Abstract
In many technical fields, single-objective optimization procedures in continuous domains involve expensive numerical simulations. In this context, an improvement of the Artificial Bee Colony (ABC) algorithm, called the Artificial super-Bee enhanced Colony (AsBeC), is presented. AsBeC is designed to provide fast convergence speed, high solution accuracy and robust performance over a wide range of problems. It implements enhancements of the ABC structure and hybridizations with interpolation strategies. The latter are inspired by the quadratic trust region approach for local investigation and by an efficient global optimizer for separable problems. Each modification and their combined effects are studied with appropriate metrics on a numerical benchmark, which is also used for comparing AsBeC with some effective ABC variants and other derivative-free algorithms. In addition, the presented algorithm is validated on two recent benchmarks adopted for competitions in international conferences. Results show remarkable competitiveness and robustness for AsBeC.
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Akay, B., & Karaboga, D. (2010). Artificial bee colony algorithm for large-scale problems and engineering design optimization. Journal of Intelligent Manufacturing, 23(4), 1001–1014.
Akay, B., & Karaboga, D. (2012). A modified artificial bee colony algorithm for real-parameter optimization. Information Sciences, 192, 120–142.
Aydin, D. (2015). Composite artificial bee colony algorithms: From component-based analysis to high-performing algorithms. Applied Soft Computing, 32, 266–285.
Bagirov, A. M., Karaszen, B., & Sezer, M. (2008). Discrete gradient method: Derivative-free method for nonsmooth optimization. Journal of Optimization Theory and Application, 137(2), 317–334.
Bartz-Beielstein, T., Lasarczyk, C., & Preuß, M. (2005). Sequential parameter optimization. In Proceedings of the 2005 IEEE congress on evolutionary computation (Vol. 1, pp. 773-780). Piscataway, NJ: IEEE Press.
Baudiš, P., & Pošík, P. (2015). Global line search algorithm hybridized with quadratic interpolation and its extension to separable functions. In Proceedings of the 2015 annual conference on genetic and evolutionary computation (pp. 257–264). New York, NY: ACM.
Berghen, F. V., & Bersini, H. (2005). CONDOR, a new parallel, constrained extension of Powell’s UOBYQA algorithm: Experimental results and comparison with the DFO algorithm. Journal of Computational and Applied Mathematics, 181(1), 157–175.
Bertini, F., Dal Mas, L., Vassio, L., & Ampellio, E. (2013). Multidisciplinary optimization for gas turbines design. XXII AIDAA Conference. http://arxiv.org/pdf/1402.0420v1. Accessed 5 Feb 2016.
Beyer, H. G., & Schwefel, H. P. (2002). Evolution strategies: A comprehensive introduction. Natural Computing, 1(1), 3–52.
Bolaji, A., Khader, A., Al-Betar, M., & Awadallah, M. (2013). Artificial Bee Colony algorithm, its variants and applications: A survey. Journal of Theoretical and Applied Information Technology, 47(2), 434–459.
Box, G. E. P., & Draper, N. (2007). Response surfaces, mixtures, and ridge analyses (2nd ed.). Hoboken, NJ: Wiley.
Buhmann, M. D. (2003). Radial basis functions: Theory and implementations. Cambridge, UK: Cambridge University Press.
Chen, Q., Liu, B., Zhang, Q., Liang, J. J., Suganthan, P. N. & Qu B. Y (2015). Problem definitions and evaluation criteria for CEC 2015 special session on bound constrained single-objective computationally expensive numerical optimization. Technical Report, Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou, Nov 2014.
Conn, A. R., Gould, G., & Toint, P. (2000). Trust region methods. Philadelphia, PA: SIAM.
Couzin, I. D., Krause, L., Ruxton, G. D., & Franks, N. R. (2002). Collective memory and spatial sorting in animal groups. Journal of Theoretical Biology, 128(1), 1–11.
Deb, K. (2012). Optimization for engineering design: Algorithms and examples (2nd ed.). New Delhi: PHI Learning Pvt.
Dorigo, M., & Stützle, T. (2004). Ant colony optimization. Cambridge, MA: MIT Press.
El-Abd, M. (2011). Opposition-based artificial bee colony algorithm. In Proceedings of the 13th annual conference on genetic and evolutionary computation (pp. 109–116). New York, NY: ACM.
Floudas, C., & Pardolos, M. (2009). Encyclopedia of optimization (2nd ed.). New York, NY: Springer.
Frish, K. (1967). The dance language and orientation of bees. Cambridge, MA: Harvard University Press.
Gao, W., & Liu, S. (2011). Improved artificial bee colony algorithm for global optimization. Information Processing Letters, 111, 871–882.
Gao, W., & Liu, S. (2012). A global best artificial bee colony algorithm for global optimization. Journal of Computational and Applied Mathematics, 236(11), 2741–2753.
Goldberg, D. (1989). Genetic algorithms in search, optimization and machine learning. Boston, MA: Addison-Wesley Longman Publishing.
Hansen, N. (2006). The CMA evolution strategy: A comparing review. In J. A. Lozano, et al. (Eds.), Towards a new evolutionary computation. Advances in estimation of distribution algorithms (pp. 75–102). Berlin: Springer.
Hansen, N., Auger, A., Finck, S., & Ros, R. (2009a). Real-parameter black-box optimization benchmarking 2009: Experimental setup. Technical Report RR-6828, INRIA.
Hansen, N., Finck, S., Ros, R., & Auger, A. (2009b). Real-parameter black-box optimization benchmarking 2009: Noiseless functions definitions. Technical Report RR-6829, INRIA.
Iliadis, J., & Jayne, C. (Eds.). (2015). Engineering applications of neural networks: Proceedings of the 16th international conference on engineering applications of neural networks. Berlin: Springer.
Jamil, M., & Yang, X. S. (2013). A literature survey of benchmark functions for global optimization problems. International Journal of Mathematical Modelling and Numerical Optimization, 4(2), 150–194.
Jones, D. R., Schonlau, M., & Welch, W. J. (1998). Efficient global optimization of expensive black-box functions. Journal of Global Optimization, 13(4), 455–492.
Kang, F., Li, J., & Xu, Q. (2009). Structural inverse analysis by hybrid simplex artificial bee colony algorithms. Computers and Structures, 87(13–14), 861–870.
Kang, F., Li, J., & Ma, Z. (2011). Rosenbrock artificial bee colony algorithm for accurate global optimization of numerical functions. Information Sciences, 181(16), 3508–3531.
Kang, F., Li, J., & Li, H. (2013). Artificial bee colony algorithm and pattern search hybridized for global optimization. Applied Soft Computing, 13(4), 1781–1791.
Karaboga, D. (2007). A powerful and efficient algorithm for numerical function optimization: Artificial bee colony (ABC) algorithm. Journal of Global Optimization, 39(3), 459–471.
Karaboga, D., & Akay, B. (2007). Artificial Bee Colony (ABC) optimization algorithm for solving constrained optimization problems. In P. Melin, et al. (Eds.), Foundations of fuzzy logic and soft computing: Proceedings of the 12th international fuzzy systems association world congress 2007 (pp. 789–798). Berlin: Springer.
Karaboga, D., & Akay, B. (2009). A comparative study of artificial Bee colony algorithm. Applied Mathematics and Computations, 214(1), 108–132.
Karaboga, D., Gorkemli, B., Ozturk, C., & Karaboga, N. (2014). A comprehensive survey: Artificial bee colony (ABC) algorithm and applications. Artificial Intelligence Review, 42(1), 21–57.
Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. Proceedings of IEEE international conference on neural networks 1995 (pp. 1942–1948). Piscataway, NJ: IEEE Press.
Kern, S., Hansen, N., & Koumoutsakos, P. (2006). Local meta-models for optimization using evolution strategies. In T. P. Runarsson, et al. (Eds.), Proceedings of the 9th international conference of parallel problem solving from nature—PPSN IX (pp. 938–948). Berlin: Springer.
Kong, X., Liu, S., & Wang, Z. (2013). An improved artificial Bee Colony algorithm and its application. International Journal of Signal Processing, Image Processing and Pattern Recognition, 6(6), 259–274.
Koziel, S., & Leifsson, L. (2013). Surrogate-based modeling and optimization, applications in engineering. New York, NY: Springer.
Lagaros, N., & Papadrakakis, M. (Eds.). (2015). Computational methods in applied sciences: Engineering and applied sciences optimization. Cham: Springer.
Levenberg, K. (1944). A method for the solution of certain non-linear problems in least square. Quarterly Journal of Applied Mathematics, 2, 164–168.
Li, B., & Li, Y. (2010). BE-ABC: Hybrid artificial Bee Colony algorithm with balancing evolution strategy. In Proceedings of the 3rd international conference on intelligent control and information processing (pp. 217–222). Piscataway, NJ: IEEE Press.
Liao, T., Aydin, D., & Stützle, T. (2013). Artificial bee colonies for continuous optimization: Experimental analysis and improvements. Swarm Intelligence, 7(4), 327–357.
Marquardt, D. (1963). An algorithm for least-squares estimation of nonlinear parameters. SIAM Journal on Applied Mathematics, 11(2), 431–441.
Powell, M. (2000). UOBYQA: Unconstrained optimization by quadratic approximation. Technical Report No. DAMTP2000/14, Department of Applied Mathematics and Theoretical Physics, University of Cambridge.
Powell, M., (2009). The BOBYQA algorithm for bound constrained optimization without derivatives. Technical report NA2009/06, Department of Applied Mathematics and Theoretical Physics, University of Cambridge.
Price, K., Storn, R., & Lampinen, J. (2005). Differential evolution—a practical approach to global optimization. Berlin: Springer.
Qu, B. Y., Liang, J. J., Wang, Z. Y., Chen, Q., & Suganthan, P. N. (2016). Novel Benchmark functions for continuous multimodal optimization with comparative results. Swarm and Evolutionary Computation, 26, 23–34.
Rao, S. (2009). Engineering optimization: Theory and practice (4th ed.). New York, NY: Wiley.
Rios, L. M., & Sahinidis, N. V. (2013). Derivative-free optimization: A review of algorithms and comparison of software implementations. Journal of Global Optimization, 56(3), 1247–1293.
Roland, F. W., & Nachtigal, N. M. (1991). QMR: A quasi-minimal residual method for non-Hermitian linear systems. Numerische Mathematik., 60(1), 315–339.
Rosenbrock, H. H. (1960). An automatic method for finding the greatest or least value of a function. The Computer Journal, 3(3), 175–184.
Simpson, T. W., Mauery, T. M., Korte, J. J., & Mistree, F. (2001). Kriging models for global approximation in simulation-based multidisciplinary design optimization. AIAA Journal, 39(12), 2233–2241.
Subotic, M., Tuba, M., & Stanarevic, N. (2011). Different approaches in parallelization of the artificial bee colony algorithm. International Journal of Mathematical Models and Methods in Applied Sciences, 5(4), 755–762.
Subotic, M. (2011). Artificial bee colony algorithm with multiple onlookers for constrained optimization problems. In Proceedings of the 5th European computing conference (pp. 251–256). Stevens Point, WI: World Scientific and Engineering Academy and Society.
Sulaiman, N., Mohamed-Saleh, J., & Abro, A. G. (2014). New enhanced Artificial Bee Colony (JA-ABC5) algorithm with application for reactive power optimization. The Scientific World Journal, 2015, 1–11.
Swarzberg, S., Seront, G., & Bersini, H. (1994), S.T.E.P.: the easiest way to optimize a function. In Proceedings of the 1st IEEE conference on evolutionary computation (pp. 519-524). Piscataway, NJ: IEEE Press.
Talbi, E. (2009). Metaheuristics: From design to implementation. Hoboken, NJ: Wiley.
Yang, X. (2009). Firefly algorithms for multimodal optimization. In Proceedings of the 5th international conference on stochastic algorithms: Foundations and applications (pp. 169–178). Berlin: Springer.
Yang, X. (2010). Engineering optimization: An introduction with metaheuristic applications. Hoboken, NJ: Wiley.
Yang, X., & He, X. (2013). Firefly algorithm: Recent advances and applications. International Journal of Swarm Intelligence, 1(1), 36–50.
Zhao, H., Pei, Z., Jiang, J., Guan, R., Wang, C., & Shi, X. (2010). A hybrid swarm intelligent method based on genetic algorithm and artificial bee colony. In Proceedings of the 1st international conference on advances in swarm intelligence (pp. 558–565). Berlin: Springer.
Zhu, G., & Kwong, S. (2010). Gbest-guided artificial bee colony algorithm for numerical function optimization. Applied Mathematics and Computation, 217(7), 3166–3173.
Acknowledgments
The authors would like to thank GE Avio S.r.l. and its Engineering Technologies department, especially Ing. F. Bertini and Ing. E. Spano. Their collaboration was fundamental for shaping the AsBeC algorithm within an industrial application framework. We are also grateful to Prof. E. Benini (Università di Padova) for his comments and reviews.
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Ampellio, E., Vassio, L. A hybrid swarm-based algorithm for single-objective optimization problems involving high-cost analyses. Swarm Intell 10, 99–121 (2016). https://doi.org/10.1007/s11721-016-0121-6
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DOI: https://doi.org/10.1007/s11721-016-0121-6