Leaf Constrained Minimal Spanning Trees Solved by a Ga with Feasible Encodings

We investigate a Genetic Algorithm (GA) solution for the NP-hard Leaf Constrained Minimal Spanning Tree (LCMST) problem on a weighted complete graph using a novel encoding for the genotype which ensures feasibility of the search space when performing crossover and mutation and when initializing the population. The feasible genotype for the LCMST problem is a permutation code (an adaptation of the simple idea of a permutation) which is then mapped into a Pr!fer code (phenotype) whose spanning tree obeys the desired leaf constraint. The effectiveness of the methodology is demonstrated by comparison of experimental results with the exact results for a LCMST problem. We claim that the use of the permutation code for the genotype exploits its inherent virtual mutation behavior and thus makes the GA more efficient.