Scaling Up the Microeconomic Dynamic Discrete Choice Model of Activity-based Scheduling
A Karlstrom, Royal Institute of Technology, SE; D Fox, P Waddell, University of Washington, US
An activity based scheduling model is considered. in a dynamic discrete choice framework. We report on many different methods and algorithms we have designed to tackle this problem in order to be able to scale up the problems we are able to estimate.
We move through life sequentially. We plan and implement decisions on where to go, when to stay, and what to do as time goes by. In an activity-based modelling, a trip cannot be seen in isolation, but should be viewed in the context of earlier behaviour and decisions, and later opportunities and constraints. As time passes, we receive new information and update our plans and decisions.
In this paper, we consider an activity based model in a microeconomic consistent dynamic discrete choice framework. In its simplest form, our framework is similar to the scheduling framework of Small (1982). However, we extend the modelling framework into a Markov Decision Problem (MDP) to model the activity schedule for an individual throughout a day, and in fact an infinite sequence of days. It should be noted that this theoretical model also extends the theory of value of time and reliability into a dynamic activity-based setting.
In our dynamic discrete choice framework, people are forward looking, considering what consequences the decision will have later. For instance, when taking car to work in the morning affects the opportunities and constraints in the afternoon, compared with choosing the transit. In fact, the accessibility pattern throughout the day may change as a consequence. Hence, to fully evaluate the mode choice in the morning, the individual considers its ramifications throughout the day.
To estimate a dynamic discrete choice activity model for a real-world problem one needs to address the computational burden. As the individual considers the ramifications throughout the day, the computational burden may be prohibitive, due to combinatorics, if the problem is of realistic size. In this paper we report the results of a few tricks and methods that we have designed and tested for estimating a activity based model in a DDC framework.
In the MDP framework, what makes the problem difficult is the dimension of states. Therefore, it is imperative to shrink the effective size of the state space. There are a number of methods available to achieve this. We explore different methods, including function approximation and feature extraction.
Continuous state variables are also challenging. In our activity model, time may be considered to be continuous, and also other variables may be viewed as essentially continuous, perhaps also two-dimensional geographical space. In this paper we explore different methods to handle continuous state variables. One is gaussian restricted boltzmann machines, another is tile coding. We discuss their different advantages and suggest that the first is used for preference parameters, while the second may be used to code geographical space, and time.
Also, any activity based model has rather demanding data requirements. Sometimes you have the possibility of designing travel surveys to feed the model of your choice. But sometimes the data set is already given. We have data sets from Stockholm and Pudget Sound, and therefore there are different data limitations to consider when designing models for each city.
We report the results from different algorithms for estimating the preference parameters of the activity model. One is based on inverted reinforcement learning, and it has earlier been used by some of us in novel applications such as crowding modelling. Another algorithm is based on MCMC, making it tractable to model preference heterogeneity. We also discuss the difference in using backward induction vs forward simulation, from a conceptual and applied point of view.
We argue that there are advantages and disadvantages with these algorithms in different settings and contexts. However, our results are also very encouraging in that there has been important progress made in making these models computationally more efficient than before.
Association for European Transport