Optimization algorithms can provide practical solutions to enhance efficiency and performance in complex systems that involve multiple variables, constraints, and objectives. Therefore, relative research contents are increasingly inadequate for addressing the rising complexity of contemporary tasks. Consequently, researchers have developed numerous novel optimization algorithms in recent years, yielding promising experimental results. Firstly, this paper presents the fundamental concepts, developmental background, classification, and classic algorithms in the field of optimization. And then, this paper conducts an in-depth analysis of the current research status on classic optimization algorithms, including the genetic algorithm, ant colony optimization algorithm, simulated annealing algorithm, particle swarm optimization algorithm, and non-dominated sorting genetic algorithm II. The paper will summarize the performance characteristics, and potential applications of the above algorithms in the future.