Research and application of the crow search algorithm for geometric covering optimization problems

Abstract

The problem of geometric covering is a special case of the optimal design problem and belongs to the class of cutting and packing problems. The challenge is to position some geometric objects on the surface to be coated so that the entire surface is covered. The complexity of the problems under consideration is due to their belonging to the class of NP-hard problems, which excludes the possibility of solving them by exact methods and requires the development of approximate optimization methods and algorithms. This article discusses the problem of geometric covering of an area with circles from a given set of radii. To solve the problem of geometric covering, a hexagonal grid coverage method with optimization by a metaheuristic algorithm is used. The crow search algorithm is such an algorithm, which is a relatively new metaheuristic algorithm based on the intelligent behavior of crows in a flock. The crow search algorithm includes two control parameters: the awareness probability and the flight length. To study the solution method and check the efficiency, a problem was modeled on the basis of a real design of automatic irrigation systems, and the results of experiments with different values of control parameters were presented.