## 4 VRPs in Dynamic Environments  
In real life, there are plenty of unpredictable factors. In these cases, making decisions is not trivial, since every choice needs to be based on partially unknown aspects. A typical unpredictable factor that concerns the VRP is the travel time. As a matter of fact, even though it is usual to consider static traveling times, they may actually be affected by several factors, such as traffic jams, accidents, road work, or weather conditions. Other aspects that are hard to predict may be customers' demands or the cost of a delivery delay in the case of VRPs with time windows. As previously discussed, solving VRPs under such dynamic factors may be difficult. Even predicting the actual quality of a given solution is not easy. Fortunately, machine learning (ML) methods can help us to develop predictive models [46]. In addition, with the support of new hardware solutions [47], once trained, most machine learning models can be executed on multiple small processors, providing a response in milliseconds. This allows for their integration with heuristics, thus bringing up the concept of learnheuristics [48]. Learnheuristics refer to the combination of metaheuristics with machine learning methods. This approach is proposed to solve combinatorial optimization problems in dynamic scenarios. Dynamic scenarios are defined by elements in the objective function or constraints. These elements might change while the solution is being constructed (they cannot be fixed in advance). For example, customers' demands might change depending on the vehicle arrival time or a pre-specified time window; thus, the demand could depend on the constructed solution, which would involve the vehicle type, number of customers that have visited, vehicle travel time, etc. Another dynamic element might be the travel time, which is affected by traffic jams; thus, it is affected by the definition of the route in a solution, especially for routes in big cities. Accordingly, the solution approach should facilitate updates of the input models used by the metaheuristic algorithm at each iteration; this solution approach can coordinate learning mechanisms that update the input models and metaheuristics (Figure 4).  
A learnheuristic-based approach was proposed by [PERSON] et al. [49] to solve the VRP in dynamic scenarios. In their problem, they considered a dynamic travel time that depended on the routing plan. Thus, the travel times changed and were updated while the solution was being constructed. In another work, [PERSON] et al. [50] studied a multi-depot VRP with heterogeneous depots in terms of their commercial offers. Customers' demands and willingness to consume depended on whether the depot assignment fit their preferences or not. Accordingly, the solution approach should consider market-segmentation strategies and distribution costs; considering market-segmentation strategies increases sales and, hence, the total income. In the proposed learnheuristic algorithm, the customer demand was estimated based on the assigned depot. The objective function was enriched by the estimated customer expenditures. This enrichment guided a local search in the utilized metaheuristics. Similarly, [PERSON] et al. [51] proposed a learnheuristic approach to solving an aerial drone surveillance problem. In the aerial drone surveillance problem, the aerial drones collected rewards by gathering information and observing a set of targets during a specified time. This collected reward was to be maximized by the objective function. The travel time between the targets was dynamic and was influenced by several factors. For example, the angle of ascent and air resistance affected the drone's acceleration, and sharp turns decreased the drone's speed. Hence, the prediction of travel times was outsourced to a machine learning algorithm.