Adaptive metaheuristic design using Savage’s minimum regret criterion: a case study in differential evolution
摘要
This article explores the intersection of decision-making under uncertainty and metaheuristic algorithms, addressing the challenges posed by complex, unpredictable environments. Decision-making under uncertainty involves assessing consequences without complete information, which is crucial in finance, healthcare, and science. Additionally, metaheuristic algorithms are powerful tools for addressing nonlinear challenges and have traditionally relied on conventional operator selection methods. The study presents an innovative approach that incorporates the “Savage Minimum Uncertainty Criterion” into metaheuristics for automatic operator selection, thereby introducing an automatic methodology for metaheuristic design. This approach is applied to differential evolution (DE), resulting in a new algorithm called SAV-DE. The approach combines Savage’s conservative decision-making criteria with the exploratory capacity of metaheuristic algorithms, allowing for a balanced selection of operators. It considers the opportunity cost of making a bad decision to improve the algorithm’s efficiency and convergence. The performance approach is supported by parametric and nonparametric tests, exploration–exploitation metrics, complexity analysis, and convergence graphs, which comprehensively evaluate its performance across various optimization scenarios, including trajectory and parameter optimization in engineering problems.