Construction of Balanced Incomplete Block Designs (BIBDs) through Variable Constrained Neighborhood Search (VCNS)

The issue of comparing two or more treatments in the presence of single or multiple covariates is a pivotal concern across various research domains. While various studies have explored optimal treatment allocation under completely randomized designs with regard to D- and A- optimality criteria but only few have addressed this challenge within a blocked framework. Addressing this problem, authors have developed an efficient, computationally tractable iterative search algorithm under the block design setup. This article extends the work by adapting the algorithm for the construction of Balanced Incomplete Block Designs (BIBDs). The primary objective of this study is to construct the Balanced Incomplete Block Designs (BIBDs) by the proposed Variable Constrained Neighborhood Search (VCNS) algorithm and assess the efficacy of the proposed VCNS algorithm with existing algorithms. The key contribution of this research lies in the extension of the previously developed VCNS algorithm to the domain of BIBD construction by offering a new computational tool that maintains competitive performance while reducing computational demands. This contribution adds value to the existing literature by bridging gaps in efficient design methodologies for treatment comparisons.