Rotation excursion algorithm with learning

We introduce a novel heuristic algorithm named the Rotation Excursion Algorithm with Learning (REAL) designed for general-purpose optimization. REAL draws inspiration from the construction mechanism inherent in CEC optimization suites, integrating three fundamental operations with a natural growth rule to address optimization tasks. The initial operation involves rotating the current feasible solutions within the search space to generate and evaluate new solutions. The excursion operation aims to relocate current feasible solutions closer to historically superior solutions stored in a list known as the "list of visible spots." The third operation involves perturbing solutions generated by the preceding operations within their respective neighborhoods. The rotation operation is geared toward comprehensive and random exploration of the entire search space, while the excursion operation exploits known information to refine current solutions. Perturbation operation functions as a form of neighborhood search to further enhance solution quality. The natural growth rule dynamically adjusts REAL's balance between exploration and exploitation throughout the entire search process. To validate the efficacy of the proposed algorithm, we apply it to address a diverse set of 67 problems, encompassing 29 benchmark optimization problems, 30 test problems from CEC 2014, one from CEC 2022, and seven engineering problems. Numerical experiments demonstrate the superior performance of REAL when compared to various other heuristics.