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).

[1]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[2]  Francis Suraweera,et al.  Encoding Graphs for Genetic Algorithms: An Investigation Using the Minimum Spanning Tree Problem , 1994, Evo Workshops.

[3]  J. Kruskal.  On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[4]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[5]  R. Prim.  Shortest connection networks and some generalizations , 1957 .

[6]  Charles C. Palmer,et al.  Representing trees in genetic algorithms , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[7]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[8]  David W. Corne,et al.  The edge-window-decoder representation for tree-based problems , 2006, IEEE Transactions on Evolutionary Computation.

[9]  A. Cayley.  A theorem on trees , 2009 .

[10]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[11]  Yacov Y. Haimes,et al.  Multiobjective Decision Making: Theory and Methodology , 1983 .

[12]  G. Raidl.  An efficient evolutionary algorithm for the degree-constrained minimum spanning tree problem , 2000, Proceedings of the 2000 Congress on Evolutionary Computation. CEC00 (Cat. No.00TH8512).

[13]  Mitsuo Gen,et al.  Genetic algorithm approach on multi-criteria minimum spanning tree problem , 1999, Eur. J. Oper. Res..

[14]  Joshua D. Knowles,et al.  A comparison of encodings and algorithms for multiobjective minimum spanning tree problems , 2001, Proceedings of the 2001 Congress on Evolutionary Computation (IEEE Cat. No.01TH8546).

[15]  Bryant A. Julstrom,et al.  Edge sets: an effective evolutionary coding of spanning trees , 2003, IEEE Trans. Evol. Comput..

[16]  Chao-Hsien Chu,et al.  Genetic algorithms for communications network design - an empirical study of the factors that influence performance , 2001, IEEE Trans. Evol. Comput..

[17]  Lawrence Davis,et al.  A Genetic Algorithm for Survivable Network Design , 1993, International Conference on Genetic Algorithms.