Title: A Grouping Genetic Algorithm for Joint Stratification and Sample Allocation Designs,
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.