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

TL;DR

This paper introduces a multi-stage heuristic combining k-means algorithms with hill climbing to efficiently solve the complex joint stratification and sample allocation problem, outperforming recent algorithms in solution quality and flexibility.

Contribution

It presents a novel multi-stage heuristic approach that integrates k-means and hill climbing algorithms for joint stratification and sample allocation, improving solution quality and computational efficiency.

Findings

Multi-stage heuristic compares well with recent algorithms in solution cost.

The approach is effective for both atomic and continuous strata.

Provides survey designers with more algorithm options.

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.