Approaches for solving the stochastic equilibrium assignment with variable demand: internal vs. external solution algorithms

Abstract

This paper proposes and compares different approaches within the general fixed-point framework that allows to deal with multi-user (stochastic) equilibrium assignment with variable demand (VD). The aim was threefold: (i) compare the efficiency and the effectiveness of the internal and the external approaches to stochastic equilibrium assignment with VD; (ii) investigate the efficiency and the effectiveness of different algorithms based on the method of successive averages and its extensions; (iii) investigate the effects of different averaging schemes, different convergence criteria and different path choice models, such as Multinomial Logit model, C-Logit model and Multinomial Probit model. Analyses were carried out with respect to a real network and considering different indicators of both efficiency and effectivenes

Location Optimization of Electric Vehicle Mobile Charging Stations Considering Multi-Period Stochastic User Equilibrium

“…As can be seen, the formulation is a nonlinear mixed integer-programming model. To simplify the procedure of problem solving, we transform the original formulation into a mixed-integer linear programming (MILP) model using linearization technology [45]. Thus, we obtain the global optimal solution using the CPLEX solver on the NEOS cloud based on the classic algorithm of the branch and bound.…”

A Methodology for Increasing Convergence Speed of Traffic Assignment Algorithms Based on the Use of a Generalised Averaging Function

“…the Refresh Memory method (RM), also indicated as Restarting MSA method (RMSA), proposed by Reference [18] and applied by Reference [12], whose ξ(k) function may be formulated as follows:…”

“…Alternative step sequences (or weighting methods) were proposed, among others, by References [9][10][11]. More recently, Reference [12] proposed three revised versions of the traditional MSA method, namely: (i) Restarting MSA (RMSA), where the iteration counter is re-initialised after a specific number of iterations; (ii) Double RMSA (R2MSA), where the iteration counter is re-initialised to a variable value; (iii) Weighted MSA (WMSA), based on the self-regulated averaging method proposed by Reference [13] for solving the stochastic user equilibrium problem. The above-mentioned MSA schemes have been adopted by Reference [14] for solving a stochastic frequency-based assignment considering pre-trip/en-route path choice behaviour.…”

A Simplified C-Logit Stochastic User Equilibrium Model on Bimodal Transportation Network

“…e MNL possesses a closed-form expression of path choice behavior but inheres in the drawback of independence of irrelevant alternative (IIA) property, that is, it is unable to account for overlapping effect and covariance among the different travel path cost [5,6]. e MNP model overcomes such a drawback by taking the path cost covariance into account, but there are relatively few studies in the area of Probit SUE, such as Lam and Xu [7], Meng et al [8], Meng and Liu [9], Cantarella et al [10], and Jing et al [11] since it does not possess a explicit closed-form expression and behavioural interpretation. Generally, the MNP model describes travelers' path choice behaviors by using some simulation-based methods [1,9,12].…”