Chaotic triangulation topology aggregation optimization algorithm

Meta-heuristic algorithms are an important area of research in artificial intelligence. In recent years, numerous meta-heuristic algorithms based on swarm intelligence have been proposed and widely adopted in the literature. Although these algorithms are designed to mimic certain behaviors of living organisms, their experimental strategies and structural modules are similar. This similarity leads to challenges in achieving the exploration-exploitation balance and reaching global optima in complex optimization problems. To address continuous optimization and engineering applications, a new math-based meta-heuristic algorithm called the triangulation topology collection optimizer (ÜTTO) has recently been proposed. However, ÜTTO tends to get stuck in local optima, produces results with low sensitivity, and has limited convergence speed. Chaotic maps aim to improve the performance of meta-heuristic algorithms by enhancing global exploration and increasing convergence rates. In this thesis, a chaotic-based Triangulation Topology Collection Optimization Algorithm (KÜTTO) is proposed by integrating chaotic maps into the optimization process of the ÜTTO algorithm. To address the issues of getting stuck in local minima and slow convergence, the KÜTTO algorithm was developed for the first time by integrating 10 chaotic maps at 4 different points into the search mechanism of the ÜTTO. This improves population diversity and global exploration, thereby increasing the accuracy rate. The performance of the KÜTTO algorithm was investigated at the IEEE Evolutionary Computing Conference (CEC) '17 using fitness functions created for the comparison of meta-heuristic algorithms and classical benchmark functions. The sequential performance comparison of the proposed methods was performed using the Friedman test, a non-parametric statistical test. Whether the median differences between the methods are statistically significant was analyzed using the Wilcoxon signed-rank test. Additionally, the algorithm's performance in real-world applications was examined on four different engineering problems: three-bar frame design, compression-tension spring design, pressure vessel design, and welded beam design. The experimental findings and statistical analysis results reveal that the KÜTTO algorithm performs better than the standard ÜTTO.