78 research outputs found
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 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
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