Using Particle Swarm Optimization to Determine the Optimal Strata Boundaries

Abstract

Stratified random sampling is a commonly used sampling methodology especially for heterogeneous populations with outliers. Stratified sampling is preferably employed due to its capability of improving statistical precision by yielding a smaller variance of the estimator, compared with simple random sampling. In order to reduce the variance of the estimator in stratified sampling, the problems of stratum boundary determination and sample allocation must be resolved initially. This paper proposes a PSO algorithm to solving the problem of stratum boundary determination in heterogeneous populations while distributing the sample size according to Neyman allocation method. The PSO algorithm is tested on two groups of populations and a comparative study with Kozak, GA and Delanius and Hodges methods have been implemented. The numerical results show the ability of the proposed algorithm to find the optimal stratified boundaries for a set of standard populations and various standard test functions compared with other algorithms.