Diplomarbeit Electric Vehicles Recharge Scheduling with Logic-Based Benders Decomposition

Electric vehicles represent a promising alternative to traditional internal combustion engine vehicles that might support the attainment of settled climate and energy targets. The widespread adoption of electric vehicles is complicated, however, by their need for frequent recharging and the rather long charging duration. Moreover, charging facilities are still relatively scarce and power constraints imposed by the electric grid have to be respected. We consider the problem of scheduling the recharging of a fleet of electric vehicles at multiple facilities with limited resources. The goal is to recharge as many vehicles as possible. Every vehicle that is scheduled for charging needs a parking spot during the entire time of its stay and shall be recharged as much as possible before departure. Facilities only have a limited number of parking spots and charging machines and a limited amount of power available for charging. Machines can work at several charging rates, but higher ones should be avoided, since they reduce battery lifetime more. First, we formulate this problem as a mixed-integer programming (MIP) model, which is a standard approach for discrete optimization problems. Moreover, a simple greedy heuristic, which quickly finds a feasible solution, is presented. The main objective of this thesis is to investigate an alternative method for solving the problem. The so-called logic-based Benders decomposition solves optimization problems iteratively on basis of systematic trial and error. For this purpose, the problem is decomposed into a master and a subproblem. In every iteration, the master problem assigns trial values to some of the variables. Assuming those fixed, optimal values of the remaining variables are determined in the subproblem, which should be much easier to solve than the original one. From the subproblem solution we deduce constraints that are added to the master problem, in order to obtain better trial values in the next iteration. Logic-based Benders algorithms for two different decompositions of the considered problem are formulated. The subproblems of the first one are mere feasibility problems, while in the second one they are optimization problems as well. Additionally, heuristic boosting strategies are proposed, in which either the master or subproblems are solved heuristically. v The evaluation of all algorithms on randomly generated test instances shows that the MIP model and the first decomposition work quite well. On instances with homogeneous facilities and enough resources available, the first Benders algorithm often terminates after a few iterations and achieves far better results than the compact MIP model. On the other hand, the MIP model frequently has a shorter runtime on instances with other specifications. The second decomposition shows a rather bad performance. In many cases, the algorithm does not find an optimal solution within the time limit. Heuristic boosting leads to an improved runtime on some instances, but for most offers no real advantage. Regarding larger instances, the MIP model cannot be solved at all due to high memory requirements, while the logic-based Benders algorithms at least return bounds on the optimal value. The first Benders algorithm even finds an optimal solution on many of the larger instances.