# iRoute--An Adaptive Route Planning Solution for Commercial Vehicle Fleets
## 2 Background  
Designing and developing software for the vehicle routing problem are very difficult tasks. Even though several types of VRPs solve real-world routing problems, our application is not limited to a single software solution. It finds solutions to problems such as capacity vehicle routing problems (CVRPs), vehicle routing problems with time windows (VRPTWs), and pickup and delivery problems with time windows (PDPTWs). The CVRP is the most common version of the VRP that takes into account vehicle capacity constraints. Each vehicle is identical and has a limited capacity to transport goods that must be delivered to different locations, starting from a central warehouse. The capable vehicle routing problem (CVRP) is a business adaptation of the vehicle routing problem having relevance in the goods distribution process [10]. The CVRP finds a set of routes having the minimum total cost for vehicles with a limited capacity serving a set of customers [11]. The CVRP offers an optimal solution when we have a closed route circle, unique customer service by a single vehicle, and the allocated vehicle capacity must not be exceeded [12]. For a routing problem, the CVRP can optimally serve up to 360 clients through heuristic methods [13]. [PERSON] et al. designed a hybrid optimization algorithm for the CVRP that searches in two stages on variable domains, which is superior to evolutionary quantum algorithms due to the simplicity and efficiency of the algorithm [14]. The CVRP is an NP-hard problem, and there are no efficient algorithms for solving large-sized problems with an acceptable computation time for a quality solution. Most research has focused on designing heuristic and meta-heuristic algorithms to obtain an optimal solution for the CVRP problem, such as adapted ant colony optimization (ACO) algorithms [15], customized genetic algorithms (GAs) [16], ant system (AS) [17], tailored particle swarm optimization (PSO) [18], adapted artificial bee colony (ABC) [19] or firefly algorithms (FAs) [20], and Tabu Search (TS) [21]. The vehicle routing problem with time windows (VRPTW) is obtained by using time constraints for visiting each node to the classic VRP problem. In the VRPTW problem, vehicles have pre-determined capacities and pre-defined delivery windows and are not allowed to visit a location outside a time window. The standard VRPTW is defined as a complete graph where customers are nodes, but for real-world solutions VRPTW must connect non-straight paths. VRPsolver is a tool that is based on Branch-Cut-and-Price to solve VRPTWs tested under real urban conditions [22]. All the obtained subproblems are defined as graphs with associated resources based on edges or vertices, and the main formula contains the objective function and the mapping function. An adaptive memetic algorithm for determining the optimal solution of the VRPTW problem was described by [PERSON] and [PERSON] [23]. The algorithm allows for changing different parameters in an adaptable way, such as the population size, the family size (parents and children), and the selection scheme. The main disadvantage is that adjusting the parameters requires a high computational cost to validate them. [PERSON] proposed a mathematical model for VRPTWs by adaptively changing the crossover probabilities based on a genetic algorithm. The results proved that the convergence speed can be improved by using the new algorithm [24]. [PERSON] et al. proposed a hybrid version of the genetic standard algorithm using constructive heuristic methods to find efficient solutions for VRPTWs minimizing the total distance and waiting time [25]. Another algorithm for solving the VRPTW solution is the one proposed by [PERSON] et al., which uses the elite ant system [26]. The initialization strategy defines a set of clients for the first delivery to increase the convergence speed of the algorithm, and the mutation strategy improves the local search capability. [PERSON] et al. proposed a new VRPTW variant, a solution used for the route of delivery vehicles for parcel lockers [27].