**1. Introduction**

Transportation simulation models are widely used for travel demand forecasting, testing design alternatives, or predicting travel behavior. In 1992, Axhausen and Gärling [1] developed a comprehensive review of conceptualizations and approaches of activity-based transportation models with special regard to the validity of behavioral assumptions of modeled population. In the course of their review, they concluded that individual travelers and households, rather than aggregates, should be identified and considered. Nevertheless, detailed travel records for individuals have never been easily accessible for several reasons, the most important being privacy issues and cost. Hence, individual travel diaries needed to be synthesized from travel surveys, census data, and publically available records. That process has since been known as population synthesis.

Population synthesizers initially were used as feeder data avenues to travel demand models [2]; however, recent shifts toward activity- and agent-based models brought population synthesizers to the spotlight, as they became determinants to the success or failure of any transportation model of that kind. Fitting is the core

of any population synthesizer, with the main focus on fitting disaggregate sample of agents (represented by tabulated demographics of a representative sample of household and individual data) to aggregate constraints (represented by available aggregate data, such as data available from census). There are several approaches for fitting including iterative proportional fitting (IPF), iterative proportional updating (IPU), combinatorial optimization, Markov-based and fitness-based syntheses (FBS), and other emerging approaches [3]. The following sections present a critical review of each approach in the chronological order by which they were introduced to illustrate the progression and evolution of each approach, with emphasis on notable and well-established efforts.
