A fractional-order JAYA algorithm with memory effect for solving global optimization problem

The JAYA algorithm is a widely used metaheuristic algorithm developed recently for solving global optimization problems. However, its simple search mechanism, which relies solely on the current best and worst individuals in the population, can easily lead to suffering from premature stagnation and getting stuck in local optimum when dealing with certain complex problems. To address this problem, this paper designs a novel fractional-order search strategy based on JAYA algorithm with memory effect , called fractional-order JAYA (FJAYA). The Grünwald–Letnikov fractional-order difference with the characteristics of long-term memory and non-locality is integrated into the JAYA algorithm. Specifically, two local attractors are generated using the best and worst individuals as well as the average position of the current population. These two local attractors then undergo fractional-order transformations to extract historical information from both the current and previous iterations. Thus, FJAYA does not solely rely on information from the current best and worst individuals, but rather effectively leverages more historical information. To validate the performance of the proposed algorithm, it is tested on 18 well-known benchmark functions. Furthermore, FJAYA is applied to solve the parameter identification on four discrete chaotic systems. The experimental results demonstrate that FJAYA enhances the search capability when facing complex optimization problems, and it also exhibits satisfying parameter identification capability for chaotic systems. • Fractional-order difference with the characteristics of longterm memory is introduced. • The two local attractors are designed to utilize current population information. • Removed the absolute value symbols from the classic JAYA formula to improve accuracy.