An RNA evolutionary algorithm based on gradient descent for function optimization

The optimization of numerical functions with multiple independent variables was a significant challenge with numerous practical applications in process control systems, data fitting, and engineering designs. Although RNA genetic algorithms offer clear benefits in function optimization, including rapid convergence, they have low accuracy and can easily become trapped in local optima. To address these issues, a new heuristic algorithm was proposed, a gradient descent-based RNA genetic algorithm. Specifically, adaptive moment estimation (Adam) was employed as a mutation operator to improve the local development ability of the algorithm. Additionally, two new operators inspired by the inner-loop structure of RNA molecules were introduced: an inner-loop crossover operator and an inner-loop mutation operator. These operators enhance the global exploration ability of the algorithm in the early stages of evolution and enable it to escape from local optima. The algorithm consists of two stages: a pre-evolutionary stage that employs RNA genetic algorithms to identify individuals in the vicinity of the optimal region and a post-evolutionary stage that applies a adaptive gradient descent mutation to further enhance the solution's quality. When compared with the current advanced algorithms for solving function optimization problems, Adam RNA Genetic Algorithm (RNA-GA) produced better optimal solutions. In comparison with RNA-GA and Genetic Algorithm (GA) across 17 benchmark functions, Adam RNA-GA ranked first with the best result of an average rank of 1.58 according to the Friedman test. In the set of 29 functions of the CEC2017 suite, compared with heuristic algorithms such as African Vulture Optimization Algorithm, Dung Beetle Optimization, Whale Optimization Algorithm, and Grey Wolf Optimizer, Adam RNA-GA ranked first with the best result of an average rank of 1.724 according to the Friedman test. Our algorithm not only achieved significant improvements over RNA-GA but also performed excellently among various current advanced algorithms for solving function optimization problems, achieving high precision in function optimization. Graphical Abstract