, this problem considers a particular case where more than one vehicle can visit the same node to establish some activities. Similar to single TSP, each vehicle has to visit all nodes only once. However, unlike the typical MTSP, each node is allowed to be visited by each vehicle only once, and for a time interval, only a vehicle can occupy the node. In CFMMSP, we consider the mission that all the vehicles must accomplish their own TSP. Our objective is to minimize the completion time of the slowest vehicle. A side-effect problem arises, i.e., collision avoidance at each visited node, especially which has more than one edge. Collision issues have appeared in numerous works [29; 30; 31; 32; 33; 34; 35; 36]. The typical definition of collision considers only vehicle-to-vehicle distance [10; 11; 12; 13; 14; 29]. Here, each vehicle has a \"safety area\" around its body that cannot be occupied by other vehicles. However, under particular motion directions, the safety area cannot guarantee the safety, since the vehicle moves faster than the minimum allowable speed toward another vehicle.