A genetic algorithm approach to determine stratum boundaries and sample sizes of each stratum in stratified sampling

Abstract

Stratified sampling is a methodology in which a heterogeneous population is partitioned into homogeneous subgroups called strata. The focus is on solving the combined problem of sample allocation and stratum boundary determination with the genetic algorithm (GA). Assuming that the number of strata and the total sample size are arbitrarily predetermined, stratum boundaries are determined using an objective function of minimum variance of the estimator; with sample size allocated through equal, proportional, Neyman, and GA allocation methods. Some numerical examples are given and the performance of GA is compared with the geometric and the cumulative root frequency methods.