Symmetric Kullback Leibler divergence-based design of experiments with estimation of unspecified values

Abstract

In this work, we propose a Symmetric Kullback Leibler divergence (SKLD)-based approach for optimal Design of Experiments (DOE) along with estimation of unspecified values in the design of experiments data matrix. Using SKLD as optimality criteria as opposed to various existing alphabetic optimality criteria, facilitates the incorporation of end-user desired performance of estimates. For the case when experimental noise is Gaussian and uncorrelated, the proposed approach results in a Mixed Integer Non-Linear Programming (MINLP) problem. This problem is NP-hard to solve. Hence, a novel heuristic solution strategy is also proposed which solves the proposed problem iteratively and sequentially. In particular, the MINLP problem is split into two sub-problems: (i) Non-Linear Programming (NLP) problem: to estimate optimal unspecified values, and (ii) Non-Linear Integer Programming (IP) problem: to obtain optimal DOE. These two subproblems are solved sequentially and iteratively until convergence is reached. The proposed solution strategy guarantees the decreasing behaviour of SKLD value. The efficacy of the proposed solution strategy is tested on an illustrative example and a Material synthesis problem, and performance is compared with Fedorov exchange algorithm, Forward Greedy search algorithm, and some of the popular MINLP solvers available in GAMS environment. Results demonstrate that the proposed solution approach outperforms most other methods.