Design of a new metaheuristic algorithm based on the movement of electricity in highly resistant environment

The term "optimization" refers to a group of mathematical ideas and techniques that are applied across various fields to tackle quantitative issues. We all unconsciously experience an optimization process in our daily life. While choosing the route or doing our shopping, we try to choose the most suitable options according to the current situation. We can solve small-scale optimization problems using our brain power or traditional algorithms, but we use computers to solve large or complex problems. Many algorithms have been designed to solve computer-aided optimization problems. Despite their simple nature, traditional algorithms are limited by their slow running times and limited applicability. Traditional algorithms are only capable of solving certain types of problems. Thanks to advancing science and technology, algorithms that work faster but are still problem-dependent have been developed. These algorithms are often called heuristic algorithms and are used to solve a particular type of problem. However, although these algorithms are faster than traditional algorithms, they are not flexible in a variety of problems. Hence, they are incomplete, and the need for improvement and change has arisen. Based on this need, meta-heuristic algorithms have been developed. The word "meta" means "beyond" or "after" in ancient Greek. Therefore, we can think of meta-heuristic algorithms as "post-heuristic" or "post-heuristic" algorithms. While meta-heuristic algorithms work faster than heuristic algorithms, they can work without being dependent on a problem or a particular problem type. In this thesis, a new nature-inspired metaheuristic optimization algorithm called EAA has been developed. It is based on how electricity moves through areas of high resistance. Like other metaheuristic algorithms, the population is necessary for EAA to start a search. Search agents with a memory and a lifetime make up this population. The EAA also has a unique structure known as negative and positive poles. Suppose we translate these terms into electrical terminology. In that case, we can say that the population is voltage, the search agents are electrons, and the negative and positive pole structures are electrical polarity structures. As a result, electrons at opposing poles tend to migrate in the same direction. The search algorithm used by EAA is based on this migration trend. EAA was put to the test using four test functions and four different datasets to tackle the NP-hard clustering issue to ascertain the suggested algorithm's efficacy and dependability. The test functions and data sets used in the thesis work are widely used in the literature. The scenarios tested with all the test functions were compared on seven different algorithms: BSA, DS, MPA, KO, GA, PSO, and HHO algorithms are algorithms with search mechanisms similar to the proposed EAA algorithm. As a result, the proposed EAA algorithm exhibits better global search, local search, and convergence properties than GA, PSO, BSA, and DS algorithms. It yielded similar results to the MPA, KO, and HHO algorithms. Additionally, the EAA method outperforms the GA, PSO, BS, and DS algorithms with a notable convergence rate. Compared to other algorithms, EAA typically finds accurate solutions in various settings. Additionally, statistical results demonstrate that EAA outperforms different compared algorithms and validate the test results. The 100 Digit Challenge test results indicate that, despite its limits, our system is capable of solving challenging tasks. Furthermore, the EAA algorithm outperformed the X-Means approach regarding clustering performance and demonstrated better clustering capability. Ten times with the corresponding settings, each test case was executed. In 10, 20, and 30 dimensions, the Rosenbrock, Ackley, Griewank, and Rastrigin functions are assessed. We can observe that in every test case, the suggested algorithm, EAA, produces nearly identical results to those of MPA, KO, and HHO. In every one of the ten rounds of six of the twelve instances, the suggested algorithm discovered an exact solution. In addition, in all ten repeating runs in six of the twelve scenarios, the HHO and the KO found a conclusive resolution. MPA, on the other hand, only discovered five precise answers. For the performance examination of the clustering problem, the Davies-Bouldin index (DB-Index) was used. The number of clusters "k" ranges from two to 10 for all datasets. Thirty-six test scenarios are available in this instance. For each EAA and X-Means method test case, the Davies-Bouldin index was computed and compared. We can see that EAA has better clustering performance than the X-Means algorithm in all test cases. Also, if we look at the dataset basis, ESA clustered better than the X-Means algorithm in each dataset. The EAA and X-Means algorithms have the same DB-Index in test cases where K is two. This outcome shows that EAA performs the same as the popular clustering algorithm X-Means algorithm in solving the clustering problem. As a result, it has been proven that the proposed algorithm can solve the clustering problem. DB-Index values are used to determine the optimum "k" number and to perform clustering analysis. Smaller DB-Index values indicate that the clusters created are compact and far apart. The EAA algorithm obtained a lower DB-Index value for each cluster size in all data sets. The low DB-Index value indicates that the clusters produced by the algorithm have a tighter structure and a higher discreteness than other clusters. We observe that increasing the time and iteration limit for problem-solving will enable our suggested algorithm to produce better outcomes. The proposed algorithm's architecture causes the search mechanism to operate sluggishly but persistently to look for worthwhile search areas. Our algorithm mainly employs short steps for global search instead of giant steps. To obtain the precise solution, the number of iterations must be increased. Even when faced with complex problems, the suggested algorithm never becomes stuck at local places because of the failure mechanism and initialization strategy. The results demonstrate that the proposed algorithm can approach the exact answer but may occasionally fail because of iteration constraints. Compared to existing metaheuristic algorithms, the suggested algorithm differs in terms of initialization method, pole search mechanism, and update method of the best solutions. A constant coefficient was used in our studies for global and local search movements. The algorithm can use a dynamic coefficient to overcome slow motion and late convergence. The diffusion coefficient of wood was applied in our studies. Future research could compare the effects of various diffusion coefficients on the algorithm. Additionally, different baseline population first initiation techniques can be investigated.