Allocating synthetic population to a finer spatial scale: An integer quadratic programming formulation

Agent-Based Models (ABMs) are being increasingly used to evaluate urban systems, urban policies and environmental impacts. One prerequisite for using the ABM framework consists of generating a synthetic population representative of the actual population, featuring the appropriate attributes with respect to model objectives. A precise spatial positioning of the synthetic population agents is often key to ensuring ABM modeling quality. This paper considers the problem of allocating synthetic population agents to a finer spatial scale. Such an allocation process is performed from a higher-level statistical area where a synthetic population can be generated, that is, a container statistical area (CSA), to several nested non-overlapping elementary statistical areas (ESAs), where only marginals are available. This allocation step relies not only on common attributes between CSA and ESA, but also on additional discriminatory attributes, that is, attributes of interest, estimated from external data sources. The case study examined herein is based on French census and fiscal data. Common attributes include eight socio-demographic variables, totaling 17 modalities. An additional attribute of interest, that is, income, has also been added. The allocation problem at hand is modeled as an integer quadratic programming problem. An exact algorithm is first applied to solve the problem; the applicability of this algorithm proves to be limited to small-size synthetic populations. A heuristic is proposed to handle the allocation of larger-size synthetic populations. Tests carried out on the case study show that this heuristic yields near-optimal solutions; it is also computationally efficient and may fulfill the needs of a majority of users.