Finding the Shortest Path in Stochastic Vehicle Routing: A Cardinality Minimization Approach

IEEE Transactions on Intelligent Transportation Systems

Volumn 17, Issue 6, 2016, Pages 1688-1702

  Cao, Zhiguang ^a,b   Guo, Hongliang ^a   Zhang, Jie ^a   Niyato, Dusit ^a   Fastenrath, Ulrich ^c  

^a NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^b NANYANG TECHNOLOGICAL UNIVERSITY   (Singapore)

^c BMW GROUP   (Germany)

Author keywords

cardinality minimization; l1 norm minimization; mixed integer linear programming; Stochastic shortest path

Indexed keywords

BIG DATA; COMPLEX NETWORKS; GRAPH THEORY; INTEGER PROGRAMMING; MATHEMATICAL TRANSFORMATIONS; PROBABILITY; PROBLEM SOLVING; ROADS AND STREETS; STOCHASTIC SYSTEMS; TRAFFIC CONTROL; TRANSPORTATION; TRAVEL TIME; VEHICLES;

CARDINALITY PROBLEMS; DATA-DRIVEN APPROACH; MINIMIZATION PROBLEMS; MINIMIZATION TECHNIQUES; MIXED INTEGER LINEAR PROGRAMMING PROBLEMS; SHORTEST PATH PROBLEM; STOCHASTIC SHORTEST PATH PROBLEM; STOCHASTIC VEHICLE ROUTING;

PROBABILITY DISTRIBUTIONS;

EID: 84949844750     PISSN: 15249050     EISSN: None     Source Type: Journal    
DOI: 10.1109/TITS.2015.2498160     Document Type: Article

References (36)

1. H. Guo, Z. Cao, J. Zhang, D. Niyato, and U. Fastenrath, "Routing multiple cars in large scale networks: Minimizing road network breakdown probability," in Proc. 17th IEEE ITSC, 2014, pp. 2180-2187.
2. E. D. Miller-Hooks and H. S. Mahmassani, "Least expected time paths in stochastic, time-varying transportation networks," Transp. Sci., vol. 34, no. 2, pp. 198-215, May 2000.
3. B. C. Dean, "Algorithms for minimum-cost paths in time-dependent networks with waiting policies," Networks, vol. 44, no. 1, pp. 41-46, Aug. 2004.
4. S. T. Waller and A. K. Ziliaskopoulos, "On the online shortest path problem with limited arc cost dependencies," Networks, vol. 40, no. 4, pp. 216-227, Dec. 2002.
5. E. Nikolova, J. A. Kelner, M. Brand, and M. Mitzenmacher, "Stochastic shortest paths via quasi-convex maximization," in Algorithms-ESA 2006. Berlin, Germany: Springer-Verlag, 2006, pp. 552-563.
6. E. Nikolova, "Approximation algorithms for reliable stochastic combinatorial optimization," in Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques. Berlin, Germany: Springer-Verlag, 2010, pp. 338-351.
7. C. E. Sigal, A. A. B. Pritsker, and J. J. Solberg, "The stochastic shortest route problem," Oper. Res., vol. 28, no. 5, pp. 1122-1129, Sep./Oct. 1980.
8. M. D. Becker and U. D. Fastenrath, "Verfahren zur Auswahl einer Route für eine dynamische Navigation von Individualverkehr," DE Patent App. DE200 710 060 590, Jun. 18, 2009.
9. H. Frank, "Shortest paths in probabilistic graphs," Oper. Res., vol. 17, no. 4, pp. 583-599, Jul./Aug. 1969.
10. Y. Fan, R. Kalaba, and J. Moore, II, "Arriving on time," J. Optim. Theory Appl., vol. 127, no. 3, pp. 497-513, Dec. 2005.
11. Y. M. Nie and X. Wu, "Shortest path problem considering on-time arrival probability," Transp. Res. B, Methodol., vol. 43, no. 6, pp. 597-613, Jul. 2009.
12. S. Lim, H. Balakrishnan, D. Gifford, S. Madden, and D. Rus, "Stochastic motion planning and applications to traffic," in Algorithmic Foundation of Robotics VIII. Berlin, Germany: Springer-Verlag, 2009, pp. 483-500.
13. J. G. Wardrop, "Road paper. Some theoretical aspects of road traffic research," Proc. Inst. Civil Eng., vol. 1, no. 3, pp. 325-362, May 1952.
14. A. Polus, "A study of travel time and reliability on arterial routes," Transportation, vol. 8, no. 2, pp. 141-151, Jun. 1979.
15. M. Mogridge and S. Fry, "Variability of car journey times on a particular route in central London," Traffic Eng. Control, vol. 25, no. 10, pp. 510-511, Oct. 1984.
16. F. Montgromery and A. May, "Factors affecting travel times on urban radial routes," Traffic Eng. Control, vol. 28, no. 9, pp. 452-458, Sep. 1987.
17. H. Rakha, I. El-Shawarby, M. Arafeh, and F. Dion, "Estimating path travel-time reliability," in Proc. IEEE ITSC, 2006, pp. 236-241.
18. K. Chen, L. Yu, J. Guo, and H. Wen, "Characteristics analysis of road network reliability in Beijing based on the data logs from taxis," in Proc. Transp. Res. Board 86th Annu. Meet., 2007, pp. 1-19.
19. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2009.
20. N. Kallus, "From predictions to data-driven decisions using machine learning," ArXiv Preprint ArXiv:1402.5481, 2014.
21. D. Solomatine, "Applications of data-driven modelling and machine learning in control of water resources," in Computational Intelligence in Control. Hershey, PA, USA: IGI Global, 2002, pp. 197-217.
22. Y. Wang, Y. Zheng, and Y. Xue, "Travel time estimation of a path using sparse trajectories," in Proc. 20th ACM SIGKDD Int. Conf. Knowl. Discov. Data Mining, 2014, pp. 25-34.
23. Z. Cao, H. Guo, J. Zhang, D. Niyato, and U. Fastenrath, "A data-driven method for stochastic shortest path problem," in Proc. 17th IEEE ITSC, 2014, pp. 1045-1052.
24. M. J. Abdi, "Cardinality optimization problems," Ph.D. dissertation, School Math., Univ. Birmingham, Birmingham, U.K., 2013.
25. M. Fazel, H. Hindi, and S. P. Boyd, "A rank minimization heuristic with application to minimum order system approximation," in Proc. Amer. Control Conf., 2001, vol. 6, pp. 4734-4739.
26. S.-J. Kim, K. Koh, S. Boyd, and D. Gorinevsky, "1 trend filtering," SIAM Rev., vol. 51, no. 2, pp. 339-360, May 2009.
27. P. D. Tao and L. T. H. An, "The dc (difference of convex functions) programming and dca revisited with dc models of real world nonconvex optimization problems," Ann. Oper. Res., vol. 133, no. 1-4, pp. 23-46, Jan. 2005.
28. Y.-B. Zhao and D. Li, "Reweighted 1 minimization for sparse solutions to underdetermined linear systems," SIAM J. Optim., vol. 22, no. 3, pp. 1065-1088, 2012.
29. Mixed-Integer Linear Programming Algorithms, MathWorks, Natick, MA, USA, 2014. [Online]. Available: http://www.mathworks.com/help/optim/ug/mixed-integer-linear-programming-algorithms.html
30. Y. Zhang, "Solving large-scale linear programs by interior-point methods under the MATLAB environment," Optim. Methods Softw., vol. 10, no. 1, pp. 1-31, Jan. 1998.
31. E. Danna, E. Rothberg, and C. Le Pape, "Exploring relaxation induced neighborhoods to improve MIP solutions," Math. Programm., vol. 102, no. 1, pp. 71-90, Jan. 2005.
32. G. L. Nemhauser and L. A.Wolsey, Integer and Combinatorial Optimization, vol. 18. New York, NY, USA: Wiley, 1988.
33. M. Fazel, H. Hindi, and S. P. Boyd, "Log-det heuristic for matrix rank minimization with applications to Hankel and Euclidean distance matrices," in Proc. Amer. Control Conf., 2003, vol. 3, pp. 2156-2162.
34. W. Zhang, "Branch-and-bound search algorithms and their computational complexity," USC Inf. Sci. Inst., Marina del Rey, CA, USA, ISI/RR-96-443, 1996.
35. N. Karmarkar, "A new polynomial-time algorithm for linear programming," in Proc. 16th Annu. ACM Symp. Theory Comput., 1984, pp. 302-311.
36. Y. Bengio et al., "Out-of-sample extensions for LLE, Isomap, MDS, Eigenmaps, and spectral clustering," in Proc. Adv. Neural Inf. Process. Syst., 2004, vol. 16, pp. 177-184.