In survey sampling theory, it is common practice to use known auxiliary information related to survey variable for efficient sampling. For example, stratification and probability proportion to size sampling. Balanced sampling also utilizes auxiliary variables for efficiency sampling. A sample is said to be balanced if Horvitz-Thompson (HT) estimators for population totals of auxiliary variables are equal to the known population totals. Cube method selects approximately balanced samples with equal or unequal fixed first-order inclusion probabilities. The realized imbalance in the sample by cube method becomes negligible if sample size is large with respect to number of balancing variables (i.e. auxiliary variables). 

Cube method does not control the expected imbalance, which is simply the variance of HT-estimator for population total of the auxiliary variable. Moreover, in case one observe a non-negligible realized balance of the selected sample, one cannot know whether the expected imbalance of the cube method is actually small or large. However, by selecting many samples and repeatedly calculating the realized imbalance, one can get an idea about the expected imbalance of cube method for a given population. Having generated many samples to check the expected imbalance, it seems natural to re-sample from the many samples using a re-sampling distribution, which can be expected to reduce the imbalance, i.e. compared to the sampling distribution under cube method, without changing the first-order inclusion probabilities implied by the cube method. We consider a constrained optimization approach for obtaining a re-sampling distribution. An optimization algorithm is used to achieve this objective. Theoretical properties of the proposed approach are discussed. To examine the improvement in term of expected imbalance a simulation study is also conducted.