## 1 Introduction  
The huge importance of solving capacitated vehicle routing problem (CVRP) in companies supporting service and logistics for supplying commodities is a strong motivation for many researchers worldwide to solve the CVRP with innovative algorithms. Capacitated Vehicle Routing Problem in general deals with some customer nodes having some sort of pre-specified demands to be served from a hub with a set of vehicles. Although there are many practical constraints in the real world like stochastic customer demand, resource restrictions and so on. There are many pieces of research that introduce practical variations of CVRP [1; 2; 3; 4; 5]. However, a large portion of practical applications are simple in nature which can be fit to CVRP. The definition of CVRP has been outlined in [6]. A vehicle picks some shipment from the depot to serve some of the customers according to their demands until its capacity permits, makes a trip to serve them, and returns to the depot. The vehicles also have additional restrictions on their maximum travelling distance which is the total of distance travelled by the vehicle and the service time it requires to handle the customers it serves. A set of nodes is given on a graph and a hub location \(h\) is specified among them. Then a vehicle routing problem can be portrayed as Figure 1, where the nodes represent customers, cities or so on. The target of solving a CVRP is to find minimum total cost, specifically minimum travelling distance, incurred by the vehicles for visiting the customer nodes to satisfy their demands. CVRP is closely related to the classical Travelling Salesperson's Problem (TSP) with a difference that vehicle capacity is limited in CVRP, but not in TSP. This makes CVRP a more complex problem than TSP. As TSP is a well-known NP hard problem, where no algorithm is available to solve TSP by polynomial time when the number of nodes increases, CVRP too is obviously an NP hard problem [7]. Even though an exact algorithm is unlikely to exist to solve CVRP, there have been a few attempts from researchers based on branch and bound technique, set partitioning technique and so on, which can handle CVRP with only few nodes [8]. Therefore, many approximate algorithms are proposed to solve CVRP effectively. Although these algorithms never find the optimal, they can find \"good\" or near-optimal solutions within a reasonable computational time. Among heuristics, [PERSON] [PERSON]'s saving algorithm is a very early introduction in the area of CVRP [9]. This technique is basically a constructive heuristic which builds tours gradually by inserting a node at each time with respect to some saving conditions till no more cluster can be constructed. There are many improvements and variations available in the literature from many researchers [10; 11; 12]. \"Cluster-First Route-Second\" [13; 14] and \"Route-First Cluster-Second\" [15] are other two well-known algorithms for handling CVRP. The former one builds some clusters of customers then a TSP tour is obtained with those customers to solve CVRP, and the latter one is the technique to make a TSP tour of all customers then cluster them into routes with respect to the given constraints. Recently many nature-inspired metaheuristics such as Genetic Algorithm (GA) [16; 17], Tabu Search (TS) [18; 19; 20] and Simulated Annealing (SA) [21; 22] have become attractive in the field of optimization. Nevertheless, there are many research articles that report their performances in dealing with CVRP [23; 24; 25; 26; 27]. It is worth mentioning that swarm optimization techniques are getting popular due to their simplicity and performance to handle optimization problems nowadays [28; 29; 30]. Swarm-based metaheuristics are mainly inspired from unique characteristics of some swarms such as birds (bird flocking), fish (fish schooling), ants (foraging), etc.