[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ skip to main content
10.1145/3557915.3560982acmconferencesArticle/Chapter ViewAbstractPublication PagesgisConference Proceedingsconference-collections
research-article
Open access

The pit stop problem: how to plan your next road trip

Published: 22 November 2022 Publication History

Abstract

Many online trip planning and navigation software need to routinely solve the problem of deciding where to take stops during a journey for various services such as refueling (or EV charging), rest stops, food, etc. The goal is to minimize the overhead of these stops while ensuring that the traveller is not starved of any essential resource (such as fuel, rest, or food) during the journey. In this paper, we formally model this problem and call it the pit stop problem. We design algorithms for this problem under various settings: single vs multiple types of stops, and offline vs online optimization (i.e., in advance of or during the trip). Our algorithms achieve provable guarantees in terms of approximating the optimal solution. We then extensively evaluate our algorithms on real world data and demonstrate that they significantly outperform baseline solutions.

References

[1]
Vural Aksakalli, O. Furkan Sahin, and Ibrahim Ari. 2016. An AO* Based Exact Algorithm for the Canadian Traveler Problem. INFORMS J. Comput. 28, 1 (2016), 96--111.
[2]
Saeed Alaei. 2014. Bayesian combinatorial auctions: Expanding single buyer mechanisms to many buyers. SIAM J. Comput. 43, 2 (2014), 930--972.
[3]
N. Bansal, A. Blum, S. Chawla, and A. Meyerson. 2004. Approximation algorithms for deadline-TSP and vehicle routing with time-windows. In STOC. 166--174.
[4]
Amotz Bar-Noy and Baruch Schieber. 1991. The Canadian Traveller Problem. In Proceedings of the Second Annual ACM/SIGACT-SIAM Symposium on Discrete Algorithms. 261--270.
[5]
A. Blum, S. Chawla, D. R. Karger, T. Lane, A. Meyerson, and M. Minkoff. 2007. Approximation algorithms for orienteering and discounted-reward TSP. SIAM J. Comput. 37, 2 (2007), 653--670.
[6]
M. Charikar, S. Khuller, and B. Raghavachari. 2001. Algorithms for capacitated vehicle routing. SIAM J. Comput. 31, 3 (2001), 665--682.
[7]
M. Charikar and B. Raghavachari. 1998. The finite capacity dial-a-ride problem. In FOCS. 458--467.
[8]
C. Chekuri, N. Korula, and M. Pál. 2012. Improved algorithms for orienteering and related problems. ACM Trans. Algorithms 8, 3 (2012), 23:1--23:27.
[9]
T. Chen, B. Zhang, H. Pourbabak, A. Kavousi-Fard, and W. Su. 2018. Optimal Routing and Charging of an Electric Vehicle Fleet for High-Efficiency Dynamic Transit Systems. IEEE Transactions on Smart Grid 9, 4 (2018), 3563--3572.
[10]
T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. 2009. Introduction to Algorithms (3. ed.). MIT Press.
[11]
DHL. [n.d.]. Self Driving Vehicles in Logistics. http://https://www.dhl.com/content/dam/downloads/g0/about_us/logistics_insights/dhl_self_driving_vehicles.pdf.
[12]
E. B. Dynkin. 1963. Optimal choice of the stopping moment of a Markov process. Dokl. Akad. Nauk SSSR 150 (1963), 238--240. Issue 2.
[13]
Patrick Eyerich, Thomas Keller, and Malte Helmert. 2010. High-Quality Policies for the Canadian Traveler's Problem. In Proceedings of the Twenty-Fourth AAAI Conference on Artificial Intelligence, AAAI 2010, Atlanta, Georgia, USA, July 11--15, 2010.
[14]
P. R. Freeman. 1983. The Secretary Problem and Its Extensions: A Review. International Statistical Review / Revue Internationale de Statistique 51, 2 (1983), 189--206.
[15]
B. L. Golden and A. A. Assad (Eds.). 1988. Vehicle Routing: Methods and Studies. Studies in Management Science and Systems, Vol. 16. North-Holland, Amsterdam.
[16]
I. L. Gørtz, V. Nagarajan, and R. Ravi. 2015. Minimum makespan multi-vehicle dial-a-ride. ACM Trans. Algorithms 11, 3 (2015), 23:1--23:29.
[17]
A. Gupta, M. T. Hajiaghayi, V. Nagarajan, and R. Ravi. 2010. Dial a ride from k-forest. ACM Trans. Algorithms 6, 2 (2010), 41:1--41:21.
[18]
M. Haimovich and A. H. G. Rinnooy Kan. 1985. Bounds and heuristics for capacitated routing problems. Math. Oper. Res. 10, 4 (1985), 527--542.
[19]
Mohammad Taghi Hajiaghayi, Robert D. Kleinberg, and Tuomas Sandholm. 2007. Automated Online Mechanism Design and Prophet Inequalities. In Proceedings of the 22nd AAAI Conference on Artificial Intelligence. 58--65.
[20]
DP Kennedy. 1987. Prophet-type inequalities for multi-choice optimal stopping. Stochastic Processes and their Applications 24, 1 (1987), 77--88.
[21]
Samir Khuller, Azarakhsh Malekian, and Julián Mestre. 2011. To fill or not to fill: The gas station problem. ACM Trans. Algorithms 7, 3 (2011), 36:1--36:16.
[22]
Robert Kleinberg. 2005. A multiple-choice secretary algorithm with applications to online auctions. In Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms. Society for Industrial and Applied Mathematics, 630--631.
[23]
Ulrich Krengel and Louis Sucheston. 1977. Semiamarts and finite values. Bull. Amer. Math. Soc. 83, 4 (1977), 745--747.
[24]
Ulrich Krengel and Louis Sucheston. 1978. On semiamarts, amarts, and processes with finite value. Probability on Banach spaces 4 (1978), 197--266.
[25]
C-L. Li and D. Simchi-Levi. 1990. Worst-case analysis of heuristics for multidepot capacitated vehicle routing problems. INFORMS Journal on Computing 2, 1 (1990), 64--73.
[26]
Jane Lin, Wei Zhou, and Ouri Wolfson. 2016. Electric vehicle routing problem. Transportation Research Procedia 12, Supplement C (2016), 508--521.
[27]
D. V. Lindley. 1961. Dynamic Programming and Decision Theory. Journal of the Royal Statistical Society. Series C (Applied Statistics) 10, 1 (1961), 39--51.
[28]
Evdokia Nikolova and David Karger. 2008. Route Planning under Uncertainty: The Canadian Traveller Problem. In Proceedings of the Twenty-Third AAAI Conference on Artificial Intelligence, AAAI. 969--974.
[29]
Christos Papadimitriou and Mihalis Yannakakis. 1991. Shortest paths without a map. Theoretical Computer Science 84 (1991), 127--150.
[30]
Martin Sachenbacher, Martin Leucker, Andreas Artmeier, and Julian Haselmayr. 2011. Efficient energy-optimal routing for electric vehicles. In Twenty-fifth AAAI conference on artificial intelligence.
[31]
Ester Samuel-Cahn. 1984. Comparison of Threshold Stop Rules and Maximum for Independent Nonnegative Random Variables. The Annals of Probability 12, 4 (1984), 1213--1216.
[32]
P. Toth and D. Vigo (Eds.). 2001. The Vehicle Routing Problem. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA.
[33]
H. Yang, Y. Deng, J. Qiu, M. Li, M. Lai, and Z. Y. Dong. 2017. Electric Vehicle Route Selection and Charging Navigation Strategy Based on Crowd Sensing. IEEE Transactions on Industrial Informatics 13, 5 (2017), 2214--2226.

Cited By

View all
  • (2025)FRI: a firefighter risk index using spatiotemporal modelling of wildfire spread and individual travelInternational Journal of Disaster Risk Reduction10.1016/j.ijdrr.2024.105151(105151)Online publication date: Jan-2025

Recommendations

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM Conferences
SIGSPATIAL '22: Proceedings of the 30th International Conference on Advances in Geographic Information Systems
November 2022
806 pages
ISBN:9781450395298
DOI:10.1145/3557915
This work is licensed under a Creative Commons Attribution International 4.0 License.

Sponsors

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 22 November 2022

Check for updates

Author Tags

  1. electric vehicle routing
  2. online algorithms

Qualifiers

  • Research-article

Funding Sources

  • NSF
  • ARO

Conference

SIGSPATIAL '22
Sponsor:

Acceptance Rates

Overall Acceptance Rate 257 of 1,238 submissions, 21%

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)155
  • Downloads (Last 6 weeks)20
Reflects downloads up to 06 Jan 2025

Other Metrics

Citations

Cited By

View all
  • (2025)FRI: a firefighter risk index using spatiotemporal modelling of wildfire spread and individual travelInternational Journal of Disaster Risk Reduction10.1016/j.ijdrr.2024.105151(105151)Online publication date: Jan-2025

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media