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.
Highlights
Online optimization has become a foundational piece of the design of networked and distributed systems that is used to capture the challenges of decision-making in uncertain environments
We introduce and study a generalization of the fractional online multiple knapsack problem (FOMKP) that is motivated by the electric vehicle (EV) charging problem and unifies the online knapsack and one-way trading literatures
We study a generalization of a fractional online multiple knapsack problem (FOMKP), where fractional refers to the fact that items can be assigned such that a fraction goes to each of multiple knapsacks
Summary
Online optimization has become a foundational piece of the design of networked and distributed systems that is used to capture the challenges of decision-making in uncertain environments.
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