Optimizing the Hyperparameters of a Mixed Integer Linear Programming Solver to Speed up Electric Vehicle Charging Control

Ishihara, T.; Limmer, Steffen

doi:10.1007/978-3-030-43722-0_3

Cited by 7 publications

(20 citation statements)

References 25 publications

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“…Last, but not least, it would be interesting to consider a problem variant in which the discharging of vehicles is allowed in order to enable the mutual charging of EVs. This idea has already been mentioned in [26]; however, its impact on the total charging costs has not yet been studied. One could further extend the model by allowing the charging station to supply energy to the electricity grid in exchange for a monetary reward.…”

Section: Discussionmentioning

confidence: 99%

Smart Charging of Electric Vehicles Considering SOC-Dependent Maximum Charging Powers

et al. 2021

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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.

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Section: Discussionmentioning

confidence: 99%

Smart Charging of Electric Vehicles Considering SOC-Dependent Maximum Charging Powers

et al. 2021

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“…A representative problem is the charging schedule of electric vehicles (EVs). Designing these schedules typically leads to integer or mixed-integer programming problems, see for example [3,[52][53][54]. We consider the following EV charging problem: An operator of charging stations needs to charge N EVs during the working hours of a business complex.…”

Section: B Charging Optimizationmentioning

confidence: 99%

“…That is, the sum of the numbers in different subsets V i = l∈Si s l for 1 ≤ i ≤ k is requested to be as similar as possible. For instance, if S = (1, 1, 2, 3, 4, 5) and k = 2, the optimal partitions are (1, 1, 2, 4) and (3,5), which in this case yields a completely balanced partition with V 1 = V 2 = 8. For the case of k = 2 the decision version of number-partitioning problem is NP-complete [64], though there are various algorithms that solve the problem efficiently in many cases.…”

Section: Multiway Number Partitioningmentioning

confidence: 99%

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Quantum approximate optimization algorithm for qudit systems with long-range interactions

Deller¹,

Schmitt²,

Lewenstein³

et al. 2022

Preprint

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A frequent starting point of quantum computation platforms are two-state quantum systems, i.e., qubits. However, in the context of integer optimization problems, relevant to scheduling optimization and operations research, it is often more resource-efficient to employ quantum systems with more than two basis states, so-called qudits. Here, we discuss the quantum approximate optimization algorithm (QAOA) for qudits, layout its implementation in platforms with long-range interactions between qudits such as trapped ions, cold atomic mixtures, Rydberg atoms and atoms in cavities. We illustrate how the QAOA can be used to formulate a variety of integer optimization problems such as graph coloring problems or electric vehicle (EV) charging optimization. In addition, we comment on the implementation of constraints and describe three methods to include these into a quantum circuit of a QAOA by penalty contributions to the cost Hamiltonian, conditional gates using ancilla qubits, and a dynamical decoupling strategy. Finally, as a showcase of qudit-based QAOA, we present numerical results for a charging optimization problem mapped onto a maxk-graph coloring problem. Our work illustrates the flexibility of qudit systems to solve integer optimization problems.

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“…The research of Sorrell [20] is fully dedicated to finding ideal settings, including screening procedures for those features that are relevant. A recent and more practical example is given in Ishihara and Limmer [21]. The authors aim to optimize solver parameters for an electric vehicle charging problem.…”

Section: Adjusting Solver Parametersmentioning

confidence: 99%

MILP performance improvement strategies for short-term batch production scheduling: a chemical industry use case

et al. 2022

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This paper presents the development and mathematical implementation of a production scheduling model utilizing mixed-integer linear programming (MILP). A simplified model of a real-world multi-product batch plant constitutes the basis. The paper shows practical extensions to the model, resulting in a digital twin of the plant. Apart from sequential arrangement, the final model contains maintenance periods, campaign planning and storage constraints to a limited extend. To tackle weak computational performance and missing model features, a condensed mathematical formulation is introduced at first. After stating that these measures do not suffice for applicability in a restrained time period, a novel solution strategy is proposed. The overall non-iterative algorithm comprises a multi-step decomposition approach, which starts with a reduced scope and incrementally complements the schedule in multiple subproblem stages. Each of those optimizations holds less decision variables and makes use of warmstart information obtained from the predecessor model. That way, a first feasible solution accelerates the subsequent improvement process. Furthermore, the optimization focus can be shifted beneficially leveraging the Gurobi solver parameters. Findings suggest that correlation may exist between certain characteristics of the scheduling scope and ideal parameter settings, which yield potential for further investigation. Another promising area for future research addresses the concurrent multi-processing of independent MILPs on a single machine. First observations indicate that significant performance gains can be achieved in some cases, though sound dependencies were not discovered yet.

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Optimizing the Hyperparameters of a Mixed Integer Linear Programming Solver to Speed up Electric Vehicle Charging Control

Cited by 7 publications

References 25 publications

Smart Charging of Electric Vehicles Considering SOC-Dependent Maximum Charging Powers

Smart Charging of Electric Vehicles Considering SOC-Dependent Maximum Charging Powers

Quantum approximate optimization algorithm for qudit systems with long-range interactions

MILP performance improvement strategies for short-term batch production scheduling: a chemical industry use case

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