# Multi-Objective Electric Vehicles Scheduling Using Elitist Non-Dominated Sorting Genetic Algorithm
## 1 Introduction  
In recent years, policymakers have given significant importance to decrease the carbon footprint, mainly in the power system and road transport sectors [1]. Hence, large investments have been made in different types of distributed energy resources (DERs). This was the case of distributed generation based on natural sources, such as wind and solar. More recently, some countries are creating mechanisms to encourage the use of electric vehicles (EVs). The increased use of EVs can bring benefits to the power systems mainly when the bidirectional vehicle-to-grid (V2G) technology [2] is considered. In this case, EVs can increase the available storage level in the power system, thereby allowing better management of the system and creating some benefits to the EVs owners [3]. Note, however, that EVs may also create new challenges, particularly in distribution grids such as congestion problems or voltage stability [4]. Within this context, smart grids rapidly evolved from a visionary concept to be widely accepted by the involved players in power systems (i.e., academic and utilities). This concept ensures proper decentralized management of power systems to overcome the adverse effects of large-scale integrationof DERs, e.g., the volatility of renewables and congestion problems [5]. Additionally, the concept of a DER aggregator entity, such as virtual power plants (VPPs) or fleet operators, has been put forward to ease the integration between the DERs and other entities operating in power systems, such as distribution system operators (DSOs) or transmission system operators (TSOs). The literature has studied several ways to improve EVs integration in the power system by resorting to intelligent EV scheduling. In general, the studies have focused on the intelligent EVs coordination to mitigate their potential problems, e.g., power transformer congestions or voltage violations. The recommendation is to incorporate other objectives in the EV scheduling problem, instead of simply considering the economic perspective (i.e., minimizing cost or maximizing profit). We can consider the reduction of greenhouse gas (GHG) emissions as a relevant goal for EVs scheduling. Since these goals can conflict with each other, this leads to a multi-objective optimization approach. For example, the generation cost of a coal power plant can be lower than other technologies, but the CO\({}_{2}\) emissions costs are very significant. In this case, the goal is to obtain the Pareto front that contains all nondominated solutions [6], then EV aggregators can select the solution that best suits their interests using different techniques such as the fuzzy-based method proposed in the present paper. We can use a linear combination of objective functions with weight factors to determine the Pareto front as a single objective function. This is the most known classic method for handling multi-objective problems [4]. The elitist nondominated sorting genetic algorithm, also called NSGA-II [7], is used in this paper, as the literature points it out to be one of the best techniques for dealing with multi-objective problems [8]. Thus, this technique suits the multi-objective problems of this study because they are complex and demanding in terms of computational performance. However, a hybrid approach, which combines the NSGA-II with a deterministic technique, is better suited to obtain good results in an acceptable time. The main goal of the approach proposed in the present paper is to improve computational performance while not significantly degrading the energy resources scheduling solution. The term deterministic technique is used to designate the group of analytical techniques, also called classical techniques, used in the field of operational research [9]. In this paper, the deterministic technique is used to generate an initial solution to each individual of the initial population.