A Quantum Field Evolution Strategy - An Adaptive Surrogate Approach

Jörg Bremer, Sebastian Lehnhoff


Evolution strategies have been successfully applied to optimization problems with rugged, multi-modal fitness landscapes, to non linear problems, and to derivative free optimization. Usually evolution is performed by exploiting the structure of the objective function. In this paper, we present an approach that harnesses the adapting quantum potential field determined by the spatial distribution of elitist solutions as guidance for the next generation. The potential field evolves to a smoother surface leveling local optima but keeping the global structure what in turn allows for a faster convergence of the solution set. We demonstrate the applicability and the competitiveness of our approach compared with particle swarm optimization and the well established evolution strategy CMA-ES.


  1. Ahrari, A. and Shariat-Panahi, M. (2013). An improved evolution strategy with adaptive population size. Optimization, 64(12):1-20.
  2. Ben-Hur, A., Siegelmann, H. T., Horn, D., and Vapnik, V. (2001). Support vector clustering. Journal of Machine Learning Research, 2:125-137.
  3. Bremer, J., Rapp, B., and Sonnenschein, M. (2010). Support vector based encoding of distributed energy resources' feasible load spaces. In IEEE PES Conference on Innovative Smart Grid Technologies Europe, Chalmers Lindholmen, Gothenburg, Sweden.
  4. Bremer, J. and Sonnenschein, M. (2014). Parallel tempering for constrained many criteria optimization in dynamic virtual power plants. In Computational Intelligence Applications in Smart Grid (CIASG), 2014 IEEE Symposium on, pages 1-8.
  5. Feng, B. and Xu, W. (2004). Quantum oscillator model of particle swarm system. In ICARCV, pages 1454-1459. IEEE.
  6. Gano, S. E., Kim, H., and Brown II, D. E. (2006). Comparison of three surrogate modeling techniques: Datascape, kriging, and second order regression. In Proceedings of the 11th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, AIAA-2006- 7048, Portsmouth, Virginia.
  7. Hansen, N. (2006). The CMA evolution strategy: a comparing review. In Lozano, J., Larranaga, P., Inza, I., and Bengoetxea, E., editors, Towards a new evolutionary computation. Advances on estimation of distribution algorithms, pages 75-102. Springer.
  8. Hansen, N. (2011). The CMA Evolution Strategy: A Tutorial. Technical report.
  9. Hansen, N. and Ostermeier, A. (2001). Completely derandomized self-adaptation in evolution strategies. Evol. Comput., 9(2):159-195.
  10. Himmelblau, D. M. (1972). Applied nonlinear programming [by] David M. Himmelblau. McGraw-Hill New York.
  11. Horn, D. and Gottlieb, A. (2001). The Method of Quantum Clustering. In Neural Information Processing Systems, pages 769-776.
  12. Horn, D. and Gottlieb, A. (2002). Algorithm for data clustering in pattern recognition problems based on quantum mechanics. Phys Rev Lett, 88(1).
  13. Kennedy, J. and Eberhart, R. (1995). Particle swarm optimization. In Neural Networks, 1995. Proceedings., IEEE International Conference on, volume 4, pages 1942-1948 vol.4. IEEE.
  14. Knight, J. N. and Lunacek, M. (2007). Reducing the spacetime complexity of the CMA-ES. In Genetic and Evolutionary Computation Conference, pages 658-665.
  15. Kramer, O. (2010). A review of constraint-handling techniques for evolution strategies. Appl. Comp. Intell. Soft Comput., 2010:1-19.
  16. Leung, Y., Zhang, J.-S., and Xu, Z.-B. (2000). Clustering by scale-space filtering. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22(12):1396- 1410.
  17. Loo, C. K. and Mastorakis, N. E. (2007). Quantum potential swarm optimization of pd controller for cargo ship steering. In Proceedings of the 11th WSEAS International Conference on APPLIED MATHEMATICS, Dallas, USA.
  18. Loshchilov, I., Schoenauer, M., and Sebag, M. (2012). Selfadaptive surrogate-assisted covariance matrix adaptation evolution strategy. CoRR, abs/1204.2356.
  19. Metropolis, N., Rosenbluth, A. W., Rosenbluth, M. N., Teller, A. H., and Teller, E. (1953). Equation of state calculations by fast computing machines. The Journal of Chemical Physics, 21(6):1087-1092.
  20. Mishra, S. (2006). Some new test functions for global optimization and performance of repulsive particle swarm method. Technical report.
  21. Parzen, E. (1962). On estimation of a probability density function and mode. The annals of mathematical statistics, 33(3):1065-1076.
  22. Rahnamayan, S., Tizhoosh, H. R., and Salama, M. M. (2007). A novel population initialization method for accelerating evolutionary algorithms. Computers & Mathematics with Applications, 53(10):1605 - 1614.
  23. Rapp, B. and Bremer, J. (2012). Design of an event engine for next generation cemis: A use case. In HansKnud Arndt, Gerlinde Knetsch, W. P. E., editor, EnviroInfo 2012 - 26th International Conference on Informatics for Environmental Protection, pages 753-760. Shaker Verlag. ISBN 978-3-8440-1248-4.
  24. Rigling, B. D. and Moore, F. W. (1999). Exploitation of sub-populations in evolution strategies for improved numerical optimization. Ann Arbor, 1001:48105.
  25. Roberts, S. (1997). Parametric and non-parametric unsupervised cluster analysis. Pattern Recognition, 30(2):261-272.
  26. Shi, Y. and Eberhart, R. (1998). A modified particle swarm optimizer. In International Conference on Evolutionary Computation.
  27. Sun, J., Feng, B., and Xu, W. (2004). Particle swarm optimization with particles having quantum behavior. In Evolutionary Computation, 2004. CEC2004. Congress on, volume 1, pages 325-331 Vol.1.
  28. Suzuki, S. and Nishimori, H. (2007). Quantum annealing by transverse ferromagnetic interaction. In Pietronero, L., Loreto, V., and Zapperi, S., editors, Abstract Book of the XXIII IUPAP International Conference on Statistical Physics. Genova, Italy.
  29. Ulmer, H., Streichert, F., and Zell, A. (2003). Evolution strategies assisted by gaussian processes with improved pre-selection criterion. In in IEEE Congress on Evolutionary Computation,CEC 2003, pages 692- 699.
  30. Weinstein, M. and Horn, D. (2009a). Dynamic quantum clustering: A method for visual exploration of structures in data. Phys. Rev. E, 80:066117.
  31. Weinstein, M. and Horn, D. (2009b). Dynamic quantum clustering: a method for visual exploration of structures in data. Computing Research Repository, abs/0908.2.
  32. Weinstein, M., Meirer, F., Hume, A., Sciau, P., Shaked, G., Hofstetter, R., Persi, E., Mehta, A., and Horn, D. (2013). Analyzing big data with dynamic quantum clustering. CoRR, abs/1310.2700.
  33. Yao, X., Liu, Y., and Lin, G. (1999). Evolutionary programming made faster. IEEE Trans. Evolutionary Computation, 3(2):82-102.
  34. Yu, Y., Qian, F., and Liu, H. (2010). Quantum clusteringbased weighted linear programming support vector regression for multivariable nonlinear problem. Soft Computing, 14(9):921-929.
  35. Used test functions (Ulmer et al., 2003; Ahrari and Shariat-Panahi, 2013; Himmelblau, 1972; Yao et al., 1999; Mishra, 2006). 2
  36. f9pxq “ x1 12x1 11 10 cosppx1{2q 8 sinp5px1q p1{5q0.5é0.5px20.5q2 , 30 d x1, x2 d 30 with x° “ p5.90133, 0.5q f9px°q “ 43.3159.
  37. f10pxq “ px1 2x2 7q2p2x1 x2 5q2, 20 d x1, x2 d 20 with x° “ p1, 3q f9px°q “ 0.

Paper Citation

in Harvard Style

Bremer J. and Lehnhoff S. (2016). A Quantum Field Evolution Strategy - An Adaptive Surrogate Approach . In Proceedings of the 8th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2016) ISBN 978-989-758-201-1, pages 21-29. DOI: 10.5220/0006037000210029

in Bibtex Style

author={Jörg Bremer and Sebastian Lehnhoff},
title={A Quantum Field Evolution Strategy - An Adaptive Surrogate Approach},
booktitle={Proceedings of the 8th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2016)},

in EndNote Style

JO - Proceedings of the 8th International Joint Conference on Computational Intelligence - Volume 1: ECTA, (IJCCI 2016)
TI - A Quantum Field Evolution Strategy - An Adaptive Surrogate Approach
SN - 978-989-758-201-1
AU - Bremer J.
AU - Lehnhoff S.
PY - 2016
SP - 21
EP - 29
DO - 10.5220/0006037000210029