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In recent years, there has been increasing interest in developing new optimization algorithms and exploring their applications across science, engineering, economics, and industry. Our primary focus in this domain is on creating innovative numerical approximation algorithms for optimization problems, encompassing both single-objective and multi-objective cases.

These algorithms include direct and gradient search algorithms, where the Jacobian and Hessian matrix is approximated using various techniques. Since the 20th century, researchers have extensively utilized heuristic and metaheuristic optimization techniques to address complex optimization problems. These methods, inspired by natural processes and problem-solving strategies, have gained popularity due to their ability to efficiently explore large and complex search spaces. Heuristic approaches often provide quick, approximate solutions, while metaheuristic techniques, such as genetic algorithms, simulated annealing, and particle swarm optimization, are designed to enhance solution quality by balancing exploration and exploitation. Their adaptability and robustness have made them indispensable tools in diverse fields, including engineering, economics, and data science.

Here, I have added various types of optimization and their real life applications