Abstract
Whether the goal is performance prediction, or insights into the relationships between algorithm performance and instance characteristics, a comprehensive set of meta-data from which relationships can be learned is needed. This paper provides a methodology to determine if the meta-data is sufficient, and demonstrates the critical role played by instance generation methods. Instances of the Travelling Salesman Problem (TSP) are evolved using an evolutionary algorithm to produce distinct classes of instances that are intentionally easy or hard for certain algorithms. A comprehensive set of features is used to characterise instances of the TSP, and the impact of these features on difficulty for each algorithm is analysed. Finally, performance predictions are achieved with high accuracy on unseen instances for predicting search effort as well as identifying the algorithm likely to perform best.
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References
Macready, W., Wolpert, D.: What makes an optimization problem hard. Complexity 5, 40–46 (1996)
Nudelman, E., Leyton-Brown, K., Hoos, H., Devkar, A., Shoham, Y.: Understanding random SAT: Beyond the clauses-to-variables ratio. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 438–452. Springer, Heidelberg (2004)
Xu, L., Hutter, F., Hoos, H., Leyton-Brown, K.: SATzilla-07: The design and analysis of an algorithm portfolio for SAT. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 712–727. Springer, Heidelberg (2007)
Cho, Y., Moore, J., Hill, R., Reilly, C.: Exploiting empirical knowledge for bi-dimensional knapsack problem heuristics. International Journal of Industrial and Systems Engineering 3(5), 530–548 (2008)
Hall, N., Posner, M.: Performance Prediction and Preselection for Optimization and Heuristic Solution Procedures. Operations Research 55(4), 703 (2007)
Smith-Miles, K.: Towards insightful algorithm selection for optimisation using meta-learning concepts. In: IEEE International Joint Conference on Neural Networks, IJCNN 2008. IEEE World Congress on Computational Intelligence, pp. 4118–4124 (2008)
Smith-Miles, K., James, R., Giffin, J., Tu, Y.: Understanding the Relationship between Scheduling Problem Structure and Heuristic Performance using Knowledge Discovery, LNCS. Springer, Heidelberg (in press, 2009)
Rice, J.: The Algorithm Selection Problem. Advances in computers 65 (1976)
van Hemert, J.: Evolving combinatorial problem instances that are difficult to solve. Evolutionary Computation 14(4), 433–462 (2006)
Gras, R.: How efficient are genetic algorithms to solve high epistasis deceptive problems? In: IEEE Congress on Evolutionary Computation, CEC 2008. IEEE World Congress on Computational Intelligence, pp. 242–249 (2008)
Locatelli, M., Wood, G.: Objective Function Features Providing Barriers to Rapid Global Optimization. Journal of Global Optimization 31(4), 549–565 (2005)
Xin, B., Chen, J., Pan, F.: Problem difficulty analysis for particle swarm optimization: deception and modality. In: Proceedings of the first ACM/SIGEVO Summit on Genetic and Evolutionary Computation, pp. 623–630 (2009)
Bachelet, V.: Métaheuristiques parallèles hybrides: application au problème d’affectation quadratique. PhD thesis, Universite des Sciences et Technologies de Lille (1999)
Reeves, C.: Landscapes, operators and heuristic search. Annals of Operations Research 86, 473–490 (1999)
Schiavinotto, T., Stützle, T.: A review of metrics on permutations for search landscape analysis. Comput. Oper. Res. 34(10), 3143–3153 (2007)
Smith-Miles, K.A., Lopes, L.B.: Measuring Combinatorial Optimization Problem Difficulty for Algorithm Selection. Annals of Mathematics and Artificial Intelligence (under review, 2009)
Pfahringer, B., Bensusan, H., Giraud-Carrier, C.: Meta-learning by landmarking various learning algorithms. In: Proceedings of the Seventeenth International Conference on Machine Learning table of contents, pp. 743–750. Morgan Kaufmann Publishers Inc., San Francisco (2000)
Burke, E., Kendall, G., Newall, J., Hart, E., Ross, P., Schulenburg, S.: Hyper-heuristics: An emerging direction in modern search technology. International Series in Operations Research and Management Science, pp. 457–474 (2003)
Battiti, R.: Using mutual information for selecting features in supervised neural net learning. IEEE Transactions on neural networks 5(4), 537–550 (1994)
Vasconcelos, N.: Feature selection by maximum marginal diversity: optimality and implications for visual recognition. In: Proceedings of 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, vol. 1 (2003)
Cheeseman, P., Kanefsky, B., Taylor, W.: Where the really hard problems are. In: Proceedings of the 12th IJCAI, pp. 331–337 (1991)
Ridge, E., Kudenko, D.: An Analysis of Problem Difficulty for a Class of Optimisation Heuristics. In: Cotta, C., van Hemert, J. (eds.) EvoCOP 2007. LNCS, vol. 4446, pp. 198–209. Springer, Heidelberg (2007)
Zhang, W., Korf, R.: A study of complexity transitions on the asymmetric traveling salesman problem. Artificial Intelligence 81(1-2), 223–239 (1996)
Zhang, W.: Phase transitions and backbones of the asymmetric traveling salesman problem. Journal of Artificial Intelligence Research 21, 471–497 (2004)
Gent, I., Walsh, T.: The TSP phase transition. Artificial Intelligence 88(1-2), 349–358 (1996)
Thiebaux, S., Slaney, J., Kilby, P.: Estimating the hardness of optimisation. In: ECAI, pp. 123–130 (2000)
Gaertner, D., Clark, K.: On optimal parameters for ant colony optimization algorithms. In: Proceedings of the 2005 International Conference on Artificial Intelligence, Citeseer, vol. 1, pp. 83–89 (2005)
Stadler, P., Schnabl, W.: The landscape of the traveling salesman problem. Phys. Lett. A 161(4), 337–344 (1992)
Kilby, P., Slaney, J., Walsh, T.: The backbone of the travelling salesperson. In: International Joint Conference on Artificial Intelligence, vol. 19, p. 175 (2005)
Lin, S., Kernighan, B.: An efficient heuristic algorithm for the traveling salesman problem. Operations Research 21(2) (1973)
van Hemert, J.: Property analysis of symmetric travelling salesman problem instances acquired through evolution. In: Raidl, G.R., Gottlieb, J. (eds.) EvoCOP 2005. LNCS, vol. 3448, pp. 122–131. Springer, Heidelberg (2005)
van Hemert, J., Urquhart, N.: Phase transition properties of clustered travelling salesman problem instances generated with evolutionary computation. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 151–160. Springer, Heidelberg (2004)
van Hemert, J.: Property analysis of symmetric travelling salesman problem instances acquired through evolution. In: Raidl, G.R., Gottlieb, J. (eds.) EvoCOP 2005. LNCS, vol. 3448, pp. 122–131. Springer, Heidelberg (2005)
Kratica, J., Ljubić, I., Tošic, D.: A genetic algorithm for the index selection problem. In: Raidl, G.R., Cagnoni, S., Cardalda, J.J.R., Corne, D.W., Gottlieb, J., Guillot, A., Hart, E., Johnson, C.G., Marchiori, E., Meyer, J.-A., Middendorf, M. (eds.) EvoIASP 2003, EvoWorkshops 2003, EvoSTIM 2003, EvoROB/EvoRobot 2003, EvoCOP 2003, EvoBIO 2003, and EvoMUSART 2003. LNCS, vol. 2611, pp. 281–291. Springer, Heidelberg (2003)
Lin, S., Kernighan, B.: An effective heuristic algorithm for the traveling salesman problem. Operations Research 21, 498–516 (1973)
Applegate, D., Cook, W., Rohe, A.: Chained lin-kernighan for large travelling salesman problems (2000), http://www.citeseer.com/applegate99chained.html
Johnson, D., McGeoch, L.: The traveling salesman problem: a case study. In: Aarts, E., Lenstra, J. (eds.) Local Search in Combinatorial Optimization, pp. 215–310. John Wiley & Sons, Inc., Chichester (1997)
Sander, J., Ester, M., Kriegel, H., Xu, X.: Density-based clustering in spatial databases: The algorithm gdbscan and its applications. Data Mining and Knowledge Discovery 2(2), 169–194 (1998)
Kohonen, T.: Self-organization maps. Proc. IEEE 78, 1464–1480 (1990)
SOMine, V.: Enterprise Edition Version 3.0, Eudaptics Software Gmbh (1999)
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Smith-Miles, K., van Hemert, J., Lim, X.Y. (2010). Understanding TSP Difficulty by Learning from Evolved Instances. In: Blum, C., Battiti, R. (eds) Learning and Intelligent Optimization. LION 2010. Lecture Notes in Computer Science, vol 6073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13800-3_29
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DOI: https://doi.org/10.1007/978-3-642-13800-3_29
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