C-SOMAQI: Self Organizing Migrating Algorithm with Quadratic Interpolation Crossover Operator for Constrained Global Optimization

  • Dipti SinghEmail author
  • Seema Agrawal
  • Kusum Deep
Part of the Studies in Computational Intelligence book series (SCI, volume 626)


SOMAQI is a variant of Self Organizing Migrating Algorithm (SOMA) in which SOMA is hybridized with Quadratic Interpolation crossover operator, presented by Singh et al. (Advances in intelligent and soft computing. Springer, India, pp. 225–234, 2014). The algorithm SOMAQI has been designed to solve unconstrained nonlinear optimization problems. Earlier it has been tested on several benchmark problems and the results obtained by this technique outperform the results taken by several other techniques in terms of population size and function evaluations. In this chapter SOMAQI has been extended for solving constrained nonlinear optimization problems (C-SOMAQI) by including a penalty parameter free approach to select the feasible solutions. This algorithm also works with small population size and converges very fast. A set of 10 constrained optimization problems has been used to test the performance of the proposed algorithm. These problems are varying in complexity. To validate the efficiency of the proposed algorithm results are compared with the results obtained by C-SOMGA and C-SOMA. On the basis of the comparison it has been concluded that C-SOMAQI is efficient to solve constrained nonlinear optimization problems.


Self organizing migrating algorithm Quadratic interpolation crossover operator Genetic algorithm Constrained global optimization 


  1. 1.
    Kim, J.H., Myung, H.: A two phase evolutionary programming for general constrained optimization problem. In: Proceedings of the Fifth Annual Conference on Evolutionary Programming, San Diego (1996)Google Scholar
  2. 2.
    Michalewicz, Z.: Genetic algorithms, numerical optimization and constraints. In: Echelman L.J. (ed.) Proceedings of the Sixth International Conference on Genetic Algorithms, pp. 151–158 (1995)Google Scholar
  3. 3.
    Myung, H., Kim, J.H.: Hybrid evolutionary programming for heavily constrained problems. Bio-Systems 38, 29–43 (1996)CrossRefGoogle Scholar
  4. 4.
    Orvosh, D., Davis, L.: Using a genetic algorithm to optimize problems with feasibility constraints. In: Echelman L.J. (ed.) Proceedings of the Sixth International Conference on Genetic Algorithms, pp. 548–552 (1995)Google Scholar
  5. 5.
    Michalewicz, Z., Attia, N.: Evolutionary optimization of constrained problems. In: Proceedings of Third Annual Conference on Evolutionary Programming, pp. 998–1008. World Scientific, River Edge (1994)Google Scholar
  6. 6.
    Joines, J., Houck, C.: On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GAs. In: Proceedings of the First IEEE Conference on Evolutionary Computation, pp. 587–602. IEEE Press, Orlando (1994)Google Scholar
  7. 7.
    Homaifar, A.A., Lai, S.H.Y., Qi, X.: Constrained optimization via genetic algorithms. Simulation 62, 242–254 (1994)CrossRefGoogle Scholar
  8. 8.
    Smith, A.E., Coit, D.W.: Constraint Handling Techniques-Penalty Functions, Handbook of Evolutionary Computation. Oxford University Press and Institute of Physics Publishing, Oxford (Chapter C 5.2) (1997)Google Scholar
  9. 9.
    Coello, C.A.: Theoretical and numerical constraint handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput. Methods Appl. Mech. Eng. 191, 1245–1287 (2002)CrossRefzbMATHGoogle Scholar
  10. 10.
    Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Eng. 186, 311–338 (2000)CrossRefzbMATHGoogle Scholar
  11. 11.
    Coello, C.A., Mezura-Montes, E.: Constraint-handling in genetic algorithms through the use of dominance-based tournamen selection. Adv. Eng. Inf. 16, 193–203 (2002)CrossRefGoogle Scholar
  12. 12.
    Deb, K., Agarwal, S.: A niched-penalty approach for constraint handling in genetic algorithms. In: Proceedings of the ICANNGA, Portoroz, Slovenia (1999)Google Scholar
  13. 13.
    Akhtar, S., Tai, K., Ray, T.: A Socio-behavioural simulation model for engineering design optimization. Eng. Optim. 34, 341–354 (2002)CrossRefGoogle Scholar
  14. 14.
    Eskandar, A., Sadollah, A., Bahreininejad, A., Hamdi, M.: Water cycle algorithm—a novel metaheuristic optimization method for solving constrained engineering optimization problems. Comput. Struct. 110–111, 151–166 (2012)CrossRefGoogle Scholar
  15. 15.
    Eskandar, A., Sadollah, A., Bahreininejad, A., Hamdi, M.: Mine blast algorithms: a new population based algorithm for solving constrained engineering optimization problems. Appl. Soft Comput. (in press) (2012)Google Scholar
  16. 16.
    Pant, M., Thangaraj, R., Abraham, A.: A new PSO algorithm with crossover operator for global optimization problems. In: Corchado E. et al. (eds.) Second International Symposium on Hybrid Artificial Intelligent Systems (HAIS’07), Soft computing Series, Innovations in Hybrid Intelligent Systems, vol. 44, pp. 215–222. Springer, Germany (2007)Google Scholar
  17. 17.
    Deep, K., Dipti, S.: A self organizing migrating genetic algorithm for constrained optimization. Appl. Math. Comput. 198, 237–250 (2008)Google Scholar
  18. 18.
    Pant, M., Thangaraj, R., Abraham, A.: New mutation schemes for differential evolution algorithm and their application to the optimization of directional over-current relay settings. Appl. Math. Comput. 216, 532–544 (2010)Google Scholar
  19. 19.
    Deep, K., Bansal, J.C.: Quadratic approximation PSO for economic dispatch problems with valve-point effects. In: International Conference on Swarm, Evolutionary and Memetic computing, SRM University, Chennai, pp. 460–467, Proceedings Springer (2010)Google Scholar
  20. 20.
    Deep, K., Das, K. N.: Hybrid Binary Coded Genetic Algorithm for Constrained Optimization. In: ICGST AIML-11 Conference, Dubai, UAE (2011)Google Scholar
  21. 21.
    Singh, D., Agrawal, S., Singh, N.: A novel variant of self organizing migrating algorithm for function optimization. In Proceedings of the 3rd International Conference on Soft Computing for Problem Solving. Advances in Intelligent and Soft Computing, vol. 258, pp. 225–234. Springer, India (2014)Google Scholar
  22. 22.
    Zelinka, I., Lampinen, J.: SOMA—Self Organizing Migrating Algorithm. In: Proceedings of the 6th International Mendel Conference on Soft Computing, pp. 177–187. Brno, Czech, Republic (2000)Google Scholar
  23. 23.
    Zelinka, I.: SOMA—Self Organizing Migrating Algorithm. In: Onwubolu G.C., Babu B.V. (eds.) New Optimization Techniques in Engineering. Springer, Berlin (2004)Google Scholar
  24. 24.
    Nolle, L., Zelinka, I.: SOMA applied to optimum work roll profile selection in the hot rolling of wide steel. In: Proceedings of the 17th European Simulation Multiconference ESM 2003, pp. 53–58. Nottingham, UK, ISBN 3-936150-25-7, 9–11 June 2003 (2003)Google Scholar
  25. 25.
    Nolle, L., Zelinka, I., Hopgood, A.A., Goodyear, A.: Comparision of an self organizing migration algorithm with simulated annealing and differential evolution for automated waveform tuning. Adv. Eng. Softw. 36, 645–653 (2005)Google Scholar
  26. 26.
    Oplatkova, Z., Zelinka, I.: Investigation on Shannon-Kotelnik theorem impact on soma algorithm performance. In: Proceedings 19th European Conference on Modelling and Simulation Yuri Merkuryev, Richard Zobel (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Applied SciencesGautam Buddha UniversityGreater NoidaIndia
  2. 2.Department of MathematicsS.S.V.P.G. CollegeHapurIndia
  3. 3.Indian Institute of Technology RoorkeeRoorkeeIndia

Personalised recommendations