Competitive Algorithms for the Online Multiple Knapsack Problem with Application to Electric Vehicle Charging

We introduce and study a general version of the fractional online knapsack problem with multiple knapsacks, heterogeneous constraints on which items can be assigned to which knapsack, and rate-limiting constraints on the assignment of items to knapsacks. This problem generalizes variations of the knapsack problem and of the one-way trading problem that have previously been treated separately, and additionally finds application to the real-time control of electric vehicle (EV) charging. We introduce a new algorithm that achieves a competitive ratio within an additive factor of one of the best achievable competitive ratios for the general problem and matches or improves upon the best-known competitive ratio for special cases in the knapsack and one-way trading literatures. Moreover, our analysis provides a novel approach to online algorithm design based on an instance-dependent primal-dual analysis that connects the identification of worst-case instances to the design of algorithms. Finally, we illustrate the proposed algorithm via trace-based experiments of EV charging

Competitive Algorithms for the Online Multiple Knapsack Problem with Application to Electric Vehicle Charging

We introduce and study a general version of the fractional online knapsack problem with multiple knapsacks, heterogeneous constraints on which items can be assigned to which knapsack, and rate-limiting constraints on the assignment of items to knapsacks. This problem generalizes variations of the knapsack problem and of the one-way trading problem that have previously been treated separately, and additionally finds application to the real-time control of electric vehicle (EV) charging. We introduce a new algorithm that achieves a competitive ratio within an additive factor of one of the best achievable competitive ratios for the general problem and matches or improves upon the best-known competitive ratio for special cases in the knapsack and one-way trading literatures. Moreover, our analysis provides a novel approach to online algorithm design based on an instance-dependent primal-dual analysis that connects the identification of worst-case instances to the design of algorithms. Finally, we illustrate the proposed algorithm via trace-based experiments of EV charging

Minimal-variance distributed scheduling under strict demands and deadlines

Many modern schedulers can dynamically adjust their service capacity to match the incoming workload. At the same time, however, variability in service capacity often incurs operational and infrastructure costs. In this abstract, we characterize an optimal distributed algorithm that minimizes service capacity variability when scheduling jobs with deadlines. Specifically, we show that Exact Scheduling minimizes service capacity variance subject to strict demand and deadline requirements under stationary Poisson arrivals. Moreover, we show how close the performance of the optimal distributed algorithm is to that of the optimal centralized algorithm by deriving a competitive-ratio-like bound

Generalized Exact Scheduling: a Minimal-Variance Distributed Deadline Scheduler

Many modern schedulers can dynamically adjust their service capacity to match the incoming workload. At the same time, however, unpredictability and instability in service capacity often incur operational and infrastructure costs. In this paper, we seek to characterize optimal distributed algorithms that maximize the predictability, stability, or both when scheduling jobs with deadlines. Specifically, we show that Exact Scheduling minimizes both the stationary mean and variance of the service capacity subject to strict demand and deadline requirements. For more general settings, we characterize the minimal-variance distributed policies with soft demand requirements, soft deadline requirements, or both. The performance of the optimal distributed policies is compared to that of the optimal centralized policy by deriving closed-form bounds and by testing centralized and distributed algorithms using real data from the Caltech electrical vehicle charging facility and many pieces of synthetic data from different arrival distribution. Moreover, we derive the Pareto-optimality condition for distributed policies that balance the variance and mean square of the service capacity. Finally, we discuss a scalable partially-centralized algorithm that uses centralized information to boost performance and a method to deal with missing information on service requirements

Learning-Augmented Scheduling for Solar-Powered Electric Vehicle Charging

We tackle the complex challenge of scheduling the charging of electric vehicles (EVs) equipped with solar panels and batteries, particularly under out-of-distribution (OOD) conditions. Traditional scheduling approaches, such as reinforcement learning (RL) and model predictive control (MPC), often fail to provide satisfactory results when faced with OOD data, struggling to balance robustness (worst-case performance) and consistency (near-optimal average performance). To address this gap, we introduce a novel learning-augmented policy. This policy employs a dynamic robustness budget, which is adapted in real-time based on the reinforcement learning policy's performance. Specifically, it leverages the temporal difference (TD) error, a measure of the learning policy's prediction accuracy, to assess the trustworthiness of the machine-learned policy. This method allows for a more effective balance between consistency and robustness in EV charging schedules, significantly enhancing adaptability and efficiency in real-world, unpredictable environments. Our results demonstrate that this approach markedly improves scheduling effectiveness and reliability, particularly in OOD contexts, paving the way for more resilient and adaptive EV charging systems

Frontiers In Operations Research For Overcoming Barriers To Vehicle Electrification

Electric vehicles (EVs) hold many promises including diversification of the transportation energy feedstock and reduction of greenhouse gas and other emissions. However, achieving large-scale adoption of EVs presents a number of challenges resulting from a current lack of supporting infrastructure and difficulties in overcoming technological barriers. This dissertation addresses some of these challenges by contributing to the advancement of theories in the areas of network optimization and mechanism design. To increase the electric driving range of plug-in hybrid electric vehicles (PHEVs), we propose a powertrain energy management control system that exploits energy efficiency dif- ferences of the electric machine and the internal combustion engine during route planning. We introduce the Energy-Efficient Routing problem (EERP) for PHEVs, and formulate this problem as a new class of the shortest path problem. We prove that the EERP is NP-complete. We then propose two exact algorithms that find optimal solutions by exploiting the transitive structure inherent in the network. To tackle the intractability of the problem, we proposed a Fully Polynomial Time Approximation Scheme (FPTAS). From a theoretic perspective, the proposed two-phase approaches improve the state-of-the-art to optimally solving shortest path problems on general constrained multi-graph networks. These novel approaches are scalable and offer broad potential in many network optimization problems. In the context of vehicle routing, this is the first study to take into account energy efficiency difference of different operating modes of PHEVs during route planning, which is a high level powertrain energy management procedure. Another challenge for EV adoption is the inefficiency of current charging systems. In addition, high electricity consumption rates of EVs during charging make the load manage- ment of micro grids a challenge. We proposed an offline optimal mechanism for scheduling and pricing of electric vehicle charging considering incentives of both EV owners and utility companies. In the offline setting, information about future supply and demand is known to the scheduler. By considering uncertainty about future demand, we then designed a family of online mechanisms for real-time scheduling of EV charging. A fundamental problem with significant economic implications is how to price the charging units at different times under dynamic demand. We propose novel bidding based mechanisms for online scheduling and pricing of electric vehicle charging. The proposed preemption-aware charging mechanisms consider incentives of both EV drivers and grid operators. We also prove incentive-compatibility of the mechanisms, that is, truthful reporting is a dominant strategy for self-interested EV drivers. The proposed mechanisms demonstrate the benefits of electric grid load management, revenue maximization, and quick response, key attributes when providing online charging services

Preemptive Scheduling of EV Charging for Providing Demand Response Services

We develop a new algorithm for scheduling the charging process of a large number of electric vehicles (EVs) over a finite horizon. We assume that EVs arrive at the charging stations with different charge levels and different flexibility windows. The arrival process is assumed to have a known distribution and that the charging process of EVs can be preemptive. We pose the scheduling problem as a dynamic program with constraints. We show that the resulting formulation leads to a monotone dynamic program with Lipschitz continuous value functions that are robust against perturbation of system parameters. We propose a simulation based fitted value iteration algorithm to determine the value function approximately, and derive the sample complexity for computing the approximately optimal solution.Comment: 21 pages, submitted to SEGA