Impact Factor (JCC): 1.1947- This article can be downloaded from www.bestjournals.in USING ARTIFICIAL BEE COLONY ALGORITHMTO DETERMINE THE OPTIMAL STRATA BOUNDARIES MOWAFAQ MUHAMMED AL-KASSAB & MUHAMMED ABDULJABBAR AL-HASAWY Department of Statistics & Informatics, College of Mathematics and Computer Sciences, University of Mosul, Mosul, Iraq ABSTRACT Stratified random sampling is used when the researcher wants to highlight a specific subgroup within the population. This technique is useful in such researches because it ensures the presence of the key subgroup within the sample. A few numerical and computational techniques have been created for this reason.Some apply to highly skewed populations and some apply to any kind of populations. This paper proposes an ABC algorithm to solve the problem of stratum boundary while distributing the sample size according to Proportional Allocation method. The ABC algorithm is tested on two groups of populations and a comparative study with Genetic Algorithm (GA) of Keskintürk and Er (2007), Kozak’s (2004), Lavallée and Hidiroglou’s (1988) and Dalenius and Hodges(1959) 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. KEYWORDS: Stratified random sampling, Artificial Bee Colony, Optimal Strata Boundaries, Proportional Allocation 1. INTRODUCTION Stratified random sampling is a generally utilized sampling procedures particularly for heterogeneous population. Stratified examining is ideally utilized because of its ability of yielding so as to enhance measurable exactness a smaller variance of the estimator, compared with simple random sampling. With a specific end goal to decrease the variance of the estimator in stratified sampling the problems of stratum limit determination and sample allocation must be resolvedinitially. A principal use of stratification, in order to obtain a better precision, is in defining what percentage of the sample must be taken from each stratum once we have chosen a non-uniform allocation scheme, that is, a non-trivial functional relation between the size of each stratum and the number of sample units to be collected in it. Thus, it is important to consider the allocation scheme itself in order to do a suitable stratification [6]. Several numerical and computational methods have been developed for obtaining the optimum boundaries in stratified sampling. Some apply to highly skewed populations and some apply to any kind of populations. An early and very simple method is the cumulative square root of the frequency method (cum√f) of Dalenius& Hodges in 1959 [8]. More recently Lavallée & Hidiroglou algorithm [16] and Gunning & Horgan's (2004) geometric method[9] have been proposed for highly skewed populations whereas Kozak's (2004) random search method [15] and Keskinturk&Er's (2007) genetic algorithm (GA) method [14] have been proposed for even non-skewed populations. This study presents the ABC algorithm for the determination of stratum boundaries. In order to explore the efficiency of ABC algorithm, we compare its efficiency with GA, Kozak, LH and Delanius and Hodges methods BEST: International Journal of Humanities, Arts, Medicine and Sciences (BEST: IJHAMS) ISSN (P): 2348-0521, ISSN (E): 2454-4728 Vol. 3, Issue 12, Dec 2015, 227-238 © BEST Journals