Skip to main content

A Differential Evolution Algorithm with a Variable Neighborhood Search for Constrained Function Optimization

  • Chapter
Adaptation and Hybridization in Computational Intelligence

Part of the book series: Adaptation, Learning, and Optimization ((ALO,volume 18))

Abstract

In this paper, a differential evolution algorithm based on a variable neighborhood search algorithm (DE_VNS) is proposed in order to solve the constrained real-parameter optimization problems. The performance of DE algorithm depends on the mutation strategies, crossover operators and control parameters. As a result, a DE_VNS algorithm that can employ multiple mutation operators in its VNS loops is proposed in order to further enhance the solution quality. We also present an idea of injecting some good dimensional values to the trial individual through the injection procedure. In addition, we also present a diversification procedure that is based on the inversion of the target individuals and injection of some good dimensional values from promising areas in the population by tournament selection. The computational results show that the simple DE_VNS algorithm was very competitive to some of the best performing algorithms from the literature.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Qin, A.K., Huang, V.L., Suganthan, P.N.: Differential Evolution Algorithm with strategy adaptation for global numerical optimization. IEEE Trans. Evol. Comput. 13, 398–417 (2009)

    Article  Google Scholar 

  2. Mohamed, A.W., Sabry, H.Z.: Constrained optimization based on modified differential evolution algorithm. Information Sciences 194, 171–208 (2012)

    Article  Google Scholar 

  3. Zamuda, A., Brest, J.: Population reduction differential evolution with multiple mutation strategies in real world industry challenges. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M., et al. (eds.) EC 2012 and SIDE 2012. LNCS, vol. 7269, pp. 154–161. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  4. Babu, B.V., Onwubolu, G.C. (eds.): New Optimization Techniques in Engineering. STUDFUZZ, vol. 141. Springer, Heidelberg (2004)

    MATH  Google Scholar 

  5. Becerra, R.L., Coello, C.C.A.: Cultural Differential Evolution for Constrained Optimization. Comput. Methods Appl. Mech. Engrg. (2005)

    Google Scholar 

  6. Chiou, J.-P., Wang, F.-S.: Hybrid Method of Evolutionary Algorithms for Static and Dynamic Optimization Problems with Applications to a Fed-Batch fermantation Process. Computers and Chemical Engineering 23, 1277–1291 (1999)

    Article  Google Scholar 

  7. Coello, C.C.A.: Theoretical and Numerical Constraint-Handling Techniques Used with Evolutionary Algorithms: A Survey of the State of the Art. Comput. Methods Appl. Mech. Engrg. 191(11-12), 1245–1287 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  8. Part Two: Differential Evolution. In: Corne, D., Dorigo, M., Glover, F. (eds.) New Ideas in Optimization, pp. 77–158. McGraw-Hill (1999)

    Google Scholar 

  9. Tizhoosh, H.R.: Opposition-based learning: a new scheme for machine intelligence. In: Proceedings of International Conference on Computational Intelligence for Modeling Control and Automation, pp. 695–701 (2005)

    Google Scholar 

  10. Wang, H., Wu, Z.J., Rahnamayan, S.: Enhanced opposition-based differential evolution for solving high-dimensional continuous optimization problems. Soft Comput. 15(11), 2127–2140 (2011)

    Article  Google Scholar 

  11. Wang, H., Wu, Z.J., Rahnamayan, S., Kang, L.S.: A scalability test for accelerated DE using generalized opposition-based learning. In: Proceedings of International Conference on Intelligent System Design and Applications, pp. 1090–1095 (2009)

    Google Scholar 

  12. Wang, H., Wu, Z.J., Rahnamayan, S., Liu, Y., Ventresca, M.: Enhancing particle swarm optimization using generalized opposition-based learning. Inform. Sci. 181(20), 4699–4714 (2011)

    Article  MathSciNet  Google Scholar 

  13. Brest, J., Sepesy Maucec, M.: Population size reduction for the differential evolution algorithm. Appl. Intell., 228–247 (2008)

    Google Scholar 

  14. Deb, K.: An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering 186, 311–338 (2000)

    Article  MATH  Google Scholar 

  15. Koziel, S., Michalewicz, Z.: Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization. Evol. Comput. 7(1), 19–44 (1999)

    Article  Google Scholar 

  16. Lampinen, J.: Multi-Constrained Optimization by the Differential Evolution. In: Proc. of the IASTED International Conference Artificial Intelligence Applications (AIA 2001), pp. 177–184 (2001)

    Google Scholar 

  17. Lampinen, J.: Solving Problems Subject to Multiple Nonlinear Constraints by the Differential Evolution. In: Proc. of the 7th International Conference on Soft Computing, MENDEL 2001, pp. 50–57 (2001)

    Google Scholar 

  18. Lampinen, J.: A Bibliography of Differential Evolution Algorithm. Technical Report, Lappeenranta University of Technology, Department of Information Technology, Laboratory of Information Processing (2001)

    Google Scholar 

  19. Lampinen, J.: A Constraint Handling approach for the Differential evolution Algorithm. In: Proc. of the Congress on Evolutionary Computation (CEC 2002), pp. 1468–1473 (2002)

    Google Scholar 

  20. Liang, J.J., Runarsson, T.P., Mezura-Montes, E., Clerc, M., Suganthan, P.N., Coello Coello, C.A., Deb, K.: Problem Definitions and Evaluation Criteria for the CEC 2006, Special Session on Constrained Real-Parameter Optimization. Technical Report, Nanyang Technological University, Singapore (2005)

    Google Scholar 

  21. Lin, Y.-C., Hwang, K.-S., Wang, F.-S.: Hybrid Differential Evolution with Multiplier updating method for Nonlinear Constrained Optimization. In: Proc. of the Congress on Evolutionary Computation (CEC 2002), pp. 872–877 (2002)

    Google Scholar 

  22. Mezura-Montes, E., Velazquez-Reyes, J., Coello, C.: Modified differential evolution for constrained optimization. In: IEEE Congress on Evolutionary Computation, pp. 25–32 (2006)

    Google Scholar 

  23. Tasgetiren, M.F., Suganthan, P.N., Pan, Q.-K., Liang, Y.-C.: A Differential Evolution Algorithm with a variable Parameter Search for Real-Parameter Continuous Function Optimization. In: The Proceeding of the World Congress on Evolutionary Computation (CEC 2009), Norway, pp. 1247–1254 (2009)

    Google Scholar 

  24. Tasgetiren, M.F., Suganthan, P.N., Pan, Q.-K.: An ensemble of discrete differential evolution algorithms for solving the generalized traveling salesman problem. Applied Mathematics and Computation 215(9), 3356–3368 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  25. Tasgetiren, M.F., Suganthan, P.N., Pan, Q.-K., Mallipedi, R., Sarman, S.: An ensemble of differential evolution algorithms for constrained function optimization. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 1–8 (2010)

    Google Scholar 

  26. Mladenovic, N., Hansen, P.: Variable neighborhood search. Computers and Operations Research 24, 1097–1100 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  27. Price, K., Storn, R., Lampinen, J.: Differential Evolution – A Practical Approach to Global Optimization. Springer (2005)

    Google Scholar 

  28. Pan, Q.-K., Suganthan, P.N., Tasgetiren, M.F.: A Harmony Search Algorithm with Ensemble of Parameter Sets. In: IEEE Congress on Evolutionary Computation, CEC 2009, May 18-21, pp. 1815–1820 (2009)

    Google Scholar 

  29. Gämperle, R., Müller, S.D., Koumoutsakos, P.: A parameter study for differential evolution. In: Proc. WSEAS Int. Conf. Advances Intell. Syst., Fuzzy Syst., Evol. Comput., pp. 293–298 (2002)

    Google Scholar 

  30. Mallipedi, R., Suganthan, P.N.: Ensemble of constraint handling techniques. IEEE Trans. Evol. Comput. 14, 561–579 (2010)

    Article  Google Scholar 

  31. Mallipedi, R., Mallipedi, S., Suganthan, P.N., Tasgetiren, M.F.: Differential Evolution Algorithm with ensemble of parameters and mutation strategies. Applied Soft Comput. 11, 1679–1696 (2011)

    Article  Google Scholar 

  32. Elsayed, S.M., Sarker, R.A., Essam, D.L.: Multi-operator based evolutionary algorithms for solving constrained optimization problems. Computers & Operations Research 38, 1877–1896 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  33. Elsayed, S.M., Sarker, R.A., Essam, D.L.: On an evolutionary approach for constrained optimization problem solving. Applied Soft Computing 12, 3208–3227 (2012)

    Article  Google Scholar 

  34. Elsayed, S.M., Sarker, R.A., Essam, D.L.: A self-adaptive combined strategies algorithm for constrained optimization using differential evolution. Applied Mathematics and Computation 241, 267–282 (2014)

    Article  MathSciNet  Google Scholar 

  35. Sarimveis, H., Nikolakopoulos, A.: A Line Up Evolutionary Algorithm for Solving Nonlinear Constrained Optimization Problems. Computers & Operations Research 32, 1499–1514 (2005)

    Article  MathSciNet  Google Scholar 

  36. Smith, A.E., Tate, D.M.: Genetic Optimization Using a Penalty Function. In: Forrest, S. (ed.) Proc. of the Fifth International Conference on genetic Algorithms, pp. 499–503. Morgan Kaufmann (1993)

    Google Scholar 

  37. Storn, R.: System Design by Constraint Adaptation and Differential Evolution. IEEE Transactions on Evolutionary Computation 3, 22–34 (1999)

    Article  Google Scholar 

  38. Storn, R., Price, K.: Differential Evolution – a Simple and Efficient Adaptive Scheme for Global Optimization over Continuous Spaces. Technical Report TR-95-012, ICSI (1995)

    Google Scholar 

  39. Storn, R., Price, K.: Differential Evolution - A Simple and Efficient Heuristic for Global Optimization over Continuous Space. Journal of Global Optimization 11, 341–359 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  40. Rahnamayan, S., Tizhoosh, H.R., Salama, M.M.A.: Opposition-based differential evolution algorithms. In: Proceedings of IEEE Congress on Evolutionary Computation, pp. 2010–2017 (2006)

    Google Scholar 

  41. Rahnamayan, S., Tizhoosh, H.R., Salama, M.M.A.: Opposition-based differential evolution for optimization of noisy problems. In: Proceedings of IEEE Congress on Evolutionary Computation (1872)

    Google Scholar 

  42. Rahnamayan, S., Tizhoosh, H.R., Salama, M.M.A.: Opposition-based differential evolution. IEEE Trans. Evol. Comput. 12(1), 64–79 (2008)

    Article  Google Scholar 

  43. Das, S., Suganthan, P.N.: Differential Evolution: A Survey of the State-of-the-Art. IEEE Trans. Evolutionary Computation 15(1), 4–31 (2011)

    Article  Google Scholar 

  44. Takahama, T., Sakai, S.: Constrained Optimization by the Constrained Differential Evolution with Gradient-Based Mutation and Feasible Elites. In: IEEE Congress on Evolutionary Computation, Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canada, pp. 1–8 (2006)

    Google Scholar 

  45. Long, W., Liang, X., Huang, Y., Chen, Y.: A hybrid differential evolution augmented Lagrangian method for constrained numerical and engineering optimization. Computer-Aided Design 45, 1562–1574 (2013)

    Article  MathSciNet  Google Scholar 

  46. Gong, W., Cai, Z., Liang, D.: Engineering Optimization by means of an improved constrained differential evolution. Comput. Methods Appl. Mech. Engrg. 268, 884–904 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  47. Wang, Y., Cai, Z., Qingfu, Z.: Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans. Evol. Comput. 15, 55–66 (2011)

    Article  Google Scholar 

  48. Jingqiao, Z., Sanderson, A.C.: JADE: adaptive differential evolution with optional external archieve. IEEE Trans. Evol. Comput. 13, 945–958 (2009)

    Article  Google Scholar 

  49. Iztok, F., Marjan, M., Bogdan, F.: Graph 3-coloring with a hybrid self-adaptive evolutionary algorithm. Computational Optimization and Applications 54(3), 741–770 (2013)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Fatih Tasgetiren .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Tasgetiren, M.F., Suganthan, P.N., Ozcan, S., Kizilay, D. (2015). A Differential Evolution Algorithm with a Variable Neighborhood Search for Constrained Function Optimization. In: Fister, I., Fister Jr., I. (eds) Adaptation and Hybridization in Computational Intelligence. Adaptation, Learning, and Optimization, vol 18. Springer, Cham. https://doi.org/10.1007/978-3-319-14400-9_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-14400-9_8

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-14399-6

  • Online ISBN: 978-3-319-14400-9

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics