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

TL;DR

This paper presents a new online algorithm for a generalized fractional multiple knapsack problem with applications to EV charging, achieving near-optimal competitive ratios through a novel primal-dual analysis.

Contribution

Introduces a new algorithm for a generalized online knapsack problem with heterogeneous and rate constraints, improving competitive ratios and applying to EV charging control.

Findings

Algorithm achieves near-optimal competitive ratio.

Applicable to real-time EV charging management.

Provides a novel instance-dependent primal-dual analysis.

Abstract

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.