Abstract
Understanding the behaviour of heuristic search methods is a challenge. This even holds for simple local search methods such as 2-OPT for the Traveling Salesperson problem. In this paper, we present a general framework that is able to construct a diverse set of instances that are hard or easy for a given search heuristic. Such a diverse set is obtained by using an evolutionary algorithm for constructing hard or easy instances that are diverse with respect to different features of the underlying problem. Examining the constructed instance sets, we show that many combinations of two or three features give a good classification of the TSP instances in terms of whether they are hard to be solved by 2-OPT.
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References
Hutter, F., Xu, L., Hoos, H.H., Leyton-Brown, K.: Algorithm runtime prediction: methods & evaluation. Artif. Intell. 206, 79–111 (2014)
Vilalta, R., Drissi, Y.: A perspective view and survey of meta-learning. Artif. Intell. Rev. 18(2), 77–95 (2002)
Eggensperger, K., Hutter, F., Hoos, H.H., Leyton-Brown, K.: Efficient benchmarking of hyperparameter optimizers via surrogates. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, 25–30 January 2015, Austin, Texas, USA, pp. 1114–1120 (2015)
Feurer, M., Springenberg, J.T., Hutter, F.: Initializing bayesian hyperparameter optimization via meta-learning. In: Proceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, 25–30 January 2015, Austin, Texas, USA, pp. 1128–1135 (2015)
Smith-Miles, K., Lopes, L.: Measuring instance difficulty for combinatorial optimization problems. Comput. Oper. Res. 39(5), 875–889 (2012)
van Hemert, J.I.: Evolving combinatorial problem instances that are difficult to solve. Evol. Comput. 14(4), 433–462 (2006)
Mersmann, O., Bischl, B., Trautmann, H., Wagner, M., Bossek, J., Neumann, F.: A novel feature-based approach to characterize algorithm performance for the traveling salesperson problem. Ann. Math. Artif. Intell. 69(2), 151–182 (2013)
Smith-Miles, K., van Hemert, J., Lim, X.Y.: Understanding TSP difficulty by learning from evolved instances. In: Blum, C., Battiti, R. (eds.) LION 4. LNCS, vol. 6073, pp. 266–280. Springer, Heidelberg (2010)
Neumann, F., Witt, C.: Bioinspired Computation in Combinatorial Optimization: Algorithms and Their Computational Complexity, 1st edn. Springer, New York (2010)
Kötzing, T., Neumann, F., Röglin, H., Witt, C.: Theoretical analysis of two ACO approaches for the traveling salesman problem. Swarm Intell. 6(1), 1–21 (2012)
Englert, M., Röglin, H., Vöcking, B.: Worst case and probabilistic analysis of the 2-Opt algorithm for the TSP. Algorithmica 68(1), 190–264 (2014)
Nallaperuma, S., Wagner, M., Neumann, F., Bischl, B., Mersmann, O., Trautmann, H.: A feature-based comparison of local search and the Christofides algorithm for the travelling salesperson problem. In: FOGA 2013, pp. 147–160 (2013)
Nallaperuma, S., Wagner, M., Neumann, F.: Parameter prediction based on features of evolved instances for ant colony optimization and the traveling salesperson problem. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds.) PPSN 2014. LNCS, vol. 8672, pp. 100–109. Springer, Heidelberg (2014)
Ulrich, T., Bader, J., Thiele, L.: Defining and optimizing indicator-based diversity measures in multiobjective search. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 707–717. Springer, Heidelberg (2010)
Ulrich, T., Bader, J., Zitzler, E.: Integrating decision space diversity into hypervolume-based multiobjective search. In: GECCO, pp. 455–462 (2010)
Croes, G.A.: A method for solving traveling-salesman problems. Oper. Res. 6(6), 791–812 (1958)
Applegate, D., Cook, W., Dash, S., Rohe, A.: Solution of a min-max vehicle routing problem. INFORMS J. Comput. 14(2), 132–143 (2002)
Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria (2015)
Cortes, C., Vapnik, V.: Support-vector networks. Mach. Learn. 20(3), 273–297 (1995)
Meyer, D., Dimitriadou, E., Hornik, K., Weingessel, A., Leisch, F.: e1071: Misc Functions of the Department of Statistics, Probability Theory Group (Formerly: E1071), TU Wien. R package version 1.6-7 (2015)
Acknowledgement
This research has been supported by the European Union Seventh Framework Programme (FP7/2007–2013) under grant agreement no. 618091 (SAGE) and by the Australian Research Council under grant agreement DP140103400.
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Gao, W., Nallaperuma, S., Neumann, F. (2016). Feature-Based Diversity Optimization for Problem Instance Classification. In: Handl, J., Hart, E., Lewis, P., López-Ibáñez, M., Ochoa, G., Paechter, B. (eds) Parallel Problem Solving from Nature – PPSN XIV. PPSN 2016. Lecture Notes in Computer Science(), vol 9921. Springer, Cham. https://doi.org/10.1007/978-3-319-45823-6_81
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DOI: https://doi.org/10.1007/978-3-319-45823-6_81
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