A Grouping Genetic Algorithm for Joint Stratification and Sample Allocation Designs

TL;DR

This paper introduces a novel grouping genetic algorithm for efficient joint stratification and sample allocation in large-scale multivariate survey designs, significantly improving solution quality and reducing costs.

Contribution

It proposes a new grouping genetic algorithm approach that outperforms traditional methods in finding optimal stratification and sample allocation.

Findings

Significant improvement in solution quality

Large monetary savings achieved

Faster convergence to near-optimal solutions

Abstract

Predicting the cheapest sample size for the optimal stratification in multivariate survey design is a problem in cases where the population frame is large. A solution exists that iteratively searches for the minimum sample size necessary to meet accuracy constraints in partitions of atomic strata created by the Cartesian product of auxiliary variables into larger strata. The optimal stratification can be found by testing all possible partitions. However the number of possible partitions grows exponentially with the number of initial strata. There are alternative ways of modelling this problem, one of the most natural is using Genetic Algorithms (GA). These evolutionary algorithms use recombination, mutation and selection to search for optimal solutions. They often converge on optimal or near-optimal solution more quickly than exact methods. We propose a new GA approach to this problem using grouping genetic operators instead of traditional operators. The results show a significant improvement in solution quality for similar computational effort, corresponding to large monetary savings.