Development of a new method for approximation equation design in metaheuristic search algorithms

With the widespread use of computers, nature-inspired metaheuristic search (MSA) algorithms have become popular for solving optimization problems. The performance of MSA algorithms depends on their success, especially in neighborhood search and diversity tasks. However, there are two main challenges that MSA algorithms face when solving complex problems. The first main challenge is that multimodal problems often get stuck in local minimum traps in their search spaces. The second main difficulty is that they cannot sufficiently converge to the global solution at the end of the search process. In this study, a new method, "Percentage Error Variation Based Convergence Equation Design Method" is proposed to improve the performance of MSA algorithms. In this method, different versions of convergence equations, rings, are designed by using guide selection methods. By calculating the scores of the designed rings, convergence chains are formed from the rings with the highest scores. In MSA algorithms, the percentage change of the error is monitored during the search process. If the change of the error is below the specified percentage error change rate, it is aimed to improve the search performance of the algorithm by using the designed chains. The positive effects of the proposed method on the DE algorithm have been clearly observed.