QLOA: A Self-Adaptive Q-Learning-Based Optimization Algorithm with Dynamic Mathematical Formulation Selection

In the field of optimization, one of the fundamental challenges of existing methods lies in their inability to dynamically adapt to the diverse characteristics of objective functions. Many algorithms rely on a fixed optimization strategy; therefore, while they may perform well on certain problems, they often lose efficiency when dealing with functions exhibiting different behaviors, such as smooth or steep landscapes. To overcome this limitation, this study introduces a smart and self-adaptive approach called the Q-Learning-Based Optimization Algorithm (QLOA). The proposed QLOA incorporates a set of diverse mathematical formulations designed to enhance both the exploration and exploitation phases. A key feature of QLOA lies in the integration of the Q-learning framework, which enables the algorithm to intelligently and adaptively select the most suitable formulation based on the problem characteristics and its performance feedback, thereby establishing a dynamic balance between exploration and exploitation at each stage of the optimization process. In addition, population refinement mechanisms—such as eliminating redundant members and applying structural adjustments—prevent the algorithm from becoming trapped in local optima. To further enhance adaptability in problems with hard and soft constraints, an extended version named QLOA with Constraint Management (QLOA-CM) is developed. Experimental results on standard benchmark functions and the CEC2019 and CEC2022 test suites demonstrate that QLOA outperforms reference algorithms in both the Friedman and Wilcoxon statistical tests, confirming its efficiency, robustness, and statistically significant superiority over existing methods. Final evaluations of QLOA-CM on engineering optimization problems and real-world challenges from CEC2020, alongside QLOA’s successful application in image segmentation tasks, further validate the effectiveness and generalization capabilities of the proposed approaches in solving complex optimization problems. The source code of the proposed algorithm is publicly available at https://github.com/MSNFV/QLOA-Q-Learning-based-Optimization-Algorithm.