Skip to main content
Log in

Parameter-less algorithm for evolutionary-based optimization

For continuous and combinatorial problems

  • Published:
Computational Optimization and Applications Aims and scope Submit manuscript

Abstract

The development of a simple, adaptive, parameter-less search algorithm was initiated by the need for an algorithm that is able to find optimal solutions relatively quick, and without the need for a control-parameter-setting specialist. Its control parameters are calculated during the optimization process, according to the progress of the search. The algorithm is intended for continuous and combinatorial problems. The efficiency of the proposed parameter-less algorithm was evaluated using one theoretical and three real-world industrial optimization problems. A comparison with other evolutionary approaches shows that the presented adaptive parameter-less algorithm has a competitive convergence with regards to the comparable algorithms. Also, it proves algorithm’s ability to finding the optimal solutions without the need for predefined control parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Algorithm 1
Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Angeli, D., Kountouriotis, P.A.: A stochastic approach to “dynamic-demand” refrigerator control. IEEE Trans. Control Syst. Technol. PP(99), 1–12 (2011)

    Google Scholar 

  2. Bäck, T.: The interaction of mutation rate, selection, and self-adaptation within a genetic algorithm. In: Männer, R., Manderick, B. (eds.) Proceedings of the 2nd Conference on Parallel Problem Solving from Nature. North-Holland, Amsterdam (1992)

    Google Scholar 

  3. Bäck, T.: Evolutionary Algorithms in Theory and Practice, 2nd edn. Oxford University Press, Heidelberg (1996)

    MATH  Google Scholar 

  4. Bäck, T., Fogel, D.B., Michalewicz, Z. (eds.): Handbook of Evolutionary Computation, 1st edn. IOP Publishing, Bristol (1997)

    MATH  Google Scholar 

  5. Beyer, H.G., Schwefel, H.P.: Evolution strategies—a comprehensive introduction. Nat. Comput. 1, 3–52 (2002). doi:10.1023/A:1015059928466. http://dl.acm.org/citation.cfm?id=584639.584641

    Article  MathSciNet  MATH  Google Scholar 

  6. Brest, J., Greiner, S., Bošković, B., Mernik, M., Žumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10(6), 646–657 (2006)

    Article  Google Scholar 

  7. Brest, J., Zumer, V., Maucec, M.: Self-adaptive differential evolution algorithm in constrained real-parameter optimization. In: IEEE Congress on Evolutionary Computation, 2006, CEC, 2006, pp. 215–222 (2006). doi:10.1109/CEC.2006.1688311

    Chapter  Google Scholar 

  8. da Graca Lobo, F.M.P.: The parameter-less genetic algorithm: Rational and automated parameter selection for simplified genetic algorithm operation. Ph.D. thesis, Universidade Nova de Lisboa (2000)

  9. De Jong, K.A.: An analysis of the behavior of a class of genetic adaptive systems. Ph.D. thesis, University of Michigan, Ann Arbor, MI, USA (1975). AAI7609381

  10. Deb, K.: A population-based algorithm-generator for real-parameter optimization. Soft Comput. 9, 236–253 (2005). doi:10.1007/s00500-004-0377-4. http://dl.acm.org/citation.cfm?id=1050483.1050486.

    Article  MATH  Google Scholar 

  11. Deb, K., Agrawal, S.: Understanding interactions among genetic algorithm parameters. In: Foundations of Genetic Algorithms, vol. 5, pp. 265–286. Morgan Kaufmann, San Mateo (1998)

    Google Scholar 

  12. Dorigo, M.: Optimization, learning and natural algorithms (in Italian). Ph.D. thesis, Dipartimento di Elettronica, Politecnico di Milano, Milan, Italy (1992)

  13. Eiben, A.E., Hinterding, R., Michalewicz, Z.: Parameter control in evolutionary algorithms. IEEE Trans. Evol. Comput. 3(2), 124–141 (1999)

    Article  Google Scholar 

  14. Eiben, A.E., Michalewicz, Z., Schoenauer, M., Smith, J.: Parameter control in evolutionary algorithms. In: Lobo, F., Lima, C., Michalewicz, Z. (eds.) Parameter Setting in Evolutionary Algorithms, Studies in Computational Intelligence, vol. 54, pp. 19–46. Springer, Berlin (2007)

    Chapter  Google Scholar 

  15. Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Longman, Boston (1989)

    MATH  Google Scholar 

  16. Gong, W., Fialho, A., Cai, Z.: Adaptive strategy selection in differential evolution. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, GECCO ’10, pp. 409–416. ACM, New York (2010). doi:10.1145/1830483.1830559

    Chapter  Google Scholar 

  17. Greenwood, G.W., Zhu, Q.J.: Convergence in evolutionary programs with self-adaptation. Evol. Comput. 9, 147–158 (2001)

    Article  Google Scholar 

  18. Harik, G., Lobo, F.: A parameter-less genetic algorithm. In: Proc. Genetic and Evolutionary Computation Conference, GECCO, 1999, pp. 258–265 (1999)

    Google Scholar 

  19. Kang, Q., Wang, L., di Wu, Q.: Research on fuzzy adaptive optimization strategy of particle swarm algorithm. Int. J. Inf. Technol. 12(3), 65–77 (2006)

    Google Scholar 

  20. Kennedy, J.F., Eberhart, R.C., Shi, Y.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001)

    Google Scholar 

  21. Kita, H.: A comparison study of self-adaptation in evolution strategies and real-coded genetic algorithms. Evol. Comput. 9, 223–241 (2001). doi:10.1162/106365601750190415

    Article  Google Scholar 

  22. Korošec, P., Šilc, J.: High-dimensional real-parameter optimization using the differential ant-stigmergy algorithm. Int. J. Intell. Comput. Cybern. 2(1), 34–51 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  23. Korošec, P., Papa, G., Vukašinović, V.: Application of memetic algorithm in production planning. In: Proc. Bioinspired Optimization Methods and Their Applications, BIOMA 2010, pp. 163–175 (2010)

    Google Scholar 

  24. Korošec, P., Šilc, J., Filipič, B.: The differential ant-stigmergy algorithm. Information Sciences 192(1), 82–97 (2012). doi:10.1016/j.ins.2010.05.002

    Article  Google Scholar 

  25. Liang, J., Runarsson, T., Mezura-Montes, E., Clerc, M., Suganthan, P., Coello, C.C., Deb, K.: Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization. Tech. Rep. 2006005, Nanyang Technological University, Singapore (2006). http://www.ntu.edu.sg/home/EPNSugan

  26. Michalewicz, Z., Fogel, D.: How to Solve It: Modern Heuristics, 2nd edn. Springer, Berlin (2004)

    Book  Google Scholar 

  27. Ong, Y.S., Lum, K.Y., Nair, P.B.: Hybrid evolutionary algorithm with Hermite radial basis function interpolants for computationally expensive adjoint solvers. Comput. Optim. Appl. 39, 97–119 (2008). doi:10.1007/s10589-007-9065-5. http://dl.acm.org/citation.cfm?id=1331380.1331383.

    Article  MathSciNet  MATH  Google Scholar 

  28. Papa, G.: Concurrent operation scheduling and unit allocation with an evolutionary technique in the process of integrated-circuit design. Ph.D. thesis, University of Ljubljana, Ljubljana, Slovenia (2002)

  29. Papa, G.: Parameter-less evolutionary search. In: Proc. Genetic and Evolutionary Computation Conference (GECCO’08), pp. 1133–1134 (2008)

    Chapter  Google Scholar 

  30. Papa, G.: Combinatorial implementation of a parameter-less evolutionary algorithm. In: Proc. 3rd International Joint Conference on Computational Intelligence, pp. 307–310. SciTePress (2011)

  31. Papa, G., Mrak, P.: Optimization of cooling appliance control parameters. In: Proceedings of the 2nd International Conference on Engineering Optimization, EngOpt2010 (2010)

    Google Scholar 

  32. Papa, G., Mrak, P.: Thermal simulation for development speed-up. In: Proc. Second International Conference on Advances in System Simulation, pp. 11–15 (2010)

    Google Scholar 

  33. Papa, G., Mrak, P.: Temperature simulations in cooling appliances. Elektroteh. Vestn. 78(1–2), 67–72 (2011)

    Google Scholar 

  34. Papa, G., Vukašinović, V., Korošec, P.: Guided restarting local search for production planning. Eng. Appl. Artif. Intell. 25(2), 242–253 (2012). doi:10.1016/j.engappai.2011.07.001. http://www.sciencedirect.com/science/article/pii/S0952197611001242

    Article  Google Scholar 

  35. Schwefel, H.P.P.: Evolution and Optimum Seeking: the Sixth Generation. Wiley, New York (1993)

    Google Scholar 

  36. Stephens, C.R., Olmedo, I.G., Vargas, J.M., Waelbroeck, H.: Self-adaptation in evolving systems. Artif. Life 4, 183–201 (1998)

    Article  Google Scholar 

  37. Storn, R., Price, K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11, 341–359 (1997). doi:10.1023/A:1008202821328. http://dl.acm.org/citation.cfm?id=596061.596146

    Article  MathSciNet  MATH  Google Scholar 

  38. Takahama, T., Sakai, S.: Constrained optimization by the ε constrained differential evolution with gradient-based mutation and feasible elites. In: IEEE Congress on Evolutionary Computation, 2006, CEC 2006, pp. 1–8 (2006)

    Chapter  Google Scholar 

  39. Tang, K., Yao, X., Suganthan, P., MacNish, C., Chen, Y., Chen, C., Yang, Z.: Benchmark functions for the CEC’2008 special session and competition on large scale global optimization. Tech. Rep. NCL-TR-2007012, University of Science and Technology of China (USTC), Nature Inspired Computation and Applications Laboratory (NICAL): Héféi, Ānhuī, China (2007)

  40. Tušar, T., Korošec, P., Papa, G., Filipič, B., Šilc, J.: A comparative study of stochastic optimization methods in electric motor design. Appl. Intell. 27(2), 101–111 (2007)

    Article  MATH  Google Scholar 

  41. Wu, L., Wang, Y., Zhou, S., Yuan, X.: Self-adapting control parameters modified differential evolution for trajectory planning of manipulators. J. Control Theory Appl. 5, 365–373 (2007). doi:10.1007/s11768-006-6178-9

    Article  MATH  Google Scholar 

  42. Zhao, S.Z., Suganthan, P.N., Das, S.: Self-adaptive differential evolution with multi-trajectory search for large-scale optimization. Soft Comput. 15(11), 2175–2185 (2011). doi:10.1007/s10589-013-9565-4

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gregor Papa.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Papa, G. Parameter-less algorithm for evolutionary-based optimization. Comput Optim Appl 56, 209–229 (2013). https://doi.org/10.1007/s10589-013-9565-4

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10589-013-9565-4

Keywords

Navigation