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Soft Computing

, Volume 18, Issue 10, pp 1931–1948 | Cite as

Adaptation of the musical composition method for solving constrained optimization problems

  • Roman Anselmo Mora-Gutiérrez
  • Javier Ramírez-Rodríguez
  • Eric Alfredo Rincón-García
  • Antonin Ponsich
  • Oscar Herrera
  • Pedro Lara-Velázquez
Methodologies and Application

Abstract

Many real-world problems may be expressed as nonlinear constrained optimization problems (CNOP). For this kind of problems, the set of constraints specifies the feasible solution space. In the last decades, several algorithms have been proposed and developed for tackling CNOP. In this paper, we present an extension of the “Musical Composition Method” (MMC) for solving constrained optimization problems. MMC was proposed by Mora et al. (Artif Intell Rev 1–15, doi: 10.1007/s10462-011-9309-8, 2012a). The MMC is based on a social creativity system used to compose music. We evaluated and analyzed the performance of MMC on 12 CNOP benchmark cases. The experimental results demonstrate that MMC significantly improves the global performances of the other tested metaheuristics on some benchmark functions.

Keywords

Particle Swarm Optimization Decision Variable Differential Evolution Constrain Optimization Problem Constraint Violation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Abbasian R, Mouhoub M, Jula A (2011) Solving graph coloring problems using cultural algorithms. In: Twenty-fourth international FLAIRS conferenceGoogle Scholar
  2. Berg S (2007) Alfred’s essentials of Jazz theory: a complete self-study course for all musicians. Alfred Publishing Company, Incorporated, Van Nuys, p 120Google Scholar
  3. Cai Z, Wang Y (2006) A multiobjective optimization-based evolutionary algorithm for constrained optimization. IEEE Trans Evol Comput 10:658–675CrossRefGoogle Scholar
  4. Center for Advanced Research on Language Acquisition (CARLA) (2011) U. M. What is Culture? http://www.carla.umn.edu/culture/definitions.html
  5. Christakis N, Fowler J (2009) Conntected the surprising power of our social networks and how they shape our lives. Little, Brown and Company/Hachette Book Group, New York, p 368. ISBN-10: 0316036137Google Scholar
  6. Chung CJ, Reynolds RG (1996) A testbed for solving optimization problems using cultural algorithms. In: Evolutionary programming, pp 225–236Google Scholar
  7. Coello Coello CA (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech Eng 191:1245–1287Google Scholar
  8. Coello Coello AC, Becerra RL (2002) Constrained optimization using an evolutionary programming-based cultural algorithm. In: Adaptive computing in design and manufacture V. Springer, London, pp 317–328Google Scholar
  9. Coello Coello CA, Landa Becerra R (2003) Evolutionary multiobjective optimization using a cultural algorithm. In: Swarm Intelligence Symposium, 2003. SIS-03. Proceedings of the 2003 IEEEGoogle Scholar
  10. Cruz Cortés N (2004) Sistema inmune artificial para solucionar problemas de optimización. Ph.D. thesis, CINVESTAV. Instituto Politecnico NacionalGoogle Scholar
  11. da Silva E, Barbosa H, Lemonge A (2011) An adaptive constraint handling technique for differential evolution with dynamic use of variants in engineering optimization. Optim Eng 12:31–54. doi: 10.1007/s11081-010-9114-2 Google Scholar
  12. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern 26:29–41CrossRefGoogle Scholar
  13. Geertz C (1989). A Interpretação das Culturas. Rio de Janeiro: Ed. Guanabara, p 213Google Scholar
  14. Gessler N (2003) Evolving cultural things-that-think. In: Computational synthesis: from basic building blocks to high level functionality. Papers from the 2003 AAAI spring symposium, Technical Report SS-03-02. Menlo Park, AAAI Press, San Francisco, pp 75–81Google Scholar
  15. Gershenson C (2010) Computing networks: a general framework to contrast neurl and swarm cognitions. Paladyn J Behav Robot 1(2):147–153CrossRefGoogle Scholar
  16. Hu X, Eberhart R (2002) Solving constrained nonlinear optimization problems with particle swarm optimization. In: 6th World multiconference on systemics, cybernetics and informatics (SCI 2002), pp 203–206Google Scholar
  17. Jin X, Reynolds RG (1999) Using knowledge-based evolutionary computation to solve nonlinear constraint optimization problems: a cultural algorithm approach. In: Proceedings of the 1999 congress on evolutionary computation, 1999. CEC 99, Washington, DC, USAGoogle Scholar
  18. Kennedy J, Eberhart RC (1995) Particle swarm optimization. In: International conference neuronal networks, pp 1942–1948Google Scholar
  19. Koziel S, Michalewicz Z (1999) Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evol Comput 7(1):19–44Google Scholar
  20. Landa Becerra R, Coello Coello CA (2005) Optimization with constraints using a cultured differential evolution approach. In: Proceedings of the GECCO conferenceGoogle Scholar
  21. Lederach JP (1995) Preparing for peace: conflict transformation across cultures. Syracuse University Press, Syracuse Google Scholar
  22. Lemonge ACC, Barbosa HJC (2004) An adaptive penalty scheme for genetic algorithms in structural optimization. Int J Numer Methods Eng 59(5):703–736Google Scholar
  23. Mezura Montes E, Coello Coello CA (2003) A simple multimembered evolution strategy to solve constrained optimization problems. IEEE Trans Evol Comput 9:1–17Google Scholar
  24. Michalewicz Z (1995) Genetic algorithms, numerical optimization, and constraints. In: Proceedings of the 6th international conference on genetic algorithms, pp 151–158Google Scholar
  25. Michalewicz Z, Deb K, Schmidtz M, Stidsenx T (2000) Test-case generator for nonlinear continuous parameter optimization techniques. IEEE Trans Evol Comput 2000(4):197–215CrossRefGoogle Scholar
  26. Michalewicz Z, Fogel DB (1998) How to solve it: modern heuristics. Springer, BerlinGoogle Scholar
  27. Michalewicz Z and Fogel DB (1998) How to solve it: modern heuristics. 2nd edn. Springer, Berlin, p 580. ISBN-10: 3540224947Google Scholar
  28. Michalewicz Z, Janikow CZ (1996) Genocop: a genetic algorithm for numerical optimization problems with linear constraints. In: Communications of the ACM—electronic supplement to the December 39: article no. 175Google Scholar
  29. Mora-Gutiérrez R, Ramírez-Rodríguez J, Rincón-García E (2012a) An optimization algorithm inspired by musical composition. Artif Intell Rev 1:15. doi: 10.1007/s10462-011-9309-8
  30. Mora-Gutiérrez R, Ramírez-Rodríguez J, Rincón-García EA, Ponsich A, Herrera O (2012b) An optimization algorithm inspired by social creativity systems. Computing 887–914. doi: 10.1007/s00607-012-0205-0
  31. Mora-Gutiérrez R (2013) Diseño y desarrollo de un método heurístico basado en un sistema socio-cultural de creatividad para la resolucin de problemas de optimización continuos no lineales y diseño de zonas electorales. Ph.D. Thesis. UNAMGoogle Scholar
  32. Rasskin-Gutman D (2005) Modularity: jumping forms inside morphospace. In: Callebaut W, Rasskin-Gutman D (eds) Modularity: understanding the development and evolution of complex natural systems. MIT Press. pp 207–222Google Scholar
  33. Ray T, Liew KM (2003) Society and civilitation: an optimization algorithm based on the simulation of social behavior. IEEE Trans Evol Comput 7:386–396CrossRefGoogle Scholar
  34. Ray T, Kang T, Chye SK (2000) An evolutionary algorithm for constrained optimization. In: GECCO’00, pp 771–777Google Scholar
  35. Reynolds RG (1994) An introduction to cultural algorithms. In: Proceedings of the 3rd annual conference on evolutionary programming. World Scientific Publishing, Singapore, pp 131–139Google Scholar
  36. Reynolds RG, Peng B, Whallon R (2005) Emergent social structures in cultural algorithms. In: Proceedings of NAACSOS, Notre Dame, Indiana, USAGoogle Scholar
  37. Reynolds R, Michalewicz Z, Cavaretta M (1995) Using cultural algorithms for constraint handling in GENOCOP. In: Evolutionary programming, vol. 4, pp 298–305. Complex adaptive systems. MIT Press, CambridgeGoogle Scholar
  38. Simon HA (1996) The sciences of the artificial, 3rd edn. MIT Press, CambridgeGoogle Scholar
  39. Schlosser G, Wagner GP (2004) Modularity in development and evolution. 1st edn. University of Chicago Press, p 600. ISBN-10: 0226738558Google Scholar
  40. Tang W, Li Y (2008) Constrained optimization using triple spaces cultured genetic algorithm. In: International conference on natural computation, vol 6. pp 589–593Google Scholar
  41. Wolpert DH, Macready WG (1995) No free lunch theorems for search. Technical Report SFI-WP-95-02-010, Santa Fe InstituteGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Roman Anselmo Mora-Gutiérrez
    • 1
  • Javier Ramírez-Rodríguez
    • 1
    • 2
  • Eric Alfredo Rincón-García
    • 1
  • Antonin Ponsich
    • 1
  • Oscar Herrera
    • 1
  • Pedro Lara-Velázquez
    • 1
  1. 1.Departamento de SistemasUniversidad Autónoma Metropolitana D.F. MéxicoMéxico
  2. 2.LIA Université d’Avignon et des Pays de VaucluseAvignonFrance

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