Developing a hybrid method based on Shuffled Frog Leaping and Gray Wolf Optimization algorithms to solve multi-objective optimization problems

When looking to the real world problems, it is seen that many of them are aimed at achieving more than one goal. While these goals are sometimes in accordance with each other, they may be in conflict with each other. Depending on these relations of objectives with each other, the difficulties of solving multi-objective problems can be different. Although a problem with goals that are in accordance with each other can be solved by transforming it to a single-objective problem, this is not possible for a problem whose goals are in conflict. When looking around, it can be seen that many of the problems we encounter are multi-objective problems whose goals are in conflict with each other. There are many classical methods used to solve these problems. The deficiency of the classical methods at the point of developing solutions due to different reasons has led researchers to develop different approaches. Nature-inspired algorithms developed by taking inspiration from the behavior of animals that generally live with a swarm in nature or plants with different habitats have been one of these approaches. Nature-inspired algorithms are more advantageous than classical methods in terms of being adaptable to different problems. In this thesis, shuffled frog leaping (SFLA) and gray wolf optimizer (GWO) algorithms developed for the solution of single-objective problems were used in a hybrid method and applied to multi-objective optimization problems. The proposed algorithm was evaluated in three stages on different problem sets. In the first stage, 36 unconstrained multi-objective optimization problems with different properties were used. The performance of the proposed algorithm was compared with the performance of the six multi-objective optimization algorithms (NSGA-II, IBEA, MOCell, MOEA/D, MOAAA and MOVS) in the first stage. In the second stage, 10 multi-objective optimization problems with different features, consisting of engineering design problems and constrained problems, were used. In this stage, the performance of the proposed algorithm was compared with NSGA-II, IBEA, MOCell and PAES algorithms. In the first two stages, hypervolume (HV), inverted generational distance (IGD), Spread and Epsilon metrics were used as performance comparison metrics. The results obtained with these four different metrics were analyzed by Friedman and Wilcoxon statistical tests. In addition, graphical drawings and box plots were used to visually present the results obtained by the algorithms. In the third and last stage, the proposed algorithm was tested in the segmentation of 10 gray level images, which are frequently used in image processing studies. In the third stage, performance comparison was made with the SFLA and GWO algorithms, which are the components of the proposed algorithm. In this section, thresholding, which is a single-objective problem, is handled as a multi-objective problem by the proposed algorithm. Peak signal to noise ratio (PSNR) was used as a performance metric at this stage where image segmentation was made. Experimental results obtained were analyzed by Friedman and Wilcoxon statistical tests. In addition, the segmented images, which were generated by the algorithms, were presented visually. Considering the experimental results obtained in three stages, it is seen that the proposed algorithm is generally more successful than the compared algorithms.