Geodesic
Non-linear optimization for continuous travel demand estimation
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 1, pp. 40-46 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Models and methods of traffic distribution are being developed by researchers all over the world. The development of this scientific field contributes to both theory and practice. In this article, the non-linear optimization of traffic flow re-assignment is examined in order to solve continuously the travel demand estimation problem. An approach has been developed in the form of computational methodology to cope with the network optimization problem. A uniqueness theorem is proved for a certain type of road network. Explicit relations between travel demand and traffic flow are obtained for a single-commodity network of non-intersecting routes with special polynomial travel time functions. The obtained findings contribute to the theory and provide a fresh perspective on the problem for transportation engineers.
Keywords: travel demand estimation, traffic assignment problem, non-linear optimization, bi-level optimization. 
@article{VSPUI_2021_17_1_a3,
     author = {A. P. Raevskaya and A. Yu. Krylatov},
     title = {Non-linear optimization for continuous travel demand estimation},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {40--46},
     year = {2021},
     volume = {17},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2021_17_1_a3/}
}
TY  - JOUR
AU  - A. P. Raevskaya
AU  - A. Yu. Krylatov
TI  - Non-linear optimization for continuous travel demand estimation
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2021
SP  - 40
EP  - 46
VL  - 17
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2021_17_1_a3/
LA  - en
ID  - VSPUI_2021_17_1_a3
ER  - 
%0 Journal Article
%A A. P. Raevskaya
%A A. Yu. Krylatov
%T Non-linear optimization for continuous travel demand estimation
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2021
%P 40-46
%V 17
%N 1
%U http://geodesic.mathdoc.fr/item/VSPUI_2021_17_1_a3/
%G en
%F VSPUI_2021_17_1_a3
A. P. Raevskaya; A. Yu. Krylatov. Non-linear optimization for continuous travel demand estimation. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 17 (2021) no. 1, pp. 40-46. http://geodesic.mathdoc.fr/item/VSPUI_2021_17_1_a3/

[1] Wardrop J., “Some theoretical aspects of road traffic research”, Proceedings of the Institute of Civil Engineers, 1:3 (1952), 325–362 | DOI

[2] Krylatov A., Zakharov V., Malygin I., “Competitive traffic assignment in road networks”, Transport and Telecommunication, 17:3 (2016), 212–221 | DOI | MR

[3] Krylatov A., Zakharov V., “Competitive traffic assignment in a green transit network”, International Game Theory Review, 18:2 (2016), 1640003 | DOI | MR | Zbl

[4] Zakharov V., Krylatov A., Ivanov D., “Equilibrium traffic flow assignment in case of two navigation providers”, IFIP Advances in Information and Communication Technology, 408 (2013), 156–163 | DOI

[5] Zakharov V., Krylatov A., “Transit network design for green vehicles routing”, Advances in Intelligent Systems and Computing, 360 (2015), 449–458 | DOI | Zbl

[6] Beckman M., McGuire C., Winsten C., Studies in economics of transportation, RM-1488, RAND Corporation Publ., Santa Monica, 1955, 232 pp.

[7] Sheffi Y., Urban transportation in networks: equilibrium analysis with mathematical programming methods, Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1985, 416 pp. | MR

[8] Yang H., Huang H.-J., “The multi-class, multi-criteria traffic network equilibrium and system optimum problem”, Transportation Research Part B, 38 (2004), 1–15 | DOI

[9] Krylatov A., “Reduction of a minimization problem for a convex separable function with linear constraints to a fixed point problem”, Journal of Applied and Industrial Mathematics, 12:1 (2018), 98–111 | DOI | MR | Zbl

[10] Krylatov A., Shirokolobova A., “Equilibrium route flow assignment in linear network as a system of linear equations”, Vestnik of Saint Petersburg University. Applied Mathematics. Computer Sciences. Control Processes, 14:2 (2018), 103–115 | DOI | MR

[11] Krylatov A., Zakharov V., Tuovinen T., Optimization models and methods for equilibrium traffic assignment, Springer Intern. Publ., New York, 2020, 239 pp. | MR

[12] Krylatov A., Shirokolobova A., “Projection approach versus gradient descent for network's flows assignment problem”, Lecture Notes in Computer Science, 10556, 2017, 345–350 | DOI