Multi - thresholding using chaos based meta-heuristic optimization methods

Optimization is the process of organizing, adjusting, or selecting a system, process, or problem to function in the best possible way for a specific purpose. Metaheuristic optimization algorithms, which perform this process, aim to evaluate multiple states and provide the best possible solution. To enhance the performance of the initial population's distribution in the problem space and to achieve more diverse potential solutions, chaotic systems have been proposed in metaheuristic optimization algorithms. By incorporating chaotic characteristics into the initial population, a non-repetitive distribution in the search space is achieved. This allows for the evaluation of more possibilities. In this study, the Archimedes Optimization Algorithm, Osprey Optimization, Whale Optimization Algorithm, Particle Swarm Optimization, Secretary Bird Optimization, War Strategy Optimization, and Zebra Optimization Algorithm were enhanced with chaotic features. The initial populations of the mentioned seven optimization algorithms were modified using the characteristics of five chaotic maps: Logistic, Chebyshev, Circle, Sine, and Piecewise. Five chaotic versions were proposed for each optimization algorithm. The performance of the original versions and the chaotic initial population versions of these algorithms were tested using 23 Benchmark functions for each. When the 42 resulting optimization algorithms were evaluated across all Benchmark functions, the WSO algorithm with a Logistic map-based initial population achieved a success rate of 52.17%, outperforming the other algorithms. Another parameter that defines metaheuristic optimization algorithms is the objective functions, which represent the value to be optimized. In this study, the objective functions of the optimization algorithms and their chaotic versions, whose performances were evaluated, were structured using multi-level image thresholding methods, commonly preferred as preprocessing techniques in image processing applications. Multi-level image thresholding divides an image into more than two segments, enabling more efficient image analysis. Otsu Method and Kapur Entropy were used as objective functions for the optimization algorithms in the context of multi-level thresholding in this research. The algorithms were applied to five different test images, with the number of threshold levels manually determined by the user. To evaluate the uniqueness of the obtained results, non-parametric statistical tests such as the Wilcoxon and Friedman tests were performed, and the differences were expressed in percentage terms. Considering the results of the statistical tests, it was determined that the optimization algorithms with chaotic versions differed by 100% in multi-level thresholding applications.