## 4 Agile Optimization Algorithms  
Different optimization algorithms could be used to optimize problems, such as exact algorithms that find the optimal solution to a problem. However, these algorithms are limited to small-size problems. For larger instances of problems and NP-hard problems, different heuristics are recommended. These heuristics construct solutions in an iterative and greedy procedure. A candidate for a solution is selected from a list of candidates at each iteration. The list of candidates is sorted according to pre-defined criteria, such as costs or traveled distance. In the end, a solution is constructed that is typically promising. Examples of these heuristics can be found in different variants of the vehicle routing problem [87] and the traveling salesman problem [88]. Local searches and perturbation movements could be adapted to improve the solutions constructed by the heuristics. These heuristics are deterministic. Thus, the same solution is constructed at each execution. Different solutions could be found by selecting candidates according to a non-uniform distribution. This approach introduces a biased randomized behavior [89]. In this approach, more promising candidates obtain a higher probability of being selected while constructing a solution. These promising candidates are found at the top of the sorted candidate list. \begin{table}
\begin{tabular}{l l l} \hline \hline
**Challenge** & **Methodology** & **References** \\ \hline Clustering vehicles/base stations & Unsupervised learning & [PERSON] et al. [83] \\ \hline Time series forecasting & Recurrent neural networks & [PERSON] et al. [84] \\ \hline Optimal control problems & Reinforcement learning & [PERSON] et al. [74] \\ \hline Latency-critical vehicular networking & Distributed machine learning & [PERSON] et al. [11] \\ \hline IoV optimization problems & Game theory & [PERSON] et al. [82] \\ \hline IoV optimization problems & Integer programming & [PERSON] et al. [85], [PERSON] et al. [86] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main challenges and methodologies employed. Assigning non-uniform probabilities to the lists of candidates plays a role in keeping the heuristic logic [90]. A theoretical probability distribution could be used to assign the non-uniform distribution of solution candidates. These theoretical distributions help to minimize the computation time required compared to defining an empirical distribution. Examples of these distributions are the geometric distribution and the decreasing triangular distribution. These distributions have few parameters and are easy to implement using analytical expressions. The geometric distribution has a single parameter \(p\). Figures 2 and 3 show the probability distribution of a geometric distribution with different \(p\) values. It can be noticed that the most promising candidate obtains the highest selection probability that equals the value of the parameter \(p\). The other candidates obtain a lower probability depending on \(p\). For example, The fourth candidate in the list has a selection probability of 0.1 compared to the probability of around 0.07 under the parameters values 0.2 and 0.5, respectively. On the one hand, the probability distribution of small parameter values (\(p\to 0\)) approaches a uniform distribution, and many elements in the list are assigned a selection probability. On the other hand, larger parameter values \(p\to 1\) assign considerable different probabilities to the top elements in the candidate list, and the probabilities are more likely to represent the greedy behavior of the heuristic. The geometric distribution has been successfully utilized to introduce the biased randomized behavior in heuristics used to solve problems in mobile cloud computing [91] and food logistics [92]. As a result, many executions of the biased randomized heuristic result in different solutions; these executions could be performed in a parallel or serial manner. In each  
Figure 3: Biased random sampling of elements from a list using a geometric with \(p=0.5\).