Sampling Alternatives from Colossal Choice Set: Application of Markov Chain Monte Carlo Algorithm

Abstract

It is often the case that a discrete choice model cannot be applied to forecasting because the choice set is unmanageably large and choice probabilities cannot be evaluated in a practical manner. For example, an activity-based analysis of travel behavior often involves an astronomical number of potential activity travel patterns, resulting in an enormous choice set when one attempts to formulate the behavior as a discrete choice. A colossal choice set makes it practically impossible to define the full choice set and to evaluate the choice probability of each pattern for forecasting. An algorithm is presented for the simulation of individuals’ activity travel choice by sampling activity travel patterns from a colossal choice set, according to their choice probabilities as determined by a discrete choice model without enumeration of the full choice set. Numerical examples demonstrate the practicality and effectiveness of the algorithm in forecasting the effects on activity travel patterns of transportation policy measures.