An ILP formulation and genetic algorithm for the Maximum Degree-Bounded Connected Subgraph problem

A general instance of a Degree-Constrained Subgraph problem may be found in an edgeweighted or vertex-weighted graph G whereas the objective is to find an optimal weighted subgraph, subject to certain degree constraints on the vertices of the subgraph. This class of combinatorial problems has been extensively studied due to its numerous applications in network design. If the input graph is bipartite, these problems are equivalent to classical transportation and assignment problems in operational research. This paper is an illustration of a research of the NP-hard Maximum Degree-Bounded Connected Subgraph problem (MDBCS). It is a classical NP-complete problem. Moreover this paper offers a first integer linear programming formulation of the (MDBCS), and a formal proof that it is correct. A genetic algorithm for obtaining the optimal solution of (MDBCS) has also been provided. The proposed solution comprises a genetic algorithm (GA) that uses binary representation, fine-grained tournament selection, one-point crossover, simple mutation with frozen genes and caching technique.