VARIANTS OF GREY WOLF OPTIMIZER AND SINE COSINE ALGORITHM FOR GLOBAL OPTIMIZATION AND THEIR APPLICATIONS

Abstract

Grey Wolf Optimizer (GWO) and Sine Cosine Algorithm (SCA) are recently developed population based metaheuristic algorithms to solve global optimization problems. The GWO is inspired by the social and leadership behaviour of grey wolves, and the SCA is designed from the inspiration of sine and cosine trigonometric functions. Although these algorithms are recently developed, their effectiveness and advantages are demonstrated in various real world applications like feature selection, thresholding, multi objective optimization, load dispatch problem in electrical engineering, clustering and training of neural network etc. The aim of this PhD Thesis is to propose some modified variants of the classical GWO and classical SCA which are more effective and reliable in terms of search strategy and solution accuracy of the optimization problems. To achieve these objectives, in the Thesis, First a modified variant of classical GWO called RW-GWO is introduced which improves the exploration as well as exploitation ability of the wolves in a grey wolf pack by introducing two different strategies. In the first strategy, a new search equation based on random walk search mechanism is introduced for the leading hunters, and in second, a greedy selection is applied at the end of each iteration corresponding to each wolf between its current and previous state. The random walk search strategy focuses on enhancing the exploration and exploitation ability of leading guidance and greedy selection preserves the discovered promising areas of the search space. The performance of the RW-GWO algorithm is analyzed and compared with classical GWO on IEEE CEC 2014 benchmark set of unconstrained optimization problems. The numerical results of these test problems demonstrate the superior search ability of proposed algorithm as compared to classical GWO. Next, another variant of the classical GWO called Memory-based Grey Wolf Optimizer (mGWO) is introduced. The mGWO algorithm utilizes the personal best history of individual wolves to enhance the collaborative strength of grey wolf pack through modified encircling and hunting mechanism. The mGWO also integrates the personal best guidance during the search to share the available best knowledge regarding the search space among the individual search agents. Hence, the leading and personal best guidance together perform the search process in the mGWO. The evaluation of the proposed mGWO is performed on IEEE CEC 2014 benchmark set of unconstrained problems. The numerical results of these test problems demonstrate the better search ability of proposed algorithm as compare to the classical GWO in all the category of optimization problems such as unimodal, multimodal, composite and hybrid functions. The comparison ii between the RW-GWO and mGWO concludes that RW-GWO can be preferred for the unimodal and composite problems and for the multimodal and hybrid problems mGWO can be preferred. To improve the search accuracy of candidate solutions, a new variant of classical SCA called m- SCA is proposed in the Thesis which is based on opposition-based learning and modified position update mechanism. The opposition-based learning is used to generate the opposite candidate solutions so that the stagnation at local optima can be avoided. The jumping rate which allows the algorithm to perform the opposition-based learning phase in the algorithm is fixed to a low value to keep the balance between exploration and exploitation. The search equation of classical SCA is modified based on the cognitive component to reduce the inefficient diversity of search agents and to maintain the balance between exploration and exploitation during the search. The performance of the m-SCA is analyzed and compared with classical SCA on unconstrained benchmark problems given in IEEE CEC 2014. The analysis of the results demonstrates the superior search ability of the m-SCA as compared to classical SCA on all category of problems such as unimodal, multimodal, composite and hybrid benchmark problems. Next, another modified variant of classical SCA called ISCA is introduced which enhances the performance of the classical SCA based on the personal best history of candidate solutions, crossover operator and modified position update mechanism. In the ISCA, the greedy selection is also employed for each candidate solution between its current and previous state to avoid its divergence from discovered promising search areas. The performance evaluation of the proposed algorithm is performed on IEEE CEC 2014 benchmark suite of unconstrained optimization problems. The numerical results of these test problems demonstrate the superior search ability of proposed algorithm as compared to the classical SCA in all category of benchmark optimization problems. The comparison between the m-SCA and ISCA concludes that ISCA can be preferred for the unimodal, multimodal and hybrid problems and for the composite problems both the algorithms are very competitive to each other. Further, the performance of classical versions of GWO and SCA, and their proposed variants called RW-GWO, mGWO, m-SCA and ISCA is evaluated on constrained optimization problems. The constrained versions of these algorithms are designed by introducing a simple constraint handling mechanism based on the constraint violation. The constrained benchmark problems given in IEEE CEC 2006 are used for experimentation. The analysis on these problems demonstrate the better search ability of the mGWO algorithm than the classical GWO and RW-GWO algorithms. Similarly, the proposed ISCA algorithm shows their better search ability to solve constrained optimization problems as compared to the classical SCA and m-SCA. iii In order to analyze the applicability of the classical GWO, classical SCA and their proposed variants, an unconstrained and nonlinear optimization problem which arises in the field of image processing is selected. The problem is defined to determine the optimal thresholds for image segmentation in grey images. To find the optimum thresholds for an image, Otsu’s between-class variance criterion is employed as the fitness function. Nine benchmark images are used for experimentation and several statistical measures are used for comparison. The analysis of results ensure that the proposed improved variant RW-GWO and mGWO perform better than classical GWO, classical SCA, m-SCA and ISCA algorithms. Next, the classical GWO, classical SCA and their proposed variants called RW-GWO, mGWO, m-SCA and ISCA are implemented on another real-life application which is unconstrained in nature and arises in the field of electrical engineering. The objective of this problem is to determine the optimal setting for the proper coordination of overcurrent relays. The IEEE 3, 4, 6, and 14-bus systems are used for experimentation and validation. The comparison of results demonstrate the better search efficiency and solution accuracy of the proposed RW-GWO algorithm than all other variants of GWO and SCA and their classical versions in finding the optimal setting for overcurrent relays. Finally, the Thesis is concluded with the limitations and scope of the proposed algorithms. Later it suggests future scope and some new directions of research in this area.