INNOVATIVE HYBRID METAHEURISTIC ALGORITHMS AND THEIR APPLICATIONS UNDER FUZZY OR DETERMINISTIC ENVIRONMENT

Abstract

The thesis focuses on developing Innovative metaheuristic algorithms (HPSO, PSOHHO, PSOHHO-V, PSOMHHO, and Fuzzy BTO) inspired by nature. Despite the proliferation of metaheuristic algorithms, a significant void exists in conducting thorough theoretical and mathematical analyses. More studies are needed, particularly in the critical domain of convergence of metaheuristic algorithms. The proposed algorithm's theoretical analysis and mathematical foundation are established to tackle this challenge by introducing the concept of signature and convergence. The stability analysis of HPSO is also discussed to strengthen it mathematically even further. The thesis also emphasizes the applications of developed metaheuristic algorithms on different real-world problems in fuzzy and deterministic atmospheres. Job scheduling problems on computational grids commonly fall into NP-completeness or NP-hardness, making the quest for optimal solutions notably time-intensive. To address this challenge expediently and effectively, scholars have predominantly turned to the exploration of metaheuristic algorithms. Hence, the developed algorithm HPSO is applied to both single-objective and multi-objective Job Scheduling problems on the computational grid. Classification problems frequently involve a surplus of features, but not all contribute to the problem's essence. Redundant or irrelevant features may impede classification accuracy. Metaheuristic algorithms are favoured for feature selection due to their simplicity and practical applicability, offering advantages over deterministic optimization algorithms. For this purpose, the real-world application of developed algorithms PSOHHO, PSOHHO-V, PSOMHHO, and Fuzzy BTO are verified on feature selection problems. They are applied to the hybrid Feature Selection problem and compared with other metaheuristic algorithms on seven UCI machine learning repository datasets. Existing literature highlights the effectiveness of forecasting methods with more diverse set types. The idea of enhancing outcomes by incorporating additional inputs is closely observed. This theoretical basis advocates the efficiency of Picture Fuzzy Sets (PFYSs) in forecasting models. Notably, there needs to be more literature regarding the joint application vii of PFYS and swarm intelligence for Fuzzy Time Series (FTS) forecasting. This chapter introduces the innovative EDSPSO-PFTS approach to address this gap. This thesis is structured into five sections, encompassing ten chapters. Part I consists of Chapter 1, an introduction, and motivation for the research work carried out. It features a comprehensive literature review emphasizing the importance of the thesis's focal issue. In Part II, the emphasis shifts to the real-world deployment of the newly created hybrid metaheuristic algorithms, specifically in the context of Job Scheduling on a computational grid. There are two chapters in this part, which are 2 and 3. Chapter 2 applies a proposed fuzzy particle swarm optimization to address single-objective job scheduling on computational grids. Focused on minimizing the makespan value, indicative of maximum task completion time across the grid, this chapter explores the impact of trapezoidal and pentagonal fuzzy numbers, presenting a detailed comparative analysis. Chapter 3 explores the application of fuzzy particle swarm optimization for multi-objective job scheduling on computational grids. The foundation established in the previous chapter is expanded upon in this chapter, which moves from single-objective to multi-objective optimization. This chapter aims to maintain a delicate balance between makespan and flowtime objectives, which are conflicting. The practical application of the proposed hybrid metaheuristic algorithms in the hybrid feature selection problem domain is the main emphasis of Part III of the thesis. There are five chapters in this section: Chapters 4, 5, 6, 7, and 8. In Chapter 4, a Hybrid Particle Swarm Optimization (HPSO) algorithm is introduced and applied to address a Hybrid Feature Selection problem. This chapter discusses the stability of the proposed HPSO algorithm through the Von Neumann stability criterion and Fourier series concepts. The convergence of HPSO is explained using the Markov chain concept. The chapter thoroughly compares results against other metaheuristic algorithms, employing statistical tests like the Friedman and Mann-Whitney U test to estimate the algorithm's statistical significance. viii In Chapter 5, an improved version of the Particle Swarm Optimization algorithm, HPSO, is thoroughly explored for its application in multi-objective feature selection. This section represents a notable progression from single-objective to multi-objective optimization, leveraging the foundation in the previous chapter. The effectiveness of HPSO is meticulously evaluated across seven UCI datasets, with robust statistical analysis facilitated by the Wilcoxon rank sum test. In Chapter 6, two innovative hybrid optimization algorithms, PSOHHO and its variant PSOHHO-V, are introduced. These algorithms enhance their exploration capabilities by integrating a dual-swarm strategy and an exponential mutation operator. The evaluation of PSOHHO and PSOHHO-V involves rigorous analysis of statistical metrics and convergence rates, with extensive testing on benchmark functions. Furthermore, the algorithms are applied to feature selection problems, and their performance is benchmarked against alternative approaches using seven UCI datasets. In Chapter 7, a ground-breaking Hybrid Swarm Optimization algorithm, PSOMHHO, is introduced, seamlessly integrating Pentagonal and Trapezoidal Fuzzy Numbers. The chapter explores the mathematical foundations by proving the algorithm's convergence using the Markov Chain property and introducing the algorithm's signature. The effectiveness of PSOMHHO is meticulously evaluated through extensive benchmark function testing, establishing its superiority over established metaheuristic algorithms. Rigorous statistical tests, including the Mann-Whitney U test and the Friedman test, affirm the exceptional performance of PSOMHHO across various metaheuristic algorithms. Chapter 8 introduces innovative hybrid swarm optimization algorithms (Fuzzy BTO and its variants). Emphasizing the critical role of parameters in optimization, this chapter introduces fuzzy concepts for dynamic parameter adaptation. The efficiency of Fuzzy BTO and its variants are rigorously evaluated through extensive benchmark functions, followed by a comprehensive comparison with established metaheuristic algorithms. The robust statistical analysis, employing the Kruskal-Wallis Test (KWT), validates the superior performance of Fuzzy BTO across various metaheuristic algorithms. ix In Part – IV of this thesis, the emphasis shifts to applying the proposed hybrid metaheuristic algorithms and Picture Fuzzy Set on Forecasting. This critical part is summarized in a singular chapter, namely Chapter 9. A novel picture fuzzy time series (PFTS) forecasting model built on the foundations of picture fuzzy sets (PFYSs) is presented in Chapter 9. This chapter develops a unique hybrid EDSPSO PFTS forecasting approach by integrating PFYS and EDSPSO. To illustrate the applicability and utility of the proposed forecasting method, it is applied to data sets from the Alabama University and the State Bank of India share price at the Bombay Stock Exchange, India. Average forecasting error (AFE) and mean square error (MSE) are used to evaluate the efficiency of the suggested approach. Thorough statistical validation and performance analysis are carried out to guarantee the validity and dependability of the proposed approach. The thesis summary for Part V is included in a single Chapter 10. It outlines the key findings from the study and points out the issues that still need to be addressed to further this field of study.