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

Abstract

In this paper we combine the k-means and/or k-means type algorithms with a hill climbing algorithm in stages to solve the joint stratification and sample allocation problem. This is a combinatorial optimisation problem in which we search for the optimal stratification from the set of all possible stratifications of basic strata. Each stratification being a solution the quality of which is measured by its cost. This problem is intractable for larger sets. Furthermore evaluating the cost of each solution is expensive. A number of heuristic algorithms have already been developed to solve this problem with the aim of finding acceptable solutions in reasonable computation times. However, the heuristics for these algorithms need to be trained in order to optimise performance in each instance. We compare the above multi-stage combination of algorithms with three recent algorithms and report the solution costs, evaluation times and training times. The multi-stage combinations generally compare well with the recent algorithms both in the case of atomic and continuous strata and provide the survey designer with a greater choice of algorithms to choose from.

A hybrid estimation of distribution algorithm for joint stratification and sample allocation

“…The execution times and total execution are, generally, significantly higher for the HEDA than some of the best alternative performing algorithms (especially the clustering algorithms considered in (O'Luing et al, 2021)). However, it is worth recalling that the HC algorithm in the above experiments had converged on a solution and would not have attained better results without adjusting the stopping conditions for algorithm or adjusting the solution.…”

“…This quality is evaluated by the Bethel-Chromy algorithm (Bethel, 1985;Chromy, 1987;Bethel, 1989) which is expensive (in computational terms). Previous contributions in this area includes work carried out by (Kozak et al, 2007;Keskintürk and Er, 2007;Benedetti et al, 2008;Rivest, 2009, 2011;Ballin and Barcaroli, 2013;O'Luing et al, 2019;Ballin and Barcaroli, 2020;O'Luing et al, 2020O'Luing et al, , 2021.…”

“…That has been our focus in earlier papers in which we presented evolutionary (a grouping genetic algorithm - (O'Luing et al, 2019)) and local search (simulated annealing algorithm - (O'Luing et al, 2020) algorithms and explored multi-stage combinations of clustering algorithms with a hill-climbing algorithm ((O'Luing et al, 2021)). We have evaluated the performance of these algorithms by the solution quality and computation time taken to find a local minimum.…”

“…We have evaluated the performance of these algorithms by the solution quality and computation time taken to find a local minimum. In (O'Luing et al, 2020) and (O'Luing et al, 2021) we also considered training times. The performance has varied according to each data stratification problem.…”

“…To expand on the details mentioned above, we explore a new paradigm of evolutionary algorithms named estimation of distribution algorithms (EDAs) (Baluja, 1994;Mühlenbein and Paaß, 1996;Larrañaga and Lozano, 2001;Pelikan et al, 2003) in the context of this problem. In particular, we consider the application of a hybridised version of an EDA and compare it against the best results achieved so far with the algorithms discussed in (O'Luing et al, 2019), (O'Luing et al, 2020) and (O'Luing et al, 2021).…”