applied sciences  
Solving Vehicle Routing Problems under Uncertainty and in Dynamic Scenarios: From Simheuristics to Agile Optimization [PERSON]\({}^{\text{\text{\textregistered}}}\)\({}^{\text{\textregistered}}\), [PERSON]\({}^{\text{\textregistered}}\)\({}^{\text{\textregistered}}\), [PERSON]\({}^{\text{\textregistered}}\)\({}^{\text{\textregistered}}\), [PERSON]\({}^{\text{\textregistered}}\)\({}^{\text{\textregistered}}\) and [PERSON]\({}^{\text{\textregistered}}\)\({}^{\text{\textregistered}}\)  
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Using the Scopus scientific database, we searched for articles containing the terms \"(vehicle routing problem) AND (uncertainty OR stochastic)\" in the title, abstract, or keywords. A total of 1025 document results were obtained. Similarly, we searched for articles with the terms \"(vehicle routing problem) AND dynamic\", obtaining a total of 1195 documents. Figure 1 shows the time evolution of both the VRP in uncertainty/stochastic scenarios and the VRP in dynamic scenarios. One should notice that despite some seminal works appearing during the 1980s, it was not until the mid-2000s that the interest in both versions of the VRP started to rise in a noticeable way. We can also observe that both versions are currently receiving a similar amount of interest from the scientific community.  
Figure 2 displays the main journals that published articles on the VRP under uncertainty/stochastic or dynamic scenarios. Notice that the journals with a larger number of publications on these two topics were the European Journal of Operational Research, Transportation Science, Computers, and Operations Research, Computers and Industrial Engineering, Transportation Research Part E, Operations Research, Experts Systems with Applications, Networks, Annals of Operations Research, and Transportation Research Part B. In addition, some other journals published articles covering either VRPs under uncertainty or VRPs under dynamic conditions. The researchers in these articles explored and investigated different approaches ranging from exact algorithms to advanced techniques to handle uncertainty and dynamic scenarios. For example, [PERSON] et al. [11] developed an algorithm based on a modified adaptive variable neighborhood search heuristic to tackle the demand and travel time uncertainty, and [PERSON] et al. [12] utilized the branch-cut-and-price algorithm to solve the capacitated VRP. In addition, approaches to solving newly defined variants of the VRP were introduced, such as [PERSON] et al. [13], who studied the heterogeneous fleet green VRP with time windows, and [PERSON] [14], who considered nonlinear charging time in the electric vehicle routing problem. This paper reviews some of these works and the solution approaches for handling uncertainty or dynamic scenarios in VRPs.  
Figure 1: Evolution of Scopus-indexed papers on VRPs with uncertainty or dynamic conditions.  
The remainder of this paper is structured as follows: Section 2 offers a short overview of trending topics on VRPs, which include rich and real-life versions of the problem that consider the sustainability and social dimensions. Section 3 provides a review on the use of simulation-optimization approaches--and simheurities in particular--to solve VRPs in uncertain scenarios. Similarly, Section 4 analyzes VRPs in dynamic scenarios and several approaches that can be used to deal with these. Among these approaches, the combination of machine learning methods with heuristics is considered. Section 5 performs a similar study, this time focusing on VRPs with synchronization issues and time-dependent events. Section 6 introduces the concept of agile optimization in the context of VRPs that need to be solved in real time, mainly in the context of self-driving vehicles in smart cities, where new data are continuously provided by Internet of Things (IoT) devices. Finally, Section 7 highlights the main conclusions of this work.