Abstract

Population synthesis has a long tradition within the micro-simulation and agent-based simulation domains. Traditional synthesis methods like Iterative Proportional Fitting (IPF) and Generalized Raking (GR) have been applied numerous times to generate agent-based populations required for simulation applications. Here we show such methods fail to generate adequate populations when trying to match aggregated counts with an incomplete set of marginals, such as those provided by the Mexican census. We discuss how and why these methods fail. We do so by studying the properties of linear systems that describe the census constraints. We then propose a new method to generate a synthetic population with integer counts based on a Mathematical Programming approach that satisfies both people and household constraints simultaneously and exactly. Our method can handle equality and inequality constraints, the latter of such being commonplace in the Mexican census. By being able to fit inequality constraints, we can naturally account for uncertainties in count statistics. Unlike methods based on IPF and GR, sample weights are optional, but can be accounted for during the fit. Furthermore, the method can generate a family of solutions, instead of a single best-fit solution, ranked by the fit statistic, a useful property for performing sensibility analysis. We demonstrate the method by generating a synthetic population for transport simulations in the Mexican city of Monterrey, analyze the properties of the fitted solutions, and perform a comparison with solutions obtained from IPF and GR.