A Hybrid Queueing Search and Gradient-Based Algorithm for Optimal Experimental Design

Abstract

Optimal experimental design is a crucial aspect of statistical planning in various scientific fields. Traditional gradient-based optimization algorithms are challenged when dealing with complex experimental conditions and large numbers of factors and parameters. Heuristic algorithms have been used as an alternative; however, they may suffer from premature convergence and cannot guarantee optimal solutions. This study aims to develop a hybrid algorithm that combines the strengths of gradient-based and heuristic optimization algorithms to improve solution quality and alleviate premature convergence issues in experimental design optimization. The proposed algorithm integrates the Multiplicative Algorithm (MA) with the Queueing Search Algorithm (QSA) to address complex optimization problems. The algorithm's performance is evaluated using numerical examples from generalized linear models (GLM), specifically logistic and Poisson models, and compared with state-of-the-art algorithms such as DE, SaDE, GA, and PSO. The numerical results demonstrate the superiority of the proposed algorithm in terms of convergence speed and solution quality. The proposed algorithm consistently outperforms other algorithms, achieving higher objective function values with fewer iterations. The integration of MA with QSA provides a more effective and robust optimization algorithm for experimental design problems. The proposed algorithm exhibits improved solution quality and competitive convergence speed while alleviating premature convergence issues, making it a promising approach for complex optimization problems in experimental design.