Vol. 4, Issue 2, Part A (2022)

Optimization plays a critical role in diverse disciplines including engineering, operations research, computer science, economics, and management sciences. It seeks to identify the best possible solution from a set of available alternatives based on defined criteria. With the increasing complexity of real-world problems, a wide range of optimization techniques—both classical and modern—have been developed to efficiently solve linear, nonlinear, deterministic, and stochastic problems. This paper provides a comprehensive overview of various optimization techniques including linear programming, nonlinear optimization, dynamic programming, genetic algorithms, and particle swarm optimization. A numerical problem is solved using selected methods to compare their performance and demonstrate practical applications. The study concludes with insights into the selection of appropriate techniques based on the nature of the problem, computational efficiency, and the balance between accuracy and execution time.