Abstract
The performance of optimization algorithms, including those based on swarm intelligence, depends on the values assigned to their parameters. To obtain high performance, these parameters must be fine-tuned. Since many parameters can take real values or integer values from a large domain, it is often possible to treat the tuning problem as a continuous optimization problem. In this article, we study the performance of a number of prominent continuous optimization algorithms for parameter tuning using various case studies from the swarm intelligence literature. The continuous optimization algorithms that we study are enhanced to handle the stochastic nature of the tuning problem. In particular, we introduce a new post-selection mechanism that uses F-Race in the final phase of the tuning process to select the best among elite parameter configurations. We also examine the parameter space of the swarm intelligence algorithms that we consider in our study, and we show that by fine-tuning their parameters one can obtain substantial improvements over default configurations.
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References
Adenso-Díaz, B., & Laguna, M. (2006). Fine-tuning of algorithms using fractional experimental designs and local search. Operations Research, 54(1), 99–114.
Ansótegui, C., Sellmann, M., & Tierney, K. (2009). A gender-based genetic algorithm for the automatic configuration of solvers. In I. P. Gent (Ed.), LNCS: Vol. 5732. Principles and practice of constraint programming—CP 2009 (pp. 142–157). Heidelberg: Springer.
Audet, C., & Dennis, J. E. (2006). Mesh adaptive direct search algorithms for constrained optimization. SIAM Journal on Optimization, 17(1), 188–217.
Auger, A., Hansen, N., Zerpa, J. M. P., Ros, R., & Schoenauer, M. (2009). Experimental comparisons of derivative free optimization algorithms. In J. Vahrenhold (Ed.), LNCS: Vol. 5526. Experimental algorithms, 8th international symposium, SEA 2009 (pp. 3–15). Heidelberg: Springer.
Bartz-Beielstein, T. (2006). Experimental research in evolutionary computation–the new experimentalism. Berlin: Springer.
Birattari, M. (2009). Tuning metaheuristics: a machine learning perspective. Berlin: Springer.
Birattari, M., Stützle, T., Paquete, L., & Varrentrapp, K. (2002). A racing algorithm for configuring metaheuristics. In W. B. Langdon, et al. (Eds.), GECCO 2002: proceedings of the genetic and evolutionary computation conference (pp. 11–18). San Francisco: Morgan Kaufmann.
Birattari, M., Zlochin, M., & Dorigo, M. (2006). Towards a theory of practice in metaheuristics design: a machine learning perspective. Theoretical Informatics and Applications, 40(2), 353–369.
Birattari, M., Yuan, Z., Balaprakash, P., & Stützle, T. (2010). F-Race and iterated F-Race: An overview. In T. Bartz-Beielstein, et al. (Eds.), Experimental methods for the analysis of optimization algorithms (pp. 311–336). Berlin: Springer.
Clerc, M. (2006). Particle swarm optimization. London: ISTE.
Clerc, M., & Kennedy, J. (2002). The particle swarm–explosion, stability, and convergence in a multidimensional complex space. IEEE Transactions on Evolutionary Computation, 6(1), 58–73.
Dorigo, M. (2007). Ant colony optimization. Scholarpedia, 2(3), 1461.
Dorigo, M., & Gambardella, L. (1997). Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Transactions on Evolutionary Computation, 1(1), 53–66.
Dorigo, M., & Stützle, T. (2004). Ant colony optimization. Cambridge: MIT Press.
Dorigo, M., Maniezzo, V., & Colorni, A. (1996). Ant system: optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man and Cybernetics. Part B. Cybernetics, 26(1), 29–41.
Dorigo, M., Birattari, M., & Stutzle, T. (2006). Ant colony optimization. IEEE Computational Intelligence Magazine, 1(4), 28–39.
Dorigo, M., Montes de Oca, M. A., & Engelbrecht, A. P. (2008). Particle swarm optimization. Scholarpedia, 3(11), 1486.
Fukunaga, A. S. (2008). Automated discovery of local search heuristics for satisfiability testing. Evolutionary Computation, 16(1), 31–61.
Hansen, N. (2006). The CMA evolution strategy: a comparing review. In J. Lozano, et al. (Eds.), Studies in fuzziness and soft computing: Vol. 192. Towards a new evolutionary computation (pp. 75–102). Berlin: Springer.
Hutter, F., Hoos, H. H., Leyton-Brown, K., & Murphy, K. P. (2009a). An experimental investigation of model-based parameter optimisation: SPO and beyond. In F. Rothlauf (Ed.), Genetic and evolutionary computation conference, GECCO 2009 (pp. 271–278). New York: ACM Press.
Hutter, F., Hoos, H. H., Leyton-Brown, K., & Stützle, T. (2009b). ParamILS: an automatic algorithm configuration framework. Journal of Artificial Intelligence Research, 36, 267–306.
Johnson, D. S., McGeoch, L. A., Rego, C., & Glover, F. (2001). 8th DIMACS implementation challenge. http://www.research.att.com/~dsj/chtsp/.
Jones, T., & Forrest, S. (1995). Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In L. J. Eshelman (Ed.), Proc. of the 6th international conference on genetic algorithms (pp. 184–192). San Francisco: Morgan Kaufmann.
Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In Proc. of IEEE international conference on neural networks (pp. 1942–1948). Piscataway: IEEE Press.
Kennedy, J., & Mendes, R. (2006). Neighborhood topologies in fully informed and best-of-neighborhood particle swarms. IEEE Transactions on Systems, Man and Cybernetics. Part C, Applications and Reviews, 36(4), 515–519.
Kennedy, J., Eberhart, R., & Shi, Y. (2001). Swarm intelligence. San Francisco: Morgan Kaufmann.
Mengshoel, O. (2008). Understanding the role of noise in stochastic local search: analysis and experiments. Artificial Intelligence, 172(8–9), 955–990.
Nannen, V., & Eiben, A. E. (2007). Relevance estimation and value calibration of evolutionary algorithm parameters. In Proc. of IJCAI 2007 (pp. 975–980). Menlo Park: AAAI Press/IJCAI.
Oltean, M. (2005). Evolving evolutionary algorithms using linear genetic programming. Evolutionary Computation, 13(3), 387–410.
Poli, R., Kennedy, J., & Blackwell, T. (2007). Particle swarm optimization. An overview. Swarm Intelligence, 1(1), 33–57.
Powell, M. J. D. (2006). The NEWUOA software for unconstrained optimization. In Nonconvex optimization and its applications: Vol. 83. Large-scale nonlinear optimization (pp. 255–297). Berlin: Springer.
Powell, M. J. D. (2009). The BOBYQA algorithm for bound constrained optimization without derivatives (Technical Report NA2009/06). Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK.
Steinmann, O., Strohmaier, A., & Stützle, T. (1997). Tabu search vs. random walk. In G. Brewka, C. Habel, & B. Nebel (Eds.), LNAI: Vol. 1303. KI-97: advances in artificial intelligence (pp. 337–348). Heidelberg: Springer.
Stützle, T. (1999). DISKI: Vol. 220. Local search algorithms for combinatorial problems: analysis, improvements, and new applications. Sankt Augustin: Infix.
Stützle, T. (2002). Software ACOTSP. http://iridia.ulb.ac.be/~mdorigo/ACO/aco-code/public-software.html.
Stützle, T., & Hoos, H. H. (1998). MAX-MIN ant system and local search for combinatorial optimization problems: Towards adaptive tools for combinatorial global optimization. In S. Voss, et al. (Eds.), Meta-heuristics: advances and trends in local search paradigms for optimization (pp. 313–329). Dordrecht: Kluwer Academic.
Stützle, T., & Hoos, H. (2000). \(\mathcal{MAX}\)–\(\mathcal{MIN}\) ant system. Future Generations Computer Systems, 16(8), 889–914.
Torczon, V. (1997). On the convergence of pattern search algorithms. SIAM Journal on Optimization, 7(1), 1–25.
Yuan, Z., Montes de Oca, M., Birattari, M., & Stützle, T. (2010a). Modern continuous optimization algorithms for tuning real and integer algorithm parameters. In M. Dorigo, et al. (Eds.), LNCS: Vol. 6234. Proceedings of ANTS 2010, the seventh international conference on swarm intelligence (pp. 204–215). Heidelberg: Springer.
Yuan, Z., Stützle, T., & Birattari, M. (2010b). MADS/F-Race: mesh adaptive direct search meets F-race. In M. Ali, et al. (Eds.), LNAI: Vol. 6096. Proceedings of IEA-AIE 2010 (pp. 41–50). Heidelberg: Springer.
Zlochin, M., Birattari, M., Meuleau, N., & Dorigo, M. (2004). Model-based search for combinatorial optimization: a critical survey. Annals of Operations Research, 131(1–4), 373–395.
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Yuan, Z., Montes de Oca, M.A., Birattari, M. et al. Continuous optimization algorithms for tuning real and integer parameters of swarm intelligence algorithms. Swarm Intell 6, 49–75 (2012). https://doi.org/10.1007/s11721-011-0065-9
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DOI: https://doi.org/10.1007/s11721-011-0065-9