Study and modeling of heuristic optimization algorithms

This paper investigates and compares various heuristic optimization algorithms used to solve problems where strict analytical solutions are lacking. Three algorithms are considered: genetic algorithms, simulated annealing, and firefly swarm optimization. Each of these methods is based on random search principles and is inspired by natural processes and the idea of role intelligence, where the behavior of individual individuals in accordance with simple rules allows finding a quasi-optimal solution. Genetic algorithms use selection, crossing-over and mutation mechanisms to find optimal solutions. The simulated annealing algorithm is inspired by the process of cooling a solid crystalline body, allowing the system to transition to less favorable states with a certain probability. The firefly swarm optimization algorithm is based on the behavior of fireflies, where agents move towards brighter individuals, which means a better value of the objective function, or move in a random direction. The article contains a computational experiment that allows us to compare the efficiency of algorithms by two criteria: proximity to the global minimum and the number of objective function calculations. The results showed that the simulated annealing algorithm is the simplest and most effective for optimizing two-dimensional multimodal functions, while genetic algorithms and the firefly algorithm require more complex parameter settings.