APPLICATION OF THE CANTOR SET IN THE MODIFIED GENETIC ALGORITHM - Bazhan, S. M. (Computer Science and Applied Mathematics, 2023)
The article explores the results of applying the Cantor set during the mutation operation when solving the problem of finding the global minimum of a function of one variable by a modified genetic algorithm. Hybrid algorithms, involving the use of algorithms with various modifications or in combination with other well-known classical algorithms, are gaining increasing popularity today. The modification of the genetic algorithm using the Cantor set for constructing points during the mutation operation represents a novel approach in the study of its applications. The mutation operation in genetic algorithms is one of the basic genetic operators that introduces random changes in genetic information, creating new elements of the search area. Its role is to expand the search area for the optimal solution, in order to check the presence of a false solution at the points of the local minimum. The paper considers the use of a modified genetic algorithm with a mutation operation, where a finite number of points of the Cantor set located outside the current search area are used. With the help of software that implements this algorithm, a visualization of the mutation procedure was obtained. The solutions of the problems of minimization of the test functions were also obtained and their analysis was carried out. A comparative analysis was conducted between the proposed algorithm and the following approaches: the PCLPSO algorithm, which utilizes a complex learning particle swarm optimizer; the nature-inspired BAT algorithm, based on the echolocation behavior of bats; and other interpretations of the genetic algorithm. The proposed approach demonstrated better results according to some criteria. The research demonstrates that the combination of Cantor set and genetic algorithms can be useful for optimizing complex functions and helping to find optimal solutions. The use of the Cantor set in the mutation operation when applying a modified genetic algorithm opens up new possibilities in solving minimization problems and structures the parameter space, facilitating the search for optimal solutions.