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

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.

Theoretically Guaranteed Online Workload Dispatching for Deadline-Aware Multi-Server Jobs

“…This assumption is widely accepted in the online resource allocation problems [22], [30]- [34]. For example, in [32], the fluctuation ratio υ ι is set as 36 in default.…”

“…To do this, we design several pseudo-social welfare functions with estimated marginal costs. In this design, we utilize an important principle for solving online resource allocation problems, i.e., estimate the cost for provisioning services to each newly arrived job as a function of resource surplus [22], [23], [31], [32], [35]. In the following sections, firstly, we show how the pseudosocial welfare functions are designed.…”

“…Proof. To prove this result, we refer to the technique named instance-dependent online primal-dual approach, proposed in [32].…”

“…When R = 1, P 1 degenerates to the general one-way trading (GOT) problem [38]. The optimal competitive ratio is proved to be 1 + ln( υ ι ) [22], [31], [32], [34], [38]. With α ≥ 1, υ ι ≥ 1, let us take y ≥ 1 as a substitute for α − 1.…”

Electric vehicle charging stations in the workplace with high-resolution data from casual and habitual users

“…At a research level, this data could be used by scholars to address questions in several possible areas of inquiry. These include, but are not limited to, energy modelling and load profiling [8][9][10][11] , power systems optimization [12][13][14][15][16] , economic and policy analysis [17][18][19][20] , energy data analytics and visualization [21][22][23] , management and innovation studies [24][25][26] , consumer behaviour research 9,27-29 , and life cycle analyses 30,31 .…”