Determining optimum cluster size and sampling unit for multivariate study

When a cluster sampling design is to be used and more than one characteristic are under study, usually it is not possible to use the individual optimum cluster size and sampling unit for one reason or the other. In such situations some criterion is needed to work out an acceptable cluster size and sampling unit which are optimum for all characteristics in some sense. Moreover, for practical implementation of sample size, we need integer values of the cluster size and sampling unit. The present paper addresses the problem of determining integer optimum compromise cluster size and sampling unit when the population means of various characteristic are of interest. The problem is formulated as an All Integer Nonlinear Programming Problem (AINLPP) and a solution procedure is proposed using evolutionary algorithm. The result shows that evolutionary algorithm can be efficiently applied in determining the sample size in multivariate cluster sampling design. A numerical example is presented to illustrate the practical application of the solution procedure.