On Class of Genetic Algorithms in Optimization Problems on Combinatorial Configurations

The concept of the Euclidean combinatorial configuration as the mapping of an abstract set into an arithmetic Euclidean space is introduced. The problem of optimization on the set of Euclidean combinatorial configurations is formulated. The peculiarities of the application of genetic algorithms for solving this class of problems are considered. Principles of formation of the initial population, selection mechanisms, choice of crossover operators and mutation are described. The proposed approach is illustrated on the problem of combinatorial optimization on the set of permutations. Examples of the construction of various crossover operators for Euclidean permutation configurations are given.