TY - JOUR

T1 - Sequential path-equilibration algorithm for highly accurate traffic flow assignment in an urban road network

AU - Крылатов, Александр Юрьевич

PY - 2023/5/22

Y1 - 2023/5/22

N2 - Nowadays, the issue of traffic flow assignment has become an interdisciplinary topic that concerns multiple research areas and branches of science. This work is focussed on the mathematical and computational aspects of the equilibrium traffic assignment problem in the case when route flows are considered to be decision variables. Firstly, we obtain a fixed-point mapping with the explicit contraction operator, which is proven to equilibrate the journey times on feasible routes between a single origin-destination pair of nodes with the quadratic rate. Remarkable that from mathematical perspectives, the developed operator generalizes most path-equilibration operators already exploited by researchers. Secondly, we use the obtained fixed-point procedure to run the sequential path-equilibration algorithm for traffic flow assignment on well-known test urban road networks with arc-additive travel time functions. Our computational results appear to demonstrate higher accuracy of user-equilibrium traffic assignment solutions than the best ones known to us. In other words, developed within this paper sequential path-equilibration algorithm leads to solutions with less goal function values compared to the best solutions for today, according to our knowledge.

AB - Nowadays, the issue of traffic flow assignment has become an interdisciplinary topic that concerns multiple research areas and branches of science. This work is focussed on the mathematical and computational aspects of the equilibrium traffic assignment problem in the case when route flows are considered to be decision variables. Firstly, we obtain a fixed-point mapping with the explicit contraction operator, which is proven to equilibrate the journey times on feasible routes between a single origin-destination pair of nodes with the quadratic rate. Remarkable that from mathematical perspectives, the developed operator generalizes most path-equilibration operators already exploited by researchers. Secondly, we use the obtained fixed-point procedure to run the sequential path-equilibration algorithm for traffic flow assignment on well-known test urban road networks with arc-additive travel time functions. Our computational results appear to demonstrate higher accuracy of user-equilibrium traffic assignment solutions than the best ones known to us. In other words, developed within this paper sequential path-equilibration algorithm leads to solutions with less goal function values compared to the best solutions for today, according to our knowledge.

KW - Sequential optimization

KW - decomposition

KW - non-linear optimization

KW - path-equilibration techniques

KW - user-equilibrium route-flow traffic assignment

UR - https://www.mendeley.com/catalogue/93448000-a496-3327-9c3b-32647f4ff7f3/

U2 - 10.1080/10556788.2023.2196725

DO - 10.1080/10556788.2023.2196725

M3 - Article

VL - 38

SP - 1081

EP - 1104

JO - Optimization Methods and Software

JF - Optimization Methods and Software

SN - 1055-6788

IS - 5

ER -