6. Conclusions
We have tackled the problem of scheduling the charging of EVs on a realworld charging station. The schedule must take into account some technical constraints of the system, while simultaneously minimise a total tardiness objective function. This work constitutes a first approach to incorporating uncertainty to the problem, to narrow the gap between the model and the real-world situation. In particular, we have considered uncertain charging times modelled as triangular fuzzy numbers. This has resulted in a new formulation of the problem, based on the deterministic one, but with considerable changes, for instance, in the translation of the constraints. Additionally, to solve the resulting problem we have proposed a GA based on a previous algorithm with good performance in the deterministic version. Although the general scheme remains the same, some operators, such as crossover, have had to be adapted to handle fuzzy numbers and a new decoding operator has been proposed, consisting on a purpose-built schedule builder. Finally, we have presented an experimental study on new benchmark fuzzy instances inspired in real-world data that show the correct convergence of the GA as well as its good performance. Additionally, the benchmark instances will be made openly available to the research community on the web, to encourage future advancements on solving this problem.
This constitutes the first approach to the charging problem with uncertainty and as such opens many lines for future research. First, we would like to establish links between the constraint formulations and possibility theory which, in turn, may suggest new and better schedule-building algorithms. It is also possible to give alternative formulations for some constraints in the uncertain setting, in particular, for the balance between lines. Regarding the solving method, it could be improved by combining the GA with local search, which would require defining good neighbourhood structures and efficient neighbour evaluation methods. Another interesting perspective, as considered in Burdett and Kozan (2015), is to consider the robustness of the obtained solutions, either as an objective function to optimise, either as a criterion to compare the fuzzy solutions and the deterministic ones. Finally, we aim at incorporating new features that make the problem closer to the real-life situation, such as having variable energy costs depending on the time of the day.
