Continuous-space embedding genetic algorithm applied to the Degree Constrained Minimum Spanning Tree Problem

This work presents an evolutionary approach for solving a difficult problem of combinatorial optimization, the DCMST (degree-constrained minimum spanning tree problem). Three genetic algorithms which embed candidate solutions in the continuous space are proposed here for solving the DCMST. The results achieved by these three algorithms have been compared with four other existing algorithms according to three merit criteria: i) quality of the best solution found; ii) computational effort spent by the algorithm, and; iii) convergence tendency of the population. The three proposed algorithms have provided better results for both solution quality and population convergence, with reasonable computational cost, in tests performed for 25-node and 50-node test instances. The results suggest that the proposed algorithms are well suited for dealing with the problem under study.