Farklı dağılım fonksiyonlarıyla optimizasyon algoritmalarının mühendislik problemlerindeki performansının iyileştirilmesi

In order to improve the performance of optimization algorithms containing stochastic processes, using different distribution functions in random processes can increase the performance of optimization algorithms. Because, in terms of literature and practice, it has become important to develop existing methods with analytical contributions such as different distribution functions and to use them in real-time engineering problems , besides suggesting new stochastic methods. Therefore, in this thesis, it is primarily aimed to suggest methods for how existing numerical optimization algorithms can be developed with analytical contributions. As it is known, one of the most critical structures in numerical optimization algorithms is the step determination phase that determines the direction of the stochastic search. Generally, random variables derived from uniform distribution are used in these methods. However, in all cases, the use of random variables derived from a uniform distribution may not be suitable for the dynamics of the current algorithm. In fact, in the studies carried out during the thesis, it has been determined that the use of uniform distribution in every motion of the algorithm affects the performance of the algorithms. Therefore, it has been observed that using different distribution functions instead of uniform distribution in determining random steps will have a positive effect on the performance of the algorithm. Therefore, in this thesis, distribution functions and statistical moments, which are among the fundamental topics of statistics, have been analyzed in detail. The obtained outputs have been applied in engineering problems by adapting them to the dynamics of optimization algorithms. In this thesis, first of all, the random parameter vector optimization method (SMDO) has been modified with different distribution functions to reveal the effect of distribution functions. The obtained distribution function based random parameter vector optimization method is presented in comparison with the results in the literature over the benchmark functions. And using different distribution functions according to the results obtained increased the performance of the related method. In addition to these, a user-friendly toolbox has been designed for this structure. Later, the monarchy butterfly optimization algorithm, which is a newly proposed algorithm in the literature, was updated with different distribution functions and the modified monarch butterfly optimization algorithm (M2BO) was proposed. M2BO optimization algorithm is first tested on benchmark functions and presented in comparison with the results in the literature. In fact, the parameters that affect the performance of distribution functions are adjusted separately for each benchmark function. Then, it was tested on 3 DOF Hover 4 engine helicopter prototype to show the performance of the proposed different distribution function approach in engineering problems. The parameters of the gain matrix, which provides the control of the system, were designed with the M2BO algorithm and the results were tested through simulation and real-time system model. Thus, it has been shown on real-time system and benchmark functions that using different distribution functions in optimization algorithms instead of uniform distribution in stochastic processes can increase the performance of algorithms. Keywords: Optimization, distribution functions, statistical moment, stochastic methods