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Development of seven hybrid methods based on collective intelligence for solving nonlinear constrained optimization problems

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Abstract

Many real-world problems can be seen as constrained nonlinear optimization problems (CNOP). These problems are relevant because they frequently appear in many industry and science fields, promoting, in the last decades, the design and development of many algorithms for solving CNOP. In this paper, seven hybrids techniques, based on particle swarm optimization, the method of musical composition and differential evolution, as well as a new fitness function formulation used to guide the search, are presented. In order to prove the performance of these techniques, twenty-four benchmark CNOP were used. The experimental results showed that the proposed hybrid techniques are competitive, since their behavior is similar to that observed for several methods reported in the specialized literature. More remarkably, new best known are identified for some test instances.

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References

  • Andreani R, Fukuda EH, Silva PJS (2013) A Gauss–Newton approach for solving constrained optimization problems using differentiable exact penalties. J Optim Theory Appl 156(2):417–449

    Article  MathSciNet  MATH  Google Scholar 

  • Aragon VS, Coello CAC (2010) A modified version of a T-cell algorithm for constrained optimization problems. Int J Numer Methods Eng 84(3):351–378

    MATH  Google Scholar 

  • Battiti R (1996) Reactive search: towards self-tuning heuristics. In: RaywardSmith VJ, Osman IH, Reeves CR, Smith GD (eds) Modern heuristic search methods. Wiley, pp 61–83

  • Battiti R, Brunato M, Mascia F (2008) Reactive search and intelligent optimization. Operations research/computer science interfaces series (book 45). Springer, Berlin

    MATH  Google Scholar 

  • Balci HH, Valenzuela JF (2004) Scheduling electric power generators using particle swarm optimization combined with the Lagrangian relaxation method. Int J Appl Math Comput Sci 14(3):411–422

    MathSciNet  MATH  Google Scholar 

  • Borghetti A, Frangioni A, Lacalandra F, Lodi A, Martello S, Nucci CA, Trebbi A (2001) Lagrangian relaxation and tabu search approaches for the unit commitment problem. In: Power tech proceedings, 2001 IEEE Porto, vol 3, pp 1–7

  • Blum C (2014) A hybrid metaheuristic based on heuristic problem instance reduction. In: The 5th International conference metaheuristic and nature inspired computing META2014, Marrakech (Morocco)

  • Blum C, Roli A (eds) (2008) Hybrid metaheuristics: an introduction. In: Hybrid metaheuristics. Springer, Berlin, pp 1–30

  • Blum C, Puchinger J, Raidl GR, Roli A (2010) A brief survey on hybrid metaheuristics. In: 4th international conference on bioinspired optimization methods and their applications, pp 3–16

  • Blum C, Puchinger J, Raidl GR, Roli A (2011) Hybrid metaheuristics in combinatorial optimization: a survey. Appl Soft Comput 11(6):4135–4151

    Article  MATH  Google Scholar 

  • Burke EK, Hart E, Kendall G, Newall J, Ross P, Schulenburg S (2003) Hyper-heuristics: an emerging direction in modern search technology. In: Glover F, Kochenberger G (eds) Handbook of metaheuristics. Kluwer, pp 457–474

  • Cai Z, Wang Y (2006) A multiobjective optimization-based evolutionary algorithm for constrained optimization. IEEE Trans Evol Comput 10:658–675

    Article  Google Scholar 

  • Cotta C (1998) A study of hybridisation techniques and their application to the design of evolutionary algorithms. AI Commun 11(3–4):223–224

    Google Scholar 

  • Cotta C, Talbi EG, Alba E (2005) Parallel hybrid metaheuristics. In: Alba E (ed) Parallel metaheuristics, a new class of algorithms. Wiley, London, pp 347–370

    Chapter  Google Scholar 

  • Das S, Suganthan PN (2011) Differential evolution: a survey of the state-of-the-art. IEEE Trans Evol Comput 15(1):4–31

    Article  Google Scholar 

  • De Backer B, Furnon V, Shaw P, Kilby P, Prosser P (2000) Solving vehicle routing problems using constraint programming and metaheuristics. J Heuristics 6(4):501–523

    Article  MATH  Google Scholar 

  • Dennis JE Jr, Schnabel RB (1996) Numerical methods for unconstrained optimization and nonlinear equations, vol 16. Siam

  • de-los-Cobos-Silva SG (2015) SC: system of convergence, theory and fundaments. Revista de Matemática: Teoría y Aplicaciones 22(2):341–367

    MathSciNet  MATH  Google Scholar 

  • de-los-Cobos-Silva SG, Gutiérrez-Andrade MA, Mora-Gutiérrez RM, Lara-Velzquez P, Rincón-Garca EA, Ponsich A (2015) An efficient algorithm for unconstrained optimization. Math Probl Eng. doi:10.1155/2015/178545

  • Dumitrescu I, Stützle T (2003) Combinations of local search and exact algorithms. In: Raidl GR et al (eds) Applications of evolutionary computation. Lecture notes in computer science, vol 2611. Springer, Berlin, pp 211–223

  • Elsayed SM, Sarker RA, Essam DL (2012) On an evolutionary approach for constrained optimization problem solving. Appl Soft Comput 12:3208–3227

    Article  Google Scholar 

  • Gallardo JE, Cotta C, Fernández AJ (2005) Solving the multidimensional knapsack problem using an evolutionary algorithm hybridized with branch and bound. In: Mira J, Álvarez JR (eds) Artificial intelligence and knowledge engineering applications: a bioinspired approach. Springer, Berlin, pp 21–30

  • 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 203–206

  • Kabanov J, Vene V (2006) Recursion schemes for dynamic programming. Mathematics of program construction. Springer, Berlin, pp 235–252

  • Kennedy J (2011) Particle swarm optimization. In: Encyclopedia of machine learning. Springer, pp 760–766

  • Kennedy J, Eberhart RC, Shi Y (2001) Swarm intelligence. Morgan Kaufmann, Burlington

    Google Scholar 

  • Koziel S, Michalewicz Z (1999) Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evol Comput 7(1):19–44

    Article  Google Scholar 

  • Landa-Becerra R, Coello-Coello CA (2005) Optimization with constraints using a cultured differential evolution approach. In: Proceedings of the GECCO conference

  • LaTorre de la Fuente A (2009) A framework for hybrid dynamic evolutionary algorithms: multiple offspring sampling (MOS). Doctoral dissertation, Informatica

  • Lemonge ACC, Barbosa HJC (2004) An adaptive penalty scheme for genetic algorithms in structural optimization. Int J Numer Methods Eng 59(5):703–736

    Article  MATH  Google Scholar 

  • Liang JJ, Runarsson TP, Mezura-Montes E, Clerc M, Suganthan PN, Coello CC, Deb K (2006) Problem definitions and evaluation criteria for the CEC 2006 special session on constrained real-parameter optimization. Technical report

  • Liu H, Cai Z, Wang Y (2010) Hybridizing particle swarm optimization with differential evolution for constrained numerical and engineering optimization. Appl Soft Comput 10(2):629–640

    Article  Google Scholar 

  • Liu C (2007) New multiobjective PSO algorithm for nonlinear constrained programming problems. In: Advances in cognitive neurodynamics ICCN 2007. Springer, Dordrecht, pp 955–962

  • Lu H, Chen W (2008) Self-adaptive velocity particle swarm optimization for solving constrained optimization problems. J Glob Opt 41(3):427–445

    Article  MathSciNet  MATH  Google Scholar 

  • Mazhoud I, Hadj-Hamou K, Bigeon J, Joyeux P (2013) Particle swarm optimization for solving engineering problems: a new constraint-handling mechanism. Eng Appl Artif Intell 26(4):1263–1273

    Article  Google Scholar 

  • Michalewicz Z (1995) Genetic algorithms, numerical optimization, and constraints. In: Proceedings of the 6th international conference on genetic algorithms, pp 151–158

  • Michalewicz Z, Fogel DB (1998) How to solve it: modern heuristics. Springer, Berlin

    MATH  Google Scholar 

  • Michalewicz Z, Deb K, Schmidtz M, Stidsenx T (2000) Test-case generator for nonlinear continuous parameter optimization techniques. IEEE Transa Evol Comput 4:197–215

    Article  Google Scholar 

  • Mazhoud I, Hadj-Hamou K, Bigeon J, Joyeux P (2013) Particle swarm optimization for solving engineering problems: a new constraint-handling mechanism. Eng Appl Artif Intell 26(4):1263–1273

    Article  Google Scholar 

  • Mezura ME, Miranda-Varela ME, Gomez-Ramon RC (2010) Differential evolution in constrained numerical optimization: an empirical study. Inf Sci 180(22):4223–4262

    Article  MathSciNet  MATH  Google Scholar 

  • Mora-Gutiérrez RA (2013) Diseño y desarrollo de un método heurístico basado en un sistema socio-cultural de creatividad para la resolución de problemas de optimización continuos no lineales y diseño de zonas electorales. Ph. D. Thesis. UNAM

  • Mora-Gutiérrez RA, Ramírez-Rodríguez J, Rincón-García EA, Ponsich A, Herrera O (2012) An optimization algorithm inspired by social creativity systems. Computing 94(11):887–914

    Article  MathSciNet  MATH  Google Scholar 

  • Mora-Gutiérrez RA, Rincón-García EA, Ramírez-Rodríguez J, Ponsich A, Herrera-Alcántara O, Lara-Velázquez P (2013) An optimization algorithm inspired by musical composition in constrained optimization problems. Revista de Matemática: Teoría y Aplicaciones 20(2):183–202

    MathSciNet  MATH  Google Scholar 

  • Mora-Gutiérrez R, Ramírez-Rodríguez J, Rincón-García E (2014a) An optimization algorithm inspired by musical composition. Artif Intell Rev 41(3):301–315

    Article  Google Scholar 

  • Mora-Gutiérrez RA, Ramírez-Rodríguez J, Rincón-García EA, Ponsich A, Herrera O, Lara-Velázquez P (2014b) Adaptation of the musical composition method for solving constrained optimization problems. Soft Comput 18(10):1931–1948

    Article  Google Scholar 

  • Moscato P (1999) Memetic algorithms: a short introduction. In: Corne FGD, Dorigo M (eds) New ideas in optimization. McGraw-Hill Ltd, Maidenhead, pp 219–234

  • Moscato P, Cotta C (2003) A gentle introduction to memetic algorithms. In: Glover F, Kochenberger G (eds) Handbook of metaheuristics, Springer, pp 105–144

  • Moscato P, Cotta C (2010) A modern introduction to memetic algorithms. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics. Springer, pp 141–183

  • Moscato P, Cotta C, Mendes A (2004) Memetic algorithms. In: Onwubolu GC, Babu BV (eds) New optimization techniques in engineering. Springer, Berlin, pp 53–85

  • Neri F, Tirronen V (2010) Recent advances in differential evolution: a survey and experimental analysis. Artif Intell Rev 33(1–2):61–106

    Article  Google Scholar 

  • Noraini MR, Geraghty J (2011) Genetic algorithm performance with different selection strategies in solving TSP. In: Proceedings of the world congress on engineering

  • Park YM, Park JB, Won JR (1998) A hybrid genetic algorithm/dynamic programming approach to optimal long-term generation expansion planning. Int J Electr Power Energy Syst 20(4):295–303

    Article  Google Scholar 

  • Palma-Méndez JT, Marín-Morales R (2008) Inteligencia artificial Técnicas, métodos y aplicaciones. Mc Graw Hill, Madrid

    Google Scholar 

  • Pisinger D, Sigurd M (2007) Using decomposition techniques and constraint programming for solving the two-dimensional bin-packing problem. INFORMS J Comput 19(1):36–51

    Article  MathSciNet  MATH  Google Scholar 

  • Price KV (1999) An introduction to differential evolution. New ideas in optimization. McGraw-Hill, New-York, pp 79–108

  • Puchinger J, Raidl GR (2005) Combining metaheuristics and exact algorithms in combinatorial optimization: a survey and classification. In: Mira J, Álvares JR (eds) Artificial intelligence and knowledge engineering applications: a bioinspired approach. Springer, Berlin, pp 41–53

  • Puchinger J, Raidl GR, Gruber M (2005) Cooperating memetic and branch-and-cut algorithms for solving the multidimensional knapsack problem. In: Proceedings of the 6th metaheuristics international conference, pp 775–780

  • Raidl GR (2006) A unified view on hybrid metaheuristics. In: Hybrid metaheuristics. Springer, Berlin, pp 1–12

  • Resende MG, Martí R, Gallego M, Duarte A (2010a) GRASP and path relinking for the maxmin diversity problem. Comput Oper Res 37(3):498–508

    Article  MathSciNet  MATH  Google Scholar 

  • Resende MG, Ribeiro CC, Glover F, Martí R (2010b) Scatter search and path-relinking: fundamentals, advances, and applications. In: Gendreau M, Potvin JY (eds) Handbook of metaheuristics. Springer, pp 87–107

  • Robles V, Peña JM, Larranaga P, Pérez MS, Herves V (2006) GA-EDA: a new hybrid cooperative search evolutionary algorithm. In: Lozano JA, Larragaña P, Inza I, Bengoetxea E (eds) Towards a new evolutionary computation. Springer, Berlin, pp 187–219

  • Simon MA, Tzur R, Heinz K, Kinzel M (2004) Explicating a mechanism for conceptual learning: elaborating the construct of reflective abstraction. J Res Math Educ 35(5):305–329

    Article  Google Scholar 

  • Storn R, Price KV (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359

    Article  MathSciNet  MATH  Google Scholar 

  • Talbi EG (2002) A taxonomy of hybrid metaheuristics. J Heuristics 8(5):541–564

    Article  Google Scholar 

  • Takahama T, Setsuko S (2006) Constrained optimization by the constrained differential evolution with gradient-based mutation and feasible elites. In: IEEE congress on evolutionary computation (CEC 2006), pp 1–8

  • Tang W, Li Y (2008) Constrained optimization using triple spaces cultured genetic algorithm. Int Conf Nat Comput 6:589–593

    Google Scholar 

  • Tessema B, Yen GG (2009) An adaptative penalty formulation for constrained evolutionary optimization. IEEE Trans Syst Man Cybern A Syst Hum 39:565–578

    Article  Google Scholar 

  • Toscano-Pulido G, Coello CAC (2004) A constraint-handling mechanism for particle swarm optimization. In: Evolutionary computation 2004 (CEC 2004), vol 2, pp 1396–1403

  • Van Geert P (1998) A dynamic systems model of basic developmental mechanisms: Piaget, Vygotsky, and beyond. Psychol Rev 105(4):634–677

    Article  Google Scholar 

  • Xin B, Chen J, Zhang J, Fang H, Peng ZH (2012) Hybridizing differential evolution and particle swarm optimization to design powerful optimizers: a review and taxonomy. IEEE Trans Syst Man Cybern C Appl Rev 42(5):744–767

    Article  Google Scholar 

  • Zhang R, Wu C (2011) A hybrid differential evolution and tree search algorithm for the job shop scheduling problem. Math Probl Eng. doi:10.1155/2011/390593

    MathSciNet  MATH  Google Scholar 

  • Zhang R, Song S, Wu C (2013) A hybrid differential evolution algorithm for job shop scheduling problems with expected total tardiness criterion. Appl Soft Comput 13(3):1448–1458

    Article  Google Scholar 

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Authors and Affiliations

  1. Departamento de Ingeniería Eléctrica, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Del. Iztapalapa, C.P. 09340, Mexico, D.F., Mexico

    Sergio Gerardo de-los-Cobos-Silva, Miguel Angel Gutiérrez-Andrade & Pedro Lara-Velázquez

  2. Departamento de Sistemas, Universidad Autónoma Metropolitana-Azcapotzalco, Av. San Pablo 180, Colonia Reynosa Tamaulipas, C.P. 02200, Mexico, D.F., Mexico

    Roman Anselmo Mora-Gutiérrez, Eric Alfredo Rincón-García & Antonin Ponsich

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  1. Sergio Gerardo de-los-Cobos-Silva
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  2. Roman Anselmo Mora-Gutiérrez
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  3. Miguel Angel Gutiérrez-Andrade
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  4. Eric Alfredo Rincón-García
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  5. Antonin Ponsich
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  6. Pedro Lara-Velázquez
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Correspondence to Roman Anselmo Mora-Gutiérrez.

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de-los-Cobos-Silva, S.G., Mora-Gutiérrez, R.A., Gutiérrez-Andrade, M.A. et al. Development of seven hybrid methods based on collective intelligence for solving nonlinear constrained optimization problems. Artif Intell Rev 49, 245–279 (2018). https://doi.org/10.1007/s10462-016-9524-4

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