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Erschienen in: Neural Computing and Applications 6/2013

01.05.2013 | Original Article

Bat algorithm for constrained optimization tasks

verfasst von: Amir Hossein Gandomi, Xin-She Yang, Amir Hossein Alavi, Siamak Talatahari

Erschienen in: Neural Computing and Applications | Ausgabe 6/2013

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Abstract

In this study, we use a new metaheuristic optimization algorithm, called bat algorithm (BA), to solve constraint optimization tasks. BA is verified using several classical benchmark constraint problems. For further validation, BA is applied to three benchmark constraint engineering problems reported in the specialized literature. The performance of the bat algorithm is compared with various existing algorithms. The optimal solutions obtained by BA are found to be better than the best solutions provided by the existing methods. Finally, the unique search features used in BA are analyzed, and their implications for future research are discussed in detail.

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Literatur
1.
Zurück zum Zitat Yang X-S (2008) Nature-inspired metaheuristic algorithms. Luniver Press, Bristol Yang X-S (2008) Nature-inspired metaheuristic algorithms. Luniver Press, Bristol
2.
Zurück zum Zitat Arora JS (1989) Introduction to optimum design. McGraw-Hill, New York Arora JS (1989) Introduction to optimum design. McGraw-Hill, New York
3.
Zurück zum Zitat Talbi E (2009) Metaheuristics: from design to implementation. Wiley, HobokenMATH Talbi E (2009) Metaheuristics: from design to implementation. Wiley, HobokenMATH
4.
Zurück zum Zitat Yang X-S (2009) Harmony search as a metaheuristic algorithm. In: Geem ZW (ed) Music-inspired harmony search: theory and applications. Springer, New York, pp 1–14 Yang X-S (2009) Harmony search as a metaheuristic algorithm. In: Geem ZW (ed) Music-inspired harmony search: theory and applications. Springer, New York, pp 1–14
5.
Zurück zum Zitat Gandomi AH, Yang XS, Talatahari S, Deb S (2012) Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization. Comput Math Appl 63(1):191–200MathSciNetMATHCrossRef Gandomi AH, Yang XS, Talatahari S, Deb S (2012) Coupled eagle strategy and differential evolution for unconstrained and constrained global optimization. Comput Math Appl 63(1):191–200MathSciNetMATHCrossRef
6.
Zurück zum Zitat Akhtar S, Tai K, Ray T (2002) A socio-behavioral simulation model for engineering design optimization. Eng Optim 34(4):341–354CrossRef Akhtar S, Tai K, Ray T (2002) A socio-behavioral simulation model for engineering design optimization. Eng Optim 34(4):341–354CrossRef
8.
Zurück zum Zitat Lee KS, Geem ZW (2004) A new meta-heuristic algorithm for continues engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194:3902–3933CrossRef Lee KS, Geem ZW (2004) A new meta-heuristic algorithm for continues engineering optimization: harmony search theory and practice. Comput Methods Appl Mech Eng 194:3902–3933CrossRef
9.
Zurück zum Zitat Yang XS, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483 Yang XS, Gandomi AH (2012) Bat algorithm: a novel approach for global engineering optimization. Eng Comput 29(5):464–483
10.
Zurück zum Zitat Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213:267–289MATHCrossRef Kaveh A, Talatahari S (2010) A novel heuristic optimization method: charged system search. Acta Mech 213:267–289MATHCrossRef
11.
Zurück zum Zitat Gandomi AH, Yang XS, Alavi AH (2012) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems, Eng Comput, in press. doi:10.1007/s00366-011-0241-y Gandomi AH, Yang XS, Alavi AH (2012) Cuckoo search algorithm: a metaheuristic approach to solve structural optimization problems, Eng Comput, in press. doi:10.​1007/​s00366-011-0241-y
12.
Zurück zum Zitat Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Gonzalez JR et al. (eds) Nature inspired cooperative strategies for optimization (NISCO 2010). Studies in computational intelligence, vol 284. Springer, Berlin, pp 65–74 Yang X-S (2010) A new metaheuristic bat-inspired algorithm. In: Gonzalez JR et al. (eds) Nature inspired cooperative strategies for optimization (NISCO 2010). Studies in computational intelligence, vol 284. Springer, Berlin, pp 65–74
13.
Zurück zum Zitat Altringham JD (1996) Bats: biology and behavior. Oxford University Press, Oxford Altringham JD (1996) Bats: biology and behavior. Oxford University Press, Oxford
14.
Zurück zum Zitat Richardson P (2008) Bats. Natural History Museum, London Richardson P (2008) Bats. Natural History Museum, London
15.
Zurück zum Zitat Hock W, Schittkowski K (1981) Test examples for nonlinear programming codes. Springer, BerlinMATHCrossRef Hock W, Schittkowski K (1981) Test examples for nonlinear programming codes. Springer, BerlinMATHCrossRef
16.
Zurück zum Zitat Michalewicz Z, Schoenauer M (1996) Evolutionary algorithms for constrained parameter optimization problems. Evol Comput 4(1):1–32CrossRef Michalewicz Z, Schoenauer M (1996) Evolutionary algorithms for constrained parameter optimization problems. Evol Comput 4(1):1–32CrossRef
17.
Zurück zum Zitat Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4(3):284–294CrossRef Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4(3):284–294CrossRef
18.
Zurück zum Zitat Hedar A, Fukushima M (2006) Derivative-free filter simulated annealing method for constrained continuous global optimization. J Glob Optim 35:521–549MathSciNetMATHCrossRef Hedar A, Fukushima M (2006) Derivative-free filter simulated annealing method for constrained continuous global optimization. J Glob Optim 35:521–549MathSciNetMATHCrossRef
19.
Zurück zum Zitat Amirjanov A (2006) The development of a changing range genetic algorithm. Comput Methods Appl Mech Eng 195:c2495–c2508MathSciNetCrossRef Amirjanov A (2006) The development of a changing range genetic algorithm. Comput Methods Appl Mech Eng 195:c2495–c2508MathSciNetCrossRef
20.
Zurück zum Zitat Aragon VS, Esquivel SC, Coello CCA (2010) A modified version of a T-cell algorithm for constrained optimization problems. Int J Numer Methods Eng 84:351–378MATH Aragon VS, Esquivel SC, Coello CCA (2010) A modified version of a T-cell algorithm for constrained optimization problems. Int J Numer Methods Eng 84:351–378MATH
21.
Zurück zum Zitat Becerra RL, Coello CAC (2006) Cultured differential evolution for constrained optimization. Comput Methods Appl Mech Eng 195(33–36):4303–4322MATHCrossRef Becerra RL, Coello CAC (2006) Cultured differential evolution for constrained optimization. Comput Methods Appl Mech Eng 195(33–36):4303–4322MATHCrossRef
22.
Zurück zum Zitat Bernardino HS, Barbosa HJC, Lemonge ACC (2006) Constraints handling in genetic algorithms via artificial immune systems. In: Genetic and evolutionary computation-GECCO 2006, genetic and evolutionary computation conference-Late Breaking Paper, Seattle, WA, USA Bernardino HS, Barbosa HJC, Lemonge ACC (2006) Constraints handling in genetic algorithms via artificial immune systems. In: Genetic and evolutionary computation-GECCO 2006, genetic and evolutionary computation conference-Late Breaking Paper, Seattle, WA, USA
23.
Zurück zum Zitat Cabrera JCF, Coello CAC (2007) Handling constraints in particle swarm optimization using a small population size. In: Alexander Gelbukh, Angel Fernando Kuri Morales (eds) MICAI 2007: advances in artificial intelligence, 6th international conference on artificial intelligence, lecture notes in artificial intelligence, vol 4827. Springer, Aguascalientes, Mexico, pp 41–51 Cabrera JCF, Coello CAC (2007) Handling constraints in particle swarm optimization using a small population size. In: Alexander Gelbukh, Angel Fernando Kuri Morales (eds) MICAI 2007: advances in artificial intelligence, 6th international conference on artificial intelligence, lecture notes in artificial intelligence, vol 4827. Springer, Aguascalientes, Mexico, pp 41–51
24.
Zurück zum Zitat Cortes NC, Trejo-Perez D, Coello CAC (2005) Handling constraints in global optimization using artificial immune system. In: Artificial immune systems, fourth international conference, ICARIS 2005, Banff, Canada. Lecture notes in computer science, vol 3627. Springer, Berlin, pp 234–247 Cortes NC, Trejo-Perez D, Coello CAC (2005) Handling constraints in global optimization using artificial immune system. In: Artificial immune systems, fourth international conference, ICARIS 2005, Banff, Canada. Lecture notes in computer science, vol 3627. Springer, Berlin, pp 234–247
25.
Zurück zum Zitat Koziel S, Michalewicz Z (1999) Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evol Comput 7(1):19–44CrossRef Koziel S, Michalewicz Z (1999) Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evol Comput 7(1):19–44CrossRef
26.
Zurück zum Zitat Montes EM, Coello CAC (2003) A simple multimembered evolution strategy to solve constrained optimization problems, Technical Report EVOCINV-04-2003, Evolutionary Computation Group at CINVESTAV, Secci′on de Computaci′on, Departamento de Ingenierıa El′ectrica, CINVESTAV-IPN, Mexico DF, Mexico Montes EM, Coello CAC (2003) A simple multimembered evolution strategy to solve constrained optimization problems, Technical Report EVOCINV-04-2003, Evolutionary Computation Group at CINVESTAV, Secci′on de Computaci′on, Departamento de Ingenierıa El′ectrica, CINVESTAV-IPN, Mexico DF, Mexico
27.
Zurück zum Zitat Tessema B, Yen G (2006) A self adaptive penalty function based algorithm for constrained optimization. In: Proceedings 2006 IEEE congress on evolutionary computation, pp 246–253 Tessema B, Yen G (2006) A self adaptive penalty function based algorithm for constrained optimization. In: Proceedings 2006 IEEE congress on evolutionary computation, pp 246–253
28.
Zurück zum Zitat Venkatraman S, Yen GG (2005) A generic framework for constrained optimization using genetic algorithms. IEEE Trans Evol Comput 9(4):424–435CrossRef Venkatraman S, Yen GG (2005) A generic framework for constrained optimization using genetic algorithms. IEEE Trans Evol Comput 9(4):424–435CrossRef
29.
Zurück zum Zitat Zhua W, Ali MM (2009) Solving nonlinearly constrained global optimization problem via an auxiliary function method. J Comput Appl Math 230:491–503MathSciNetCrossRef Zhua W, Ali MM (2009) Solving nonlinearly constrained global optimization problem via an auxiliary function method. J Comput Appl Math 230:491–503MathSciNetCrossRef
30.
Zurück zum Zitat Barbosa HJC, Lemonge ACC (2002) An adaptive penalty scheme in genetic algorithms for constrained optimization problems. In: Langdon WB, Cantu-Paz E, Mathias K, Roy R, Davis D, Poli R, Balakrishnan K, Honavar V, Rudolph G, Wegener J, Bull L, Potter MA, Schultz AC, Miller JF, Burke E, Jonoska N (eds) Proceedings of the genetic and evolutionary computation conference (GECCO’2002). Morgan Kaufmann, San Francisco, pp 287–294 Barbosa HJC, Lemonge ACC (2002) An adaptive penalty scheme in genetic algorithms for constrained optimization problems. In: Langdon WB, Cantu-Paz E, Mathias K, Roy R, Davis D, Poli R, Balakrishnan K, Honavar V, Rudolph G, Wegener J, Bull L, Potter MA, Schultz AC, Miller JF, Burke E, Jonoska N (eds) Proceedings of the genetic and evolutionary computation conference (GECCO’2002). Morgan Kaufmann, San Francisco, pp 287–294
31.
Zurück zum Zitat Bernardino HS, Barbosa HJC, Lemonge ACC (2007) A hybrid genetic algorithm for constrained optimization problems in mechanical engineering. In: 2007 IEEE congress on evolutionary computation (CEC 2007), Singapore. IEEE Press, New York, pp 646–653 Bernardino HS, Barbosa HJC, Lemonge ACC (2007) A hybrid genetic algorithm for constrained optimization problems in mechanical engineering. In: 2007 IEEE congress on evolutionary computation (CEC 2007), Singapore. IEEE Press, New York, pp 646–653
32.
Zurück zum Zitat Bernardino HS, Barbosa HJC, Lemonge ACC, Fonseca LG (2008) A new hybrid AIS-GA for constrained optimization problems in mechanical engineering. In: 2008 congress on evolutionary computation (CEC’2008), Hong Kong. IEEE Service Center, Piscataway, pp 1455–1462 Bernardino HS, Barbosa HJC, Lemonge ACC, Fonseca LG (2008) A new hybrid AIS-GA for constrained optimization problems in mechanical engineering. In: 2008 congress on evolutionary computation (CEC’2008), Hong Kong. IEEE Service Center, Piscataway, pp 1455–1462
33.
Zurück zum Zitat Cagnina LC, Esquivel SC, Coello CAC (2008) Solving engineering optimization problems with the simple constrained particle swarm optimizer. Informatica 32:319–326MATH Cagnina LC, Esquivel SC, Coello CAC (2008) Solving engineering optimization problems with the simple constrained particle swarm optimizer. Informatica 32:319–326MATH
34.
Zurück zum Zitat Cai J, Thierauf G (1997) Evolution strategies in engineering optimization. Eng Optim 29(1):177–199CrossRef Cai J, Thierauf G (1997) Evolution strategies in engineering optimization. Eng Optim 29(1):177–199CrossRef
35.
Zurück zum Zitat Cao YJ, Wu QH. Mechanical design optimization by mixed variable evolutionary programming, In Proc 1997 Int Conf on Evolutionary Computation, Indianapolis; 1997, p. 443–446. Cao YJ, Wu QH. Mechanical design optimization by mixed variable evolutionary programming, In Proc 1997 Int Conf on Evolutionary Computation, Indianapolis; 1997, p. 443–446.
36.
Zurück zum Zitat Coello CAC (1999) Self-adaptive penalties for GA based optimization. Proc Congr Evol Comput 1:573–580 Coello CAC (1999) Self-adaptive penalties for GA based optimization. Proc Congr Evol Comput 1:573–580
37.
Zurück zum Zitat Coello CAC (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113–127CrossRef Coello CAC (2000) Use of a self-adaptive penalty approach for engineering optimization problems. Comput Ind 41(2):113–127CrossRef
38.
Zurück zum Zitat Coello CAC (2000) Constraint-handling using an evolutionary multiobjective optimization technique. Civil Eng Environ Syst 17:319–346CrossRef Coello CAC (2000) Constraint-handling using an evolutionary multiobjective optimization technique. Civil Eng Environ Syst 17:319–346CrossRef
39.
Zurück zum Zitat Coello CAC (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193–203CrossRef Coello CAC (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inform 16(3):193–203CrossRef
40.
Zurück zum Zitat Coello CAC (2004) Hybridizing a genetic algorithm with an artificial immune system for global optimization. Eng Optim 36(5):607–634MathSciNetCrossRef Coello CAC (2004) Hybridizing a genetic algorithm with an artificial immune system for global optimization. Eng Optim 36(5):607–634MathSciNetCrossRef
41.
Zurück zum Zitat Coello CAC, Cortés NC (2004) Hybridizing a genetic algorithm with an artificial immune system for global optimization. Eng Optim 36(5):607–634MathSciNetCrossRef Coello CAC, Cortés NC (2004) Hybridizing a genetic algorithm with an artificial immune system for global optimization. Eng Optim 36(5):607–634MathSciNetCrossRef
42.
Zurück zum Zitat Coello CAC, Montes EM (2001) Use of dominance-based tournament selection to handle constraints in genetic algorithms, In Intelligent Engineering Systems through Artificial Neural Networks (ANNIE2001), Vol. 11, ASME Press, St. Louis, Missouri, pp 177–182. Coello CAC, Montes EM (2001) Use of dominance-based tournament selection to handle constraints in genetic algorithms, In Intelligent Engineering Systems through Artificial Neural Networks (ANNIE2001), Vol. 11, ASME Press, St. Louis, Missouri, pp 177–182.
43.
Zurück zum Zitat Deb K, Gene AS (1997) A robust optimal design technique for mechanical component design. Evolutionary Algorithms in Engineering Applications, Springer, pp 497–514. Deb K, Gene AS (1997) A robust optimal design technique for mechanical component design. Evolutionary Algorithms in Engineering Applications, Springer, pp 497–514.
44.
Zurück zum Zitat Dos Santos Coelho L (2010) Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems. Expert Syst Appl 37(2):1676–1683 Dos Santos Coelho L (2010) Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems. Expert Syst Appl 37(2):1676–1683
45.
Zurück zum Zitat Fu J, Fenton RG, Cleghorn WL (1991) A mixed integer discrete continuous programming method and its application to engineering design optimization. Eng Optim 17:263–280CrossRef Fu J, Fenton RG, Cleghorn WL (1991) A mixed integer discrete continuous programming method and its application to engineering design optimization. Eng Optim 17:263–280CrossRef
46.
47.
Zurück zum Zitat He Q, Wang L (2006) An effective co-evolutionary particle swarm optimization for engineering optimization problems. Eng Appl Artif Intell 20:89–99CrossRef He Q, Wang L (2006) An effective co-evolutionary particle swarm optimization for engineering optimization problems. Eng Appl Artif Intell 20:89–99CrossRef
48.
Zurück zum Zitat He S, Prempain E, Wu QH (2004) An improved particle swarm optimizer for mechanical design optimization problems. Eng Optim 36(5):585–605MathSciNetCrossRef He S, Prempain E, Wu QH (2004) An improved particle swarm optimizer for mechanical design optimization problems. Eng Optim 36(5):585–605MathSciNetCrossRef
49.
Zurück zum Zitat Homaifar A, Lai SHY, Qi X (1994) Constrained optimization via genetic algorithms. Simulation 62(4):242–254CrossRef Homaifar A, Lai SHY, Qi X (1994) Constrained optimization via genetic algorithms. Simulation 62(4):242–254CrossRef
50.
Zurück zum Zitat Hu X, Eberhart RC, Shi Y (2003) Engineering optimization with particle swarm. In: Proc 2003 IEEE swarm intelligence symposium, pp 53–57 Hu X, Eberhart RC, Shi Y (2003) Engineering optimization with particle swarm. In: Proc 2003 IEEE swarm intelligence symposium, pp 53–57
51.
Zurück zum Zitat Huang FZ, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356MathSciNetMATHCrossRef Huang FZ, Wang L, He Q (2007) An effective co-evolutionary differential evolution for constrained optimization. Appl Math Comput 186(1):340–356MathSciNetMATHCrossRef
52.
Zurück zum Zitat Joines J, Houck C (1994) On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GAs. In: Fogel D (ed) Proc first IEEE conf on evolutionary computation, Orlando, Florida. IEEE Press, pp 579–584 Joines J, Houck C (1994) On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GAs. In: Fogel D (ed) Proc first IEEE conf on evolutionary computation, Orlando, Florida. IEEE Press, pp 579–584
53.
Zurück zum Zitat Kannan BK, Kramer SN (1994) An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. J Mech Des Trans 116:318–320 Kannan BK, Kramer SN (1994) An augmented Lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. J Mech Des Trans 116:318–320
54.
Zurück zum Zitat Lemonge ACC, Barbosa HJC (2004) An adaptive penalty scheme for genetic algorithms in structural optimization. Int J Numer Methods Eng 59:703–736MATHCrossRef Lemonge ACC, Barbosa HJC (2004) An adaptive penalty scheme for genetic algorithms in structural optimization. Int J Numer Methods Eng 59:703–736MATHCrossRef
55.
Zurück zum Zitat Li HL, Chang CT (1998) An approximate approach of global optimization for polynomial programming problems. Eur J Oper Res 107(3):625–632MathSciNetMATHCrossRef Li HL, Chang CT (1998) An approximate approach of global optimization for polynomial programming problems. Eur J Oper Res 107(3):625–632MathSciNetMATHCrossRef
56.
Zurück zum Zitat Li HL, Chou CT (1994) A global approach for nonlinear mixed discrete programming in design optimization. Eng Optim 22:109–122CrossRef Li HL, Chou CT (1994) A global approach for nonlinear mixed discrete programming in design optimization. Eng Optim 22:109–122CrossRef
57.
Zurück zum Zitat Litinetski VV, Abramzon BM (1998) Mars—a multistart adaptive random search method for global constrained optimization in engineering applications. Eng Optim 30(2):125–154CrossRef Litinetski VV, Abramzon BM (1998) Mars—a multistart adaptive random search method for global constrained optimization in engineering applications. Eng Optim 30(2):125–154CrossRef
58.
Zurück zum Zitat Michalewicz Z, Attia N (1994) Evolutionary optimization of constrained problems. In: Proceedings of the 3rd annual conf on evolutionary programming. World Scientific, pp 98–108 Michalewicz Z, Attia N (1994) Evolutionary optimization of constrained problems. In: Proceedings of the 3rd annual conf on evolutionary programming. World Scientific, pp 98–108
59.
Zurück zum Zitat Montes EM, Coello CAC (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37(4):443–473MathSciNetMATHCrossRef Montes EM, Coello CAC (2008) An empirical study about the usefulness of evolution strategies to solve constrained optimization problems. Int J Gen Syst 37(4):443–473MathSciNetMATHCrossRef
60.
Zurück zum Zitat Montes EM, Ocaña BH (2008) Bacterial foraging for engineering design problems: preliminary results. In: Proceedings of the 4th Mexican congress on evolutionary computation (COMCEV’2008), pp 33–38, CIMAT, México, Oct 2008 Montes EM, Ocaña BH (2008) Bacterial foraging for engineering design problems: preliminary results. In: Proceedings of the 4th Mexican congress on evolutionary computation (COMCEV’2008), pp 33–38, CIMAT, México, Oct 2008
61.
Zurück zum Zitat Montes EM, Coello CAC, Velázquez-Reyes J, Muñoz-Dávila L (2007) Multiple trial vectors in differential evolution for engineering design. Eng Optim 39(5):567–589MathSciNetCrossRef Montes EM, Coello CAC, Velázquez-Reyes J, Muñoz-Dávila L (2007) Multiple trial vectors in differential evolution for engineering design. Eng Optim 39(5):567–589MathSciNetCrossRef
62.
Zurück zum Zitat Parsopoulos KE, Vrahatis MN (2005) Unified particle swarm optimization for solving constrained engineering optimization problems. In: Lecture notes in computer science (LNCS), vol 3612, pp 582–591 Parsopoulos KE, Vrahatis MN (2005) Unified particle swarm optimization for solving constrained engineering optimization problems. In: Lecture notes in computer science (LNCS), vol 3612, pp 582–591
63.
Zurück zum Zitat Ray T, Liew KM (2003) Society and civilization: an optimization algorithm based on the simulation of social behavior. IEEE Trans Evol Comput 7(4):386–396CrossRef Ray T, Liew KM (2003) Society and civilization: an optimization algorithm based on the simulation of social behavior. IEEE Trans Evol Comput 7(4):386–396CrossRef
64.
Zurück zum Zitat Sandgren E (1988) Nonlinear integer and discrete programming in mechanical design. In: Proc ASME design technology conf, Kissimine, FL, pp 95–105 Sandgren E (1988) Nonlinear integer and discrete programming in mechanical design. In: Proc ASME design technology conf, Kissimine, FL, pp 95–105
65.
Zurück zum Zitat Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization. ASME J Mech Des 112(2):223–229CrossRef Sandgren E (1990) Nonlinear integer and discrete programming in mechanical design optimization. ASME J Mech Des 112(2):223–229CrossRef
66.
Zurück zum Zitat Shih CJ, Lai TK (1995) Mixed-discrete fuzzy programming for nonlinear engineering optimization. Eng Optim 23(3):187–199CrossRef Shih CJ, Lai TK (1995) Mixed-discrete fuzzy programming for nonlinear engineering optimization. Eng Optim 23(3):187–199CrossRef
67.
Zurück zum Zitat Tsai JF, Li HL, Hu NZ (2002) Global optimization for signomial discrete programming problems in engineering design. Eng Optim 34(6):613–622CrossRef Tsai JF, Li HL, Hu NZ (2002) Global optimization for signomial discrete programming problems in engineering design. Eng Optim 34(6):613–622CrossRef
68.
Zurück zum Zitat Wu SJ, Chow PT (1995) Genetic algorithms for nonlinear mixed discrete-integer optimization problems via meta-genetic parameter optimization. Eng Optim 24:137–159CrossRef Wu SJ, Chow PT (1995) Genetic algorithms for nonlinear mixed discrete-integer optimization problems via meta-genetic parameter optimization. Eng Optim 24:137–159CrossRef
69.
Zurück zum Zitat Yun YS (2005) Study on Adaptive hybrid genetic algorithm and its applications to engineering design problems. Waseda University, MSc Thesis Yun YS (2005) Study on Adaptive hybrid genetic algorithm and its applications to engineering design problems. Waseda University, MSc Thesis
70.
Zurück zum Zitat Zahara E, Kao YT (2009) Hybrid Nelder–Mead simplex search and particle swarm optimization for constrained engineering design problems. Expert Syst Appl 36:3880–3886CrossRef Zahara E, Kao YT (2009) Hybrid Nelder–Mead simplex search and particle swarm optimization for constrained engineering design problems. Expert Syst Appl 36:3880–3886CrossRef
71.
Zurück zum Zitat Zhang C, Wang HP (1993) Mixed-discrete nonlinear optimization with simulated annealing. Eng Optim 17(3):263–280 Zhang C, Wang HP (1993) Mixed-discrete nonlinear optimization with simulated annealing. Eng Optim 17(3):263–280
72.
Zurück zum Zitat Leite JPB, Topping BHV (1998) Improved genetic operators for structural engineering optimization. Adv Eng Softw 29(7–9):529–562CrossRef Leite JPB, Topping BHV (1998) Improved genetic operators for structural engineering optimization. Adv Eng Softw 29(7–9):529–562CrossRef
73.
Zurück zum Zitat Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186:311–338MATHCrossRef Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186:311–338MATHCrossRef
74.
Zurück zum Zitat Deb K (1991) Optimal design of a welded beam via genetic algorithms. AIAA J 29(11):2013–2015CrossRef Deb K (1991) Optimal design of a welded beam via genetic algorithms. AIAA J 29(11):2013–2015CrossRef
75.
Zurück zum Zitat Atiqullah Mir M, Rao SS (2000) Simulated annealing and parallel processing: an implementation for constrained global design optimization. Eng Optim 32(5):659–685 Atiqullah Mir M, Rao SS (2000) Simulated annealing and parallel processing: an implementation for constrained global design optimization. Eng Optim 32(5):659–685
76.
Zurück zum Zitat Liu J-L (2005) Novel orthogonal simulated annealing with fractional factorial analysis to solve global optimization problems. Eng Optim 37(5):499–519MathSciNetCrossRef Liu J-L (2005) Novel orthogonal simulated annealing with fractional factorial analysis to solve global optimization problems. Eng Optim 37(5):499–519MathSciNetCrossRef
77.
Zurück zum Zitat Hwang S-F, He R-S (2006) A hybrid real-parameter genetic algorithm for function optimization. Adv Eng Inform 20:7–21CrossRef Hwang S-F, He R-S (2006) A hybrid real-parameter genetic algorithm for function optimization. Adv Eng Inform 20:7–21CrossRef
78.
Zurück zum Zitat Zhang J, Liang C, Huang Y, Wu J, Yang S (2009) An effective multiagent evolutionary algorithm integrating a novel roulette inversion operator for engineering optimization. Appl Math Comput 211:392–416MathSciNetMATHCrossRef Zhang J, Liang C, Huang Y, Wu J, Yang S (2009) An effective multiagent evolutionary algorithm integrating a novel roulette inversion operator for engineering optimization. Appl Math Comput 211:392–416MathSciNetMATHCrossRef
79.
Zurück zum Zitat Gandomi AH, Yang X-S, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89(23–24):2325–2336CrossRef Gandomi AH, Yang X-S, Alavi AH (2011) Mixed variable structural optimization using firefly algorithm. Comput Struct 89(23–24):2325–2336CrossRef
80.
Zurück zum Zitat Siddall JN (1972) Analytical decision-making in engineering design. Prentice-Hall, Englewood Cliffs Siddall JN (1972) Analytical decision-making in engineering design. Prentice-Hall, Englewood Cliffs
81.
Zurück zum Zitat Ragsdell KM, Phillips DT (1976) Optimal design of a class of welded structures using geometric programming. ASME J Eng Ind 98(3):1021–1025CrossRef Ragsdell KM, Phillips DT (1976) Optimal design of a class of welded structures using geometric programming. ASME J Eng Ind 98(3):1021–1025CrossRef
82.
Zurück zum Zitat Zhang M, Luo W, Wang X (2008) Differential evolution with dynamic stochastic selection for constrained optimization. Inf Sci 178(15):3043–3074CrossRef Zhang M, Luo W, Wang X (2008) Differential evolution with dynamic stochastic selection for constrained optimization. Inf Sci 178(15):3043–3074CrossRef
83.
Zurück zum Zitat Belegundu AD (1982) A study of mathematical programming methods for structural optimization. Department of Civil and Environmental Engineering, University of Iowa, Iowa Belegundu AD (1982) A study of mathematical programming methods for structural optimization. Department of Civil and Environmental Engineering, University of Iowa, Iowa
84.
Zurück zum Zitat Coello CAC, Becerra RL (2004) Efficient evolutionary through the use of a cultural algorithm. Eng Optim 36:219–236CrossRef Coello CAC, Becerra RL (2004) Efficient evolutionary through the use of a cultural algorithm. Eng Optim 36:219–236CrossRef
85.
Zurück zum Zitat Hsu YL, Liu TC (2007) Developing a fuzzy proportional-derivative controller optimization engine for engineering design optimization problems. Eng Optim 39(6):679–700MathSciNetCrossRef Hsu YL, Liu TC (2007) Developing a fuzzy proportional-derivative controller optimization engine for engineering design optimization problems. Eng Optim 39(6):679–700MathSciNetCrossRef
86.
Zurück zum Zitat Ray T, Saini P (2001) Engineering design optimization using a swarm with an intelligent information sharing among individuals. Eng Optim 33(3):735–748CrossRef Ray T, Saini P (2001) Engineering design optimization using a swarm with an intelligent information sharing among individuals. Eng Optim 33(3):735–748CrossRef
Metadaten
Titel
Bat algorithm for constrained optimization tasks
verfasst von
Amir Hossein Gandomi
Xin-She Yang
Amir Hossein Alavi
Siamak Talatahari
Publikationsdatum
01.05.2013
Verlag
Springer-Verlag
Erschienen in
Neural Computing and Applications / Ausgabe 6/2013
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-012-1028-9

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