## 4 Review of Case Studies: Electric Vehicle Routing Optimization  
Numerous case studies have been carried out to explore the efficiency of GAs in optimizing routing for EVs. The distribution of these studies considered in this work over the years is depicted in Figure 3.  
Figure 2: Pareto Front-Multi-Objective Solutions. One notable study by [PERSON] et al. [30] addressed the personal electric vehicle routing problem (pEVRP) with the objective of optimizing the travel time and recharging costs for a single electric vehicle. They aim to minimize travel time and charging process as objective function, represented by Equation (4). The first three terms of Equation (4) denote the time taken to reach the destination node \(D\) from the source node \(S\) and the next three terms are associated with the charging process. \[min\sum_{i\in V}\frac{w_{i}^{S}d_{Si}}{v}+\sum_{i\in V}\sum_{j\in V}\frac{x_{ij }d_{ij}}{v}+\sum_{i\in V}\frac{w_{i}^{D}d_{iD}}{v}+\sum_{i\in V}\frac{z_{i} \delta_{i}}{v}+\sum_{i\in V}z_{i}w_{i}+\sum_{i\in V}\frac{z_{i}y_{i}C}{L_{i}} \tag{4}\]  
Real-life factors such as traffic delays, detour distances, and variable pricing were incorporated into the problem formulation. The study formulated a mixed-integer nonlinear programming (MINLP) problem and employed the \(\epsilon\)-constraint method to obtain a set of non-dominated points representing the first Pareto front. Meta-heuristic techniques, including GA and PSO, were applied to find globally optimal solutions. The results demonstrated that the proposed methods effectively optimized travel time and recharging costs, providing valuable insights into decision-making in personal electric vehicle routing. Similarly, [PERSON] and [PERSON] [22] addressed the IRP with a focus on optimizing fuel consumption and pollutant emissions in the transportation sector. They used comprehensive modal emission model (CMEM) for computing fuel consumption rate and greenhouse gas emission based on vehicle speed, load weight and road gradient. They computed fuel consumption using Equation (5). \[FR^{h}=\xi\frac{k^{h}N^{h}V^{h}+P^{h}/\eta}{k} \tag{5}\]  
where \(\xi\) is the mass rates of fuel to the air. \(k^{h}\) is the vehicle type h engine friction. \(N^{h}\) is engine speed, and \(V^{h}\) is engine displacement vehicle type \(h\). \(\eta\) and k are constant values and the diesel engine efficiency parameter and thermal value of diesel fuel, respectively. \(P^{h}\) is momentary engine power output vehicle type \(h\) (in kW). A bi-objective model is proposed, considering fleet composition as heterogeneous to enhance practicality. The proposed model is solved using a multi-objective quantum algorithm, and its performance is compared to other methods like NSGA-II and exact methods. The results demonstrated the superior performance of the proposed algorithm in terms of defined criteria. The paper concluded by suggesting future research directions, including the incorporation of additional concepts and policies, fuel consumption models, and solution methods to further enhance the model's scope and effectiveness in addressing inventory routing optimization, fuel consumption, and environmental sustainability. In another study, [PERSON] et al. [32] focused on optimizing the navigation system for EVs considering both charging and routing aspects. Their study addressed the challenges posed by the introduction of a real-time pricing (RTP) policy, which aimed to manage load shaving during fast charging. The proposed approach extended the original traffic network to a feasible state graph using EV arrival states and traffic parameters. An improved chrono-SPT (ICS) algorithm is introduced to determine the optimal decision sequence for routing and charging policies. To simplify the computational complexity, a simplify-charge-control (SCC) algorithm is presented.