Solving the MDBCS Problem Using the Metaheuric–Genetic Algorithm

The problems degree-limited graph of nodes considering the weight of the vertex or weight of the edges, with the aim to find the optimal weighted graph in terms of certain restrictions on the degree of the vertices in the subgraph. This class of combinatorial problems was extensively studied because of the implementation and application in network design, connection of networks and routing algorithms. It is likely that solution of MDBCS problem will find its place and application in these areas. The paper is given an ILP model to solve the problem MDBCS, as well as the genetic algorithm, which calculates a good enough solution for the input graph with a greater number of nodes. An important feature of the heuristic algorithms is that can approximate, but still good enough to solve the problems of exponential complexity. However, it should solve the problem heuristic algorithms may not lead to a satisfactory solution, and that for some of the problems, heuristic algorithms give relatively poor results. This is particularly true of problems for which no exact polynomial algorithm complexity. Also, heuristic algorithms are not the same, because some parts of heuristic algorithms differ depending on the situation and problems in which they are used. These parts are usually the objective function (transformation), and their definition significantly affects the efficiency of the algorithm. By mode of action, genetic algorithms are among the methods directed random search space solutions are looking for a global optimum. Keywordsgraph theory; NP-complete problems; the degreebounded graphs; Integer linear programming; genetic algorithms.