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

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Published:15 June 2021Publication History
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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.

References

  1. Jacob D Abernethy, Elad Hazan, and Alexander Rakhlin. 2009. Competing in the dark: An efficient algorithm for bandit linear optimization. (2009).Google ScholarGoogle Scholar
  2. Micah Adler, Ramesh K Sitaraman, and Harish Venkataramani. 2011. Algorithms for optimizing the bandwidth cost of content delivery. Computer Networks , Vol. 55, 18 (2011), 4007--4020. Google ScholarGoogle ScholarDigital LibraryDigital Library
  3. Muhammad Abdullah Adnan, Ryo Sugihara, and Rajesh K Gupta. 2012. Energy efficient geographical load balancing via dynamic deferral of workload. In 2012 IEEE Fifth International Conference on Cloud Computing. IEEE, 188--195. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Shipra Agrawal, Zizhuo Wang, and Yinyu Ye. 2014. A dynamic near-optimal algorithm for online linear programming. Operations Research , Vol. 62, 4 (2014), 876--890. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Bahram Alinia, Mohammad H Hajiesmaili, and Noël Crespi. 2019. Online EV charging scheduling with on-arrival commitment. IEEE Transactions on Intelligent Transportation Systems , Vol. 20, 12 (2019), 4524--4537.Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Bahram Alinia, Mohammad H Hajiesmaili, Zachary J Lee, Noel Crespi, and Enrique Mallada. 2020. Online EV scheduling algorithms for adaptive charging networks with global peak constraints. IEEE Transactions on Sustainable Computing (2020).Google ScholarGoogle Scholar
  7. Bahram Alinia, Mohammad Sadegh Talebi, Mohammad H Hajiesmaili, Ali Yekkehkhany, and Noel Crespi. 2018. Competitive online scheduling algorithms with applications in deadline-constrained EV charging. In 2018 IEEE/ACM 26th International Symposium on Quality of Service (IWQoS). IEEE, 1--10.Google ScholarGoogle ScholarCross RefCross Ref
  8. Stephen Boyd, Stephen P Boyd, and Lieven Vandenberghe. 2004. Convex optimization .Cambridge university press. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Niv Buchbinder and Joseph Naor. 2009a. The design of competitive online algorithms via a primal-dual approach .Now Publishers Inc. Google ScholarGoogle ScholarDigital LibraryDigital Library
  10. Niv Buchbinder and Joseph Naor. 2009b. Online primal-dual algorithms for covering and packing. Mathematics of Operations Research , Vol. 34, 2 (2009), 270--286. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Deeparnab Chakrabarty, Yunhong Zhou, and Rajan Lukose. 2008. Online knapsack problems. In Workshop on internet and network economics (WINE) .Google ScholarGoogle Scholar
  12. Junting Chen and Vincent KN Lau. 2011. Convergence analysis of saddle point problems in time varying wireless systems?Control theoretical approach. IEEE Transactions on Signal Processing , Vol. 60, 1 (2011), 443--452. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. Francis YL Chin, Bin Fu, Jiuling Guo, Shuguang Han, Jueliang Hu, Minghui Jiang, Guohui Lin, Hing-Fung Ting, Luping Zhang, Yong Zhang, et almbox. 2015. Competitive algorithms for unbounded one-way trading. Theoretical Computer Science , Vol. 607 (2015), 35--48. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Nikhil R. Devanur and Kamal Jain. 2012. Online Matching with Concave Returns. In Proceedings of the Forty-Fourth Annual ACM Symposium on Theory of Computing (New York, New York, USA) (STOC '12). Association for Computing Machinery, New York, NY, USA, 137--144. Google ScholarGoogle ScholarDigital LibraryDigital Library
  15. Ran El-Yaniv, Amos Fiat, Richard M Karp, and Gordon Turpin. 2001. Optimal search and one-way trading online algorithms. Algorithmica , Vol. 30, 1 (2001), 101--139.Google ScholarGoogle ScholarCross RefCross Ref
  16. Hiroshi Fujiwara, Kazuo Iwama, and Yoshiyuki Sekiguchi. 2011. Average-case competitive analyses for one-way trading. Journal of Combinatorial Optimization , Vol. 21, 1 (2011), 83--107. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Edward F Grove. 1991. The harmonic online k-server algorithm is competitive. In Proceedings of the twenty-third annual ACM symposium on Theory of computing. 260--266. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Linqi Guo, Karl F Erliksson, and Steven H Low. 2017. Optimal online adaptive electric vehicle charging. In 2017 IEEE Power & Energy Society General Meeting. IEEE, 1--5.Google ScholarGoogle ScholarCross RefCross Ref
  19. Vani Gupta, Prashant Shenoy, and Ramesh K Sitaraman. 2019. Combining Renewable Solar and Open Air Cooling for Greening Internet-Scale Distributed Networks. In Proc. of ACM eEnergy. 303--314. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Kazuo Iwama and Shiro Taketomi. 2002. Removable online knapsack problems. In International Colloquium on Automata, Languages, and Programming. Springer, 293--305. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. G Stephen Jones. 1964. Fundamental inequalities for discrete and discontinuous functional equations. J. Soc. Indust. Appl. Math. , Vol. 12, 1 (1964), 43--57.Google ScholarGoogle ScholarCross RefCross Ref
  22. Hans Kellerer, Ulrich Pferschy, and David Pisinger. 2004. Multiple Knapsack Problems .Springer Berlin Heidelberg, Berlin, Heidelberg, 285--316.Google ScholarGoogle Scholar
  23. Zachary Lee, Tongxin Li, and S. H. Low. 2019. ACN-Data charging dataset: analysis and applications. In Proc. of ACM eEnergy .Google ScholarGoogle Scholar
  24. Zachary J Lee, Daniel Chang, Cheng Jin, George S Lee, Rand Lee, Ted Lee, and Steven H Low. 2018. Large-scale adaptive electric vehicle charging. In 2018 IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm). IEEE, 1--7.Google ScholarGoogle Scholar
  25. Qiulin Lin, Hanling Yi, John Pang, Minghua Chen, Adam Wierman, Michael Honig, and Yuanzhang Xiao. 2019. Competitive online optimization under inventory constraints. Proceedings of the ACM on Measurement and Analysis of Computing Systems , Vol. 3, 1 (2019), 1--28. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Zhenhua Liu, Minghong Lin, Adam Wierman, Steven Low, and Lachlan LH Andrew. 2014. Greening geographical load balancing. IEEE/ACM Transactions on Networking , Vol. 23, 2 (2014), 657--671. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. Brendan Lucier, Ishai Menache, Joseph Naor, and Jonathan Yaniv. 2013. Efficient online scheduling for deadline-sensitive jobs. In Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures . 305--314. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. George S Lueker. 1998. Average-case analysis of off-line and on-line knapsack problems. Journal of Algorithms , Vol. 29, 2 (1998), 277--305. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Jianying Luo, Lei Rao, and Xue Liu. 2013. Temporal load balancing with service delay guarantees for data center energy cost optimization. IEEE Transactions on Parallel and Distributed Systems , Vol. 25, 3 (2013), 775--784. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. Dragoslav S Mitrinovic, Josip Pecaric, and Arlington M Fink. 1991. Inequalities involving functions and their integrals and derivatives. Vol. 53. Springer Science & Business Media.Google ScholarGoogle Scholar
  31. John Noga and Veerawan Sarbua. 2005. An online partially fractional knapsack problem. In 8th International Symposium on Parallel Architectures, Algorithms and Networks (ISPAN'05). IEEE, 5--pp. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. S. Paris, J. Leguay , L. Maggi, M. Draief, and S. Chouvardas. 2016. Online experts for admission control in SDN. In NOMS 2016 - 2016 IEEE/IFIP Network Operations and Management Symposium. 1003--1004.Google ScholarGoogle Scholar
  33. David Pisinger. 2005. Where are the hard knapsack problems? Computers & Operations Research , Vol. 32, 9 (2005), 2271--2284. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Guannan Qu and Na Li. 2018. On the exponential stability of primal-dual gradient dynamics. IEEE Control Systems Letters , Vol. 3, 1 (2018), 43--48.Google ScholarGoogle ScholarCross RefCross Ref
  35. Asfandyar Qureshi, Rick Weber, Hari Balakrishnan, John Guttag, and Bruce Maggs. 2009. Cutting the electric bill for internet-scale systems. In Proceedings of the ACM SIGCOMM 2009 conference on Data communication. 123--134. Google ScholarGoogle ScholarDigital LibraryDigital Library
  36. Pascal Schroeder, Robert Dochow, and Günter Schmidt. 2018. Optimal solutions for the online time series search and one-way trading problem with interrelated prices and a profit function. Computers & Industrial Engineering , Vol. 119 (2018), 465--471.Google ScholarGoogle ScholarCross RefCross Ref
  37. Kevin Spiteri, Rahul Urgaonkar, and Ramesh K Sitaraman. 2020. BOLA: Near-Optimal Bitrate Adaptation for Online Videos. IEEE/ACM Transactions on Networking (2020).Google ScholarGoogle Scholar
  38. Bo Sun, Tongxin Li, Steven H Low, and Danny HK Tsang. 2020. ORC: An Online Competitive Algorithm for Recommendation and Charging Schedule in Electric Vehicle Charging Network. In Proceedings of the Eleventh ACM International Conference on Future Energy Systems. 144--155. Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. X. Tan, A. Leon-Garcia, Y. Wu, and D. H. K. Tsang. 2020. Online Combinatorial Auctions for Resource Allocation With Supply Costs and Capacity Limits. IEEE Journal on Selected Areas in Communications , Vol. 38, 4 (2020), 655--668.Google ScholarGoogle ScholarCross RefCross Ref
  40. Xiaoqi Tan, Bo Sun, Alberto Leon-Garcia, Yuan Wu, and Danny H.K. Tsang. 2020. Mechanism Design for Online Resource Allocation: A Unified Approach. In Abstracts of the 2020 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems (Boston, MA, USA) (SIGMETRICS '20). Association for Computing Machinery, New York, NY, USA, 11--12. Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. Cong Wang and Michael Zink. 2019. Sustainable Cloud Encoding for Adaptive Bitrate Streaming over CDNs. In 2019 IEEE International Symposium on Local and Metropolitan Area Networks (LANMAN) . 1--6.Google ScholarGoogle ScholarCross RefCross Ref
  42. Wei Wang, Liying Wang, Yingjie Lan, and Jean X Zhang. 2016. Competitive difference analysis of the one-way trading problem with limited information. European Journal of Operational Research , Vol. 252, 3 (2016), 879--887.Google ScholarGoogle ScholarCross RefCross Ref
  43. Lin Yang, Mohammad H Hajiesmaili, Ramesh Sitaraman, Adam Wierman, Enrique Mallada, and Wing S Wong. 2020. Online Linear Optimization with Inventory Management Constraints. Proceedings of the ACM on Measurement and Analysis of Computing Systems , Vol. 4, 1 (2020), 1--29. Google ScholarGoogle ScholarDigital LibraryDigital Library
  44. Lin Yang, Mohammad H Hajiesmaili, and Wing S Wong. 2019. Online Linear Programming with Uncertain Constraints. In 2019 53rd Annual Conference on Information Sciences and Systems (CISS). IEEE, 1--6.Google ScholarGoogle Scholar
  45. Zijun Zhang, Zongpeng Li, and Chuan Wu. 2017. Optimal Posted Prices for Online Cloud Resource Allocation. Proc. ACM Meas. Anal. Comput. Syst. , Vol. 1, 1 (June 2017), bibinfonumpages26 pages. Google ScholarGoogle ScholarDigital LibraryDigital Library
  46. Zizhan Zheng and Ness Shroff. 2014. Online welfare maximization for electric vehicle charging with electricity cost. In Proceedings of the 5th international conference on Future energy systems . 253--263. Google ScholarGoogle ScholarDigital LibraryDigital Library
  47. Zizhan Zheng and Ness B Shroff. 2016. Online multi-resource allocation for deadline sensitive jobs with partial values in the cloud. In IEEE INFOCOM 2016-The 35th Annual IEEE International Conference on Computer Communications. IEEE, 1--9.Google ScholarGoogle ScholarDigital LibraryDigital Library
  48. Yunhong Zhou, Deeparnab Chakrabarty, and Rajan Lukose. 2008. Budget constrained bidding in keyword auctions and online knapsack problems. In International Workshop on Internet and Network Economics. Springer, 566--576. Google ScholarGoogle ScholarDigital LibraryDigital Library

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