Comparison of tree encoding schemes for Biobjective Minimum Spanning Tree problem

Minimum Spanning Trees (MST) problem is a classical problem in operation research and network design problem is an important application of it. Minimum Spanning Tree (MST) problem can be solved efficiently, but its Biobjective versions are NP hard. In this paper, we compare three tree encoding schemes using Biobjective evolutionary algorithm. Three different tree encoding methods in the evolutionary algorithms are being used to solve three different instances of Biobjective Minimum Spanning Tree problem; comparative study of the tree encoding schemes used is done on the basis of Pareto optimal front obtained. Our approach involves Biobjective Minimum Spanning Tree problem using Nondominated Sorting Genetic Algorithm II (NSGAII). We compare Edge Set encoding, Prüfer encoding, Characteristic Vector encoding using evolutionary algorithm for Biobjective Minimum Spanning Tree, we find that edge sets encoding performs better than Prüfer and Characteristic Vector for Biobjective Minimum Spanning Tree problem while we are solving Biobjective Minimum Spanning Tree problem using Nondominated Sorting Genetic Algorithm II (NSGAII).