Computational Optimization and Applications

, Volume 56, Issue 1, pp 209–229 | Cite as

Parameter-less algorithm for evolutionary-based optimization

For continuous and combinatorial problems
  • Gregor Papa


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.


Optimization Evolutionary Adaptive Parameter-less Continuous Combinatorial 


  1. 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. 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. 3.
    Bäck, T.: Evolutionary Algorithms in Theory and Practice, 2nd edn. Oxford University Press, Heidelberg (1996) zbMATHGoogle Scholar
  4. 4.
    Bäck, T., Fogel, D.B., Michalewicz, Z. (eds.): Handbook of Evolutionary Computation, 1st edn. IOP Publishing, Bristol (1997) zbMATHGoogle Scholar
  5. 5.
    Beyer, H.G., Schwefel, H.P.: Evolution strategies—a comprehensive introduction. Nat. Comput. 1, 3–52 (2002). doi: 10.1023/A:1015059928466. MathSciNetzbMATHCrossRefGoogle Scholar
  6. 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) CrossRefGoogle Scholar
  7. 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 CrossRefGoogle Scholar
  8. 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) Google Scholar
  9. 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 Google Scholar
  10. 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. zbMATHCrossRefGoogle Scholar
  11. 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. 12.
    Dorigo, M.: Optimization, learning and natural algorithms (in Italian). Ph.D. thesis, Dipartimento di Elettronica, Politecnico di Milano, Milan, Italy (1992) Google Scholar
  13. 13.
    Eiben, A.E., Hinterding, R., Michalewicz, Z.: Parameter control in evolutionary algorithms. IEEE Trans. Evol. Comput. 3(2), 124–141 (1999) CrossRefGoogle Scholar
  14. 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) CrossRefGoogle Scholar
  15. 15.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Longman, Boston (1989) zbMATHGoogle Scholar
  16. 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 CrossRefGoogle Scholar
  17. 17.
    Greenwood, G.W., Zhu, Q.J.: Convergence in evolutionary programs with self-adaptation. Evol. Comput. 9, 147–158 (2001) CrossRefGoogle Scholar
  18. 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. 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. 20.
    Kennedy, J.F., Eberhart, R.C., Shi, Y.: Swarm Intelligence. Morgan Kaufmann, San Francisco (2001) Google Scholar
  21. 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 CrossRefGoogle Scholar
  22. 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) MathSciNetzbMATHCrossRefGoogle Scholar
  23. 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. 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 CrossRefGoogle Scholar
  25. 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).
  26. 26.
    Michalewicz, Z., Fogel, D.: How to Solve It: Modern Heuristics, 2nd edn. Springer, Berlin (2004) CrossRefGoogle Scholar
  27. 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. MathSciNetzbMATHCrossRefGoogle Scholar
  28. 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) Google Scholar
  29. 29.
    Papa, G.: Parameter-less evolutionary search. In: Proc. Genetic and Evolutionary Computation Conference (GECCO’08), pp. 1133–1134 (2008) CrossRefGoogle Scholar
  30. 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) Google Scholar
  31. 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. 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. 33.
    Papa, G., Mrak, P.: Temperature simulations in cooling appliances. Elektroteh. Vestn. 78(1–2), 67–72 (2011) Google Scholar
  34. 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. CrossRefGoogle Scholar
  35. 35.
    Schwefel, H.P.P.: Evolution and Optimum Seeking: the Sixth Generation. Wiley, New York (1993) Google Scholar
  36. 36.
    Stephens, C.R., Olmedo, I.G., Vargas, J.M., Waelbroeck, H.: Self-adaptation in evolving systems. Artif. Life 4, 183–201 (1998) CrossRefGoogle Scholar
  37. 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. MathSciNetzbMATHCrossRefGoogle Scholar
  38. 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) CrossRefGoogle Scholar
  39. 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) Google Scholar
  40. 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) zbMATHCrossRefGoogle Scholar
  41. 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 zbMATHCrossRefGoogle Scholar
  42. 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 CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Jožef Stefan InstituteLjubljanaSlovenia

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