## 1 Introduction  
The most effective and definitive way to solve problems is classical mathematical solutions. However, in some cases, obtaining an analytical solution is either very difficult or disadvantageous in terms of time. There are three main techniques for solving problems: experimental, analytical, and numerical. Experimental methods are costly and have disadvantages in terms of time. They are also not very useful in changing parameters. Analytical methods are precise in terms of solution but difficult to use in complex problems. Numerical methods have become popular with the advancement of computational techniques. They produce approximate solutions to the problems. Their accuracy rates are also considered sufficient for engineering studies [1]. Data environments are growing day by day due to increasing technological devices, sensors, and resources, etc. The huge increase in the volume of data makes it difficult to analyze such large data. For this reason, it can sometimes be very difficult or impossible to obtain a solution using analytical methods. In places where analytical solutions are insufficient, artificial intelligence and several different methods that support artificial intelligence come into play instead of classical analytical methods. Today's computers can process large amounts of data very quickly. Thanks to this capacity, they contribute greatly to problem solving in every field. Artificial intelligence and optimization are important fields that bring a perspective other than classical solutionsto problems. In this way, we can shorten the problem-solving processes or reach alternative solutions [2]. Real-world problems require significant computational costs and many complex solution methods. Therefore, mathematical programming approaches or optimization techniques, called metaheuristics, have been proposed many times to solve these problems [3]. Metaheuristic methods are used in cases where developing analytical solutions are not possible or very difficult. Metaheuristic methods are algorithms inspired by nature. Every method has a living thing or event from which it draws inspiration [4]. The motivation of this study is from metaheuristic algorithms and clustering. The proposed artificial afterimage algorithm (AAIA) is an algorithm that has not been proposed before in the literature. Therefore, a list of different metaheuristic algorithms on clustering is presented below. [PERSON], [PERSON], et al. [5] propose a metaheuristic algorithm based on cognitive feature integration in their study. The proposed algorithm uses no parameter density estimation and maximum likelihood estimation to integrate cognitive features and finally produces clustering results. [PERSON], P., [PERSON], et al. [6] propose a new metaheuristic method for a graph-based topic modeling technique in their study. Latent Dirichlet analysis (LDA) and the Gibbs sampling Dirichlet mixture model (GSDMM) are popularly used methods for topic modeling. [PERSON], [PERSON], et al. [7] propose the improved gray wolf clustering algorithm (IGWOA). It improves the gray wolf algorithm's convergence rate and reduces the risk of getting stuck in the local optimum in their study. There has been a proposed study to cluster students' stress levels. [PERSON], [PERSON], et al. [8] present a hyperheuristic clustering algorithm based on diversity detection and optimization detection operators in their study, in order to determine when to switch from one metaheuristic algorithm to another in order to improve the clustering result. [PERSON], I., [PERSON], et al. [9] propose a new and effective metaheuristic algorithm for minimizing the distance of the weighted sum of squares appearing on the Euclidean surface in many biomass supply-chain management applications in their study. [PERSON] [10] presents new and effective parameter-free metaheuristic methods for clustering large datasets in her thesis. The first proposed method is a fast heuristic method called the transitive heuristic method.