A tutorial on recursive models for analyzing and predicting path choice behavior

The problem at the heart of this tutorial consists in modeling the path choice behavior of network users. This problem has been extensively studied in transportation science, where it is known as the route choice problem. In this literature, individuals' choice of paths are typically predicted using discrete choice models. This article is a tutorial on a specific category of discrete choice models called recursive, and it makes three main contributions: First, for the purpose of assisting future research on route choice, we provide a comprehensive background on the problem, linking it to different fields including inverse optimization and inverse reinforcement learning. Second, we formally introduce the problem and the recursive modeling idea along with an overview of existing models, their properties and applications. Third, we extensively analyze illustrative examples from different angles so that a novice reader can gain intuition on the problem and the advantages provided by recursive models in comparison to path-based ones

A model-free approach for solving choice-based competitive facility location problems using simulation and submodularity

This paper considers facility location problems in which a firm entering a market seeks to open a set of available locations so as to maximize its expected market share, assuming that customers choose the alternative that maximizes a random utility function. We introduce a novel deterministic equivalent reformulation of this probabilistic model and, extending the results of previous studies, show that its objective function is submodular under any random utility maximization model. This reformulation characterizes the demand based on a finite set of preference profiles. Estimating their prevalence through simulation generalizes a sample average approximation method from the literature and results in a maximum covering problem for which we develop a new branch-and-cut algorithm. The proposed method takes advantage of the submodularity of the objective value to replace the least influential preference profiles by an auxiliary variable that is bounded by submodular cuts. This set of profiles is selected by a knee detection method. We provide a theoretical analysis of our approach and show that its computational performance, the solution quality it provides, and the efficiency of the knee detection method it exploits are directly connected to the entropy of the preference profiles in the population. Computational experiments on existing and new benchmark sets indicate that our approach dominates the classical sample average approximation method on large instances, can outperform the best heuristic method from the literature under the multinomial logit model, and achieves state-of-the-art results under the mixed multinomial logit model.Comment: 36 pages, 6 figures, 6 table

Random Sampling of Alternatives in a Route Choice Context

In this paper we present a new point of view on choice set generation and route choice modeling. Choice sets of paths need to be defined when model-ing route choice behavior using random utility models. Existing approaches generate paths and assume that actual choice sets are found. On the contrary, we assume that actual choice sets are the sets of all paths connecting each origin-destination pair. These sets are however unknown and we propose a stochastic path generation algorithm that corresponds to an importance sam-pling approach. The path utilities should then be corrected according to the used sampling protocol in order to obtain unbiased parameter estimates. We derive such a sampling correction for the proposed algorithm. Furthermore, based on the assumption that actual choice sets contain all paths, we argue that Path Size (or Commonality Factor) attributes should be computed on all paths (or as many as possible) in order to reflect the true correlation struc-ture. We present numerical results based on synthetic data. The results show that models including a sampling correction are remarkably better than the ones that do not. Moreover, unbiased estimation results are obtained if the Path Size attribute is computed based on all paths and not on generated choice sets. In real networks the set of all paths is unknown, we therefore study how many paths are needed for the Path Size computation in order to obtain unbiased results. The parameter estimates improve rather rapidly with the number of paths which is promising for real applications

A decomposition method for estimating recursive logit based route choice models

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On the similarities between random regret minimization and mother logit: The case of recursive route choice models

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A nested recursive logit model for route choice analysis

We propose a route choice model that relaxes the independence from irrelevant alternatives property of the logit model by allowing scale parameters to be link specific. Similar to the the recursive logit (RL) model proposed by Fosgerau et al. (2013), the choice of path is modelled as a sequence of link choices and the model does not require any sampling of choice sets. Furthermore, the model can be consistently estimated and efficiently used for prediction. A key challenge lies in the computation of the value functions, i.e. the expected maximum utility from any position in the network to a destination. The value functions are the solution to a system of non-linear equations. We propose an iterative method with dynamic accuracy that allows to efficiently solve these systems. We report estimation results and a cross-validation study for a real network. The results show that the NRL model yields sensible parameter estimates and the fit is significantly better than the RL model. Moreover, the NRL model outperforms the RL model in terms of prediction

A misspecification test for logit based route choice models

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Bike route choice modeling using GPS data without choice sets of paths

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