Methodology 

In combinatorial optimsation the aim is to select a combination of household from a sample survey that, when aggregated, best-fit known small-area constraints (i.e. published tabular counts). In essence this is a survey reweighting problem - finding a set of (integer) household survey weights that simultaneously satisfy a range of external person- and household-level constraints (see Figure 1).

A variety of survey reweighting approaches exist, including Generalised Regression (GREG), raking (a direct equivalent to Iterative Proportional Fitting) and Combinatorial Optimisation (CO). Unfortunately GREG and Raking-based reweighting approaches suffer from convergence problems, a problem which becomes more severe as area size reduces and/or the numer of constraints to be satisfied increases. The CO algorithm uses a form of guided random search (simulated annealing) to avoid these convergence problems. Simulated annealing is a variant of a straightforward random 'hill-climbing' approach, in which occasional 'backwards' steps are allowed to avoid getting stuck in a local sub-optima.

Full details of the CO approach are described in print, and in a series of working papers.