Abstract
A major challenge to solving multiobjective optimization problems is to capture possibly all the (representative) equivalent and diverse solutions at convergence. In this paper, we attempt to solve the generic multi-objective spanning tree (MOST) problem using an evolutionary algorithm (EA). We consider, without loss of generality, edge-cost and tree-diameter as the two objectives, and use a multiobjective evolutionary algorithm (MOEA) that produces diverse solutions without needing a priori knowledge of the solution space. We test this approach for generating (near-) optimal spanning trees, and compare the solutions obtained from other conventional approaches.
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References
Marathe, M.V., Ravi, R., Sundaram, R., Ravi, S.S., Rosenkrantz, D.J., Hunt, H.B.: Bicriteria Network Design Problems. J. Algorithms 28, 142–171 (1998)
Ravi, R., Marathe, M.V., Ravi, S.S., Rosenkrantz, D.J., Hunt, H.B.: Approximation Algorithms for Degree-Constrained Minimum-Cost Network Design Problems. Algorithmica 31, 58–78 (2001)
Boldon, N., Deo, N., Kumar, N.: Minimum-Weight Degree-Constrained Spanning Tree Problem: Heuristics and Implementation on an SIMD Parallel Machine. Parallel Computing 22, 369–382 (1996)
Deo, N., Abdalla, A.: Computing a diameter-constrained minimum spanning tree in parallel. In: Bongiovanni, G., Petreschi, R., Gambosi, G. (eds.) CIAC 2000. LNCS, vol. 1767, pp. 17–31. Springer, Heidelberg (2000)
Deo, N., Micikevicius, P.: Comparison of Prüfer-like Codes for Labeled Trees. In: Proc. 32nd South-Eastern Int. Conf. Combinatorics, Graph Theory and Computing (2001)
Raidl, G.R., Julstrom, B.A.: Greedy Heuristics and an Evolutionary Algorithm for the Bounded-Diameter Minimum Spanning Tree Problem. In: Proc. 18th ACM Symposium on Applied Computing (SAC 2003), pp. 747–752 (2003)
Julstrom, B.A., Raidl, G.R.: Edge Sets: An Effective Evolutionary Coding of Spanning Trees. IEEE Trans. Evolutionary Computation 7, 225–239 (2003)
Knowles, J.D., Corne, D.W.: A New Evolutionary Approach to the Degree-Constrained Minimum Spanning Tree Problem. IEEE Trans. Evolutionary Computation 4, 125–133 (2000)
Knowles, J.D., Corne, D.W.: A Comparison of Encodings and Algorithms forMultiobjective Minimum Spanning Tree Problems. In: Proc. 2001 Congress on Evolutionary Computation (CEC-2001), vol. 1, pp. 544–551 (2001)
Deb, K.: Multiobjective Optimization Using Evolutionary Algorithms. Wiley, Chichester (2001)
Kumar, R., Rockett, P.I.: Improved Sampling of the Pareto-front in Multiobjective Genetic Optimization by Steady-State Evolution: A Pareto Converging Genetic Algorithm. Evolutionary Computation 10, 283–314 (2002)
Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: Combining Convergence and Diversity in Evolutionary Multiobjective Optimization. Evolutionary Computation 10, 263–282 (2002)
Zohu, G., Gen, M.: Genetic Algorithm Approach on Multi-CriteriaMinimum Spanning Tree Problem. European J. Operations Research 114, 141–152 (1999)
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Kumar, R., Singh, P.K., Chakrabarti, P.P. (2004). Multiobjective Genetic Search for Spanning Tree Problem. In: Pal, N.R., Kasabov, N., Mudi, R.K., Pal, S., Parui, S.K. (eds) Neural Information Processing. ICONIP 2004. Lecture Notes in Computer Science, vol 3316. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30499-9_32
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DOI: https://doi.org/10.1007/978-3-540-30499-9_32
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