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In this paper we combine the k-means and/or k-means type algorithms with ahill climbing algorithm in stages to solve the joint stratification and sampleallocation problem. This is a combinatorial optimisation problem in which wesearch for the optimal stratification from the set of all possiblestratifications of basic strata. Each stratification being a solution thequality of which is measured by its cost. This problem is intractable forlarger sets. Furthermore evaluating the cost of each solution is expensive. Anumber of heuristic algorithms have already been developed to solve thisproblem with the aim of finding acceptable solutions in reasonable computationtimes. However, the heuristics for these algorithms need to be trained in orderto optimise performance in each instance. We compare the above multi-stagecombination of algorithms with three recent algorithms and report the solutioncosts, evaluation times and training times. The multi-stage combinationsgenerally compare well with the recent algorithms both in the case of atomicand continuous strata and provide the survey designer with a greater choice ofalgorithms to choose from.

Combining K-means type algorithms with Hill Climbing for Joint Stratification and Sample Allocation Designs