The aim of this work is to schedule the charging of electric vehicles (EVs) at a single charging station such that the temporal availability of each EV as well as the maximum available power at the station are considered. The total costs for charging the vehicles should be minimized w.r.t. time-dependent electricity costs. A particular challenge investigated in this work is that the maximum power at which a vehicle can be charged is dependent on the current state of charge (SOC) of the vehicle. Such a consideration is particularly relevant in the case of fast charging. Considering this aspect for a discretized time horizon is not trivial, as the maximum charging power of an EV may also change in between time steps. To deal with this issue, we instead consider the energy by which an EV can be charged within a time step. For this purpose, we show how to derive the maximum charging energy in an exact as well as an approximate way. Moreover, we propose two methods for solving the scheduling problem. The first is a cutting plane method utilizing a convex hull of the, in general, nonconcave SOC–power curves. The second method is based on a piecewise linearization of the SOC–energy curve and is effectively solved by branch-and-cut. The proposed approaches are evaluated on benchmark instances, which are partly based on real-world data. To deal with EVs arriving at different times as well as charging costs changing over time, a model-based predictive control strategy is usually applied in such cases. Hence, we also experimentally evaluate the performance of our approaches for such a strategy. The results show that optimally solving problems with general piecewise linear maximum power functions requires high computation times. However, problems with concave, piecewise linear maximum charging power functions can efficiently be dealt with by means of linear programming. Approximating an EV’s maximum charging power with a concave function may result in practically infeasible solutions, due to vehicles potentially not reaching their specified target SOC. However, our results show that this error is negligible in practice.

This article presents a cooperative optimization approach (COA) for distributing service points for mobility applications, which generalizes and refines a previously proposed method. COA is an iterative framework for optimizing service point locations, combining an optimization component with user interaction on a large scale and a machine learning component that learns user needs and provides the objective function for the optimization. The previously proposed COA was designed for mobility applications in which single service points are sufficient for satisfying individual user demand. This framework is generalized here for applications in which the satisfaction of demand relies on the existence of two or more suitably located service stations, such as in the case of bike/car sharing systems. A new matrix factorization model is used as surrogate objective function for the optimization, allowing us to learn and exploit similar preferences among users w.r.t. service point locations. Based on this surrogate objective function, a mixed integer linear program is solved to generate an optimized solution to the problem w.r.t. the currently known user information. User interaction, refinement of the matrix factorization, and optimization are iterated. An experimental evaluation analyzes the performance of COA with special consideration of the number of user interactions required to find near optimal solutions. The algorithm is tested on artificial instances, as well as instances derived from real-world taxi data from Manhattan. Results show that the approach can effectively solve instances with hundreds of potential service point locations and thousands of users, while keeping the user interactions reasonably low. A bound on the number of user interactions required to obtain full knowledge of user preferences is derived, and results show that with 50% of performed user interactions the solutions generated by COA feature optimality gaps of only 1.45% on average.