An N-path user equilibrium for transportation networks

Two-Stage Multiclass Modeling Approach for Intermodal Rail-Road Transport Networks

“…A way to compute the arc flows corresponding to such equilibrium involves finding the optimum solution of the Beckmann's Transformation [37]. The N-Path Restricted variant of the aforementioned model [38] is obtained by constraining the assignment to a priori defined sets of admissible paths, which do not necessarily include all the possible ones for each origin-destination pair. This allows to avoid all the paths that are theoretically possible but quite implausible in practice.…”

“…Steady-state speed relationships defined for railway and roadway arcs (i, j) ∈ A H ∪ A R for each time step k (37), (38), (39) have been excluded. Then, denoted with l, l = 1, .…”

A modified Physarum-inspired model for the user equilibrium traffic assignment problem

“…According to the Eqs. (9)(10)(11)(12), the network Poisson equation for the pressure is derived as following:…”

“…In the existing literatures, many algorithms were designed to address the UE problem [9,10,11], which can be totally classed into three types: link based algorithms, path based algorithms and origin based algorithms. The linear approximation method of Frank and Wolfe (FW) [12] has been the most popular algorithm in practice because of its simplicity.…”

Extragradient algorithms for variational inequality, fixed point and generalized mixed equilibrium problems

“…In real world, there are many problems are reduced to finding solutions of equilibrium problems, which cover variational inequalities, fixed point problems, saddle point problems, complementarity problems as special cases. Equilibrium problem, which was first introduced by Fan [1] and further studied by Blum and Oettli [2], has been extensively studied as an effective and powerful tool for a wide class of real world problems which arise in economics, finance, image reconstruction, ecology, transportation, network and related optimization problems; see [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and the references therein. For solving solutions of variational inequalities, projection algorithms are efficient.…”