Constrained Optimization via Multiobjective Evolutionary Algorithms

Natural Computing Series

Volumn , Issue , 2008, Pages 53-75

  Mezura Montes, Efrén ^a   Coello, Carlos A Coello ^b  

^a National Laboratory of Advanced Informatics Xalapa   (Mexico)

^b DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84973603670     PISSN: 16197127     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-72964-8_3     Document Type: Chapter

References (56)

1. Shamim Akhtar, Kang Tai, and Tapabrata Ray. A Socio-Behavioural Simulation Model for Engineering Design Optimization. Engineering Optimization, 34(4):341–354, 2002.
2. Anders Angantyr, Johan Andersson, and Jan-Olov Aidanpaa. Constrained Optimization based on a Multiobjective Evolutionary Algorithms. In Proceedings of the Congress on Evolutionary Computation 2003 (CEC’2003), volume 3, pages 1560–1567, Piscataway, New Jersey, December 2003. Canberra, Australia, IEEE Service Center.
3. Eduardo Camponogara and Sarosh N. Talukdar. A Genetic Algorithm for Constrained and Multiobjective Optimization. In Jarmo T. Alander, editor, 3rd Nordic Workshop on Genetic Algorithms and Their Applications (3NWGA), pages 49–62, Vaasa, Finland, August 1997. University of Vaasa.
4. C. W. Carroll. The created response surface technique for optimizing nonlinear restrained systems. Operations Research, 9:169–184, 1961.
5. Carlos A. Coello Coello. Constraint-handling using an evolutionary multiobjective optimization technique. Civil Engineering and Environmental Systems, 17:319–346, 2000.
6. Carlos A. Coello Coello. Treating Constraints as Objectives for Single-Objective Evolutionary Optimization. Engineering Optimization, 32(3):275–308, 2000.
7. Carlos A. Coello Coello. Theoretical and Numerical Constraint Handling Techniques used with Evolutionary Algorithms: A Survey of the State of the Art. Computer Methods in Applied Mechanics and Engineering, 191(11-12):1245– 1287, January 2002.
8. Carlos A. Coello Coello and Arturo Hernández Aguirre. Design of Combinational Logic Circuits through an Evolutionary Multiobjective Optimization Approach. Artificial Intelligence for Engineering, Design, Analysis and Manufacture, 16(1):39–53, 2002.
9. Carlos A. Coello Coello and Efrén Mezura-Montes. Handling Constraints in Genetic Algorithms Using Dominance-Based Tournaments. In I.C. Parmee, editor, Proceedings of the Fifth International Conference on Adaptive Computing in Design and Manufacture (ACDM’2002), volume 5, pages 273–284, University of Exeter, Devon, UK, April 2002. Springer-Verlag.
10. Carlos A. Coello Coello, David A. Van Veldhuizen, and Gary B. Lamont. Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, June 2002.
11. R. Courant. Variational Methods for the Solution of Problems of Equilibrium and Vibrations. Bulletin of the American Mathematical Society, 49:1–23, 1943.
12. Carlos Manuel Mira de Fonseca. Multiobjective Genetic Algorithms with Applications to Control Engineering Problems. PhD thesis, Department of Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK, September 1995.
13. Hugo de Garis. Genetic Programming: Building Artificial Nervous Systems using Genetically Programmed Neural Networks Models. In R. Porter and B. Mooney, editors, Proceedings of the 7th International Conference on Machine Learning, pages 132–139. Morgan Kaufmann Publishers, 1990.
14. Kalyanmoy Deb. Genetic algorithms in multimodal function optimization. Master’s thesis, University of Alabama, Alabama, USA, 1989.
15. Kalyanmoy Deb. An Efficient Constraint Handling Method for Genetic Algorithms. Computer Methods in Applied Mechanics and Engineering, 186(2/4):311–338, 2000.
16. Kalyanmoy Deb, Amrit Pratap, Sameer Agarwal, and T. Meyarivan. A Fast and Elitist Multiobjective Genetic Algorithm: NSGA–II. IEEE Transactions on Evolutionary Computation, 6(2):182–197, April 2002.
17. A. V. Fiacco and G. P. McCormick. Extensions of SUMT for nonlinear programming: equality constraints and extrapolation. Management Science, 12(11):816– 828, 1968.
18. Carlos M. Fonseca and Peter J. Fleming. Genetic Algorithms for Multiobjective Optimization: Formulation, Discussion and Generali zation. In Stephanie Forrest, editor, Proceedings of the Fifth International Conference on Genetic Algorithms, pages 416–423, San Mateo, California, 1993. Morgan Kauffman Publishers.
19. Carlos M. Fonseca and Peter J. Fleming. Multiobjective optimization and multiple constraint handling with evolutionary algorithms—Part I: A unified formulation. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans, 28(1):26–37, 1998.
20. David Goldberg. The Design of Innovation. Kluwer Academic Publishers, New York, June 2002. ISBN 1-4020-7098-5.
21. Arturo Hernández-Aguirre, Salvador Botello-Rionda, Carlos A. Coello Coello, Giovanni Lizárraga-Lizárraga, and Efrén Mezura-Montes. Handling Constraints using Multiobjective Optimization Concepts. International Journal for Numerical Methods in Engineering, 59(15):1989–2017, April 2004.
22. Robert Hinterding and Zbigniew Michalewicz. Your Brains and My Beauty: Parent Matching for Constrained Optimisation. In Proceedings of the 5th International Conference on Evolutionary Computation, pages 810–815, Anchorage, Alaska, May 1998.
23. Jeffrey Horn, Nicholas Nafpliotis, and David E. Goldberg. A Niched Pareto Genetic Algorithm for Multiobjective Optimization. In Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, volume 1, pages 82–87, Piscataway, New Jersey, June 1994. IEEE Service Center.
24. F. Jiménez, A.F. Gómez-Skarmeta, and G. Sánchez. How Evolutionary Multiobjective Optimization can be used for Goals and Priorities based Optimization. In Primer Congreso Español de Algoritmos Evolutivos y Bioinspirados (AEB’02), pages 460–465. Mérida España, 2002.
25. Joshua D. Knowles and David W. Corne. Approximating the Nondominated Front Using the Pareto Archived Evolution Strategy. Evolutionary Computation, 8(2):149–172, 2000.
26. Saku Kukkonen and Jouni Lampinen. Constrained Real-Parameter Optimization with Generalized Differential Evolution. In 2006 IEEE Congress on Evolutionary Computation (CEC’2006), pages 911–918, Vancouver, Canada, July 2006. IEEE Press.
27. J.J. Liang and P.N. Suganthan. Dynamic Multi-Swarm Particle Swarm Optimizer with a Novel Constraint-Handling Mechanism. In 2006 IEEE Congress on Evolutionary Computation (CEC’2006), pages 316–323, Vancouver, Canada, July 2006. IEEE Press.
28. Efrén Mezura-Montes and Carlos A. Coello Coello. Adding a Diversity Mechanism to a Simple Evolution Strategy to Solve Constrained Optimization Problems. In Proceedings of the Congress on Evolutionary Computation 2003 (CEC’2003), volume 1, pages 6–13, Piscataway, New Jersey, December 2003. Canberra, Australia, IEEE Service Center.
29. Efrén Mezura-Montes and Carlos A. Coello Coello. Multiobjective-Based Concepts to Handle Constraints in Evolutionary Algorithms. In Edgar Chávez, Jesús Favela, Marcelo Mejía, and Alberto Oliart, editors, Proceedings of the Fourth Mexican International Conference on Computer Science (ENC’2003), pages 192–199, Los Alamitos, CA, September 2003. Apizaco, Tlaxcala, México, IEEE Computer Society.
30. Efrén Mezura-Montes and Carlos A. Coello Coello. A Simple Multimembered Evolution Strategy to Solve Constrained Optimization Problems. IEEE Transactions on Evolutionary Computation, 9(1):1–17, February 2005.
31. Efrén Mezura-Montes, Carlos A. Coello Coello, and Ricardo Landa-Becerra. Engineering Optimization Using a Simple Evolutionary Algorithm. In Proceedings of the Fiftheenth International Conference on Tools with Artificial Intelligence (ICTAI’2003), pages 149–156, Los Alamitos, CA, November 2003. Sacramento, California, IEEE Computer Society.
32. Zbigniew Michalewicz, Kalyanmoy Deb, Martin Schmidt, and Thomas Stid-sen. Test-Case Generator for Nonlinear Continuous Parameter Optimization Techniques. IEEE Transactions on Evolutionary Computation, 4(3):197–215, September 2000.
33. Zbigniew Michalewicz and David B. Fogel. How to Solve It: Modern Heuristics. Springer, Germany, 2nd edition, 2004.
34. Zbigniew Michalewicz and Cezary Z. Janikow. Handling Constraints in Genetic Algorithms. In R. K. Belew and L. B. Booker, editors, Proceedings of the Fourth International Conference on Genetic Algorithms (ICGA-91), pages 151– 157, San Mateo, California, 1991. University of California, San Diego, Morgan Kaufmann Publishers.
35. Zbigniew Michalewicz and G. Nazhiyath. Genocop III: A co-evolutionary algorithm for numerical optimization with nonlinear constraints. In David B. Fogel, editor, Proceedings of the Second IEEE International Conference on Evolutionary Computation, pages 647–651, Piscataway, New Jersey, 1995. IEEE Press.
36. Zbigniew Michalewicz and Marc Schoenauer. Evolutionary Algorithms for Constrained Parameter Optimization Problems. Evolutionary Computation, 4(1):1– 32, 1996.
37. D. Ortiz-Boyer, C. Hervás-Martínez, and N. García-Pedrajas. Crossover Operator Effect in Functions Optimization with Constraints. In J. J. Merelo-Guervós and et al., editors, Proceedings of the 7th Parallel Problem Solving from Nature (PPSN VII), pages 184–193, Heidelberg, Germany, September 2002. Granada, Spain, Springer-Verlag. Lecture Notes in Computer Science Vol. 2439.
38. Domingo Ortiz-Boyer, Rafael Del-Castillo-Gomariz, Nicolas Garcia-Pedrajas, and Cesar Hervas-Martinez. Crossover effect over penalty methods in function optimization with constraints. In 2005 IEEE Congress on Evolutionary Computation (CEC’2005), volume 2, pages 1127–1134, Edinburgh, Scotland, September 2005. IEEE Service Center.
39. Akira Oyama, Koji Shimoyama, and Kozo Fujii. New Constraint-Handling Method for Multi-Objective Multi-Constraint Evolutionary Optimization and Its Application to Space Plane Design. In R. Schilling, W. Haase, J. Periaux, H. Baier, and G. Bugeda, editors, Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems (EUROGEN 2005), Munich, Germany, 2005.
40. I. C. Parmee and G. Purchase. The development of a directed genetic search technique for heavily constrained design spaces. In I. C. Parmee, editor, Adaptive Computing in Engineering Design and Control-’94, pages 97–102, Plymouth, UK, 1994. University of Plymouth.
41. David Powell and Michael M. Skolnick. Using genetic algorithms in engineering design optimization with non-linear constraints. In Stephanie Forrest, editor, Proceedings of the Fifth International Conference on Genetic Algorithms (ICGA-93), pages 424–431, San Mateo, California, July 1993. University of Illinois at Urbana-Champaign, Morgan Kaufmann Publishers.
42. Tapabrata Ray, Tai Kang, and Seow Kian Chye. An Evolutionary Algorithm for Constrained Optimization. In Darrell Whitley, David Goldberg, Erick Cantú-Paz, Lee Spector, Ian Parmee, and Hans-Georg Beyer, editors, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO’2000), pages 771–777, San Francisco, California, July 2000. Morgan Kaufmann.
43. Tapabrata Ray and K.M. Liew. Society and Civilization: An Optimization Algorithm Based on the Simulation of Social Behavior. IEEE Transactions on Evolutionary Computation, 7(4):386–396, August 2003.
44. Tapabrata Ray and Kang Tai. An Evolutionary Algorithm with a Multilevel Pairing Strategy for Single and Multiobjective Optimization. Foundations of Computing and Decision Sciences, 26:75–98, 2001.
45. Colin B. Reeves. Modern Heuristic Techniques for Combinatorial Problems. John Wiley and Sons, Great Britain, 1993.
46. Thomas Philip Runarsson and Xin Yao. Search biases in constrained evolutionary optimization. IEEE Transactions on Systems, Man, and Cybernetics Part C—Applications and Reviews, 35(2):233–243, May 2005.
47. J. David Schaffer. Multiple Objective Optimization with Vector Evaluated Genetic Algorithms. In Genetic Algorithms and their Applications: Proceedings of the First International Conference on Genetic Algorithms, pages 93–100. Lawrence Erlbaum, 1985.
48. Marc Schoenauer and Zbigniew Michalewicz. Evolutionary Computation at the Edge of Feasibility. In H.-M. Voigt, W. Ebeling, I. Rechenberg, and H.-P. Schwefel, editors, Proceedings of the Fourth Conference on Parallel Problem Solving from Nature (PPSN IV), pages 245–254, Heidelberg, Germany, September 1996. Berlin, Germany, Springer-Verlag.
49. Marc Schoenauer and Spyros Xanthakis. Constrained GA Optimization. In Stephanie Forrest, editor, Proceedings of the Fifth International Conference on Genetic Algorithms (ICGA-93), pages 573–580, San Mateo, California, July 1993. University of Illinois at Urbana-Champaign, Morgan Kauffman Publishers.
50. Alice E. Smith and David W. Coit. Constraint Handling Techniques—Penalty Functions. In Thomas Bäck, David B. Fogel, and Zbigniew Michalewicz, editors, Handbook of Evolutionary Computation, chapter C 5.2. Oxford University Press and Institute of Physics Publishing, 1997.
51. Patrick D. Surry and Nicholas J. Radcliffe. The COMOGA Method: Constrained Optimisation by Multiobjective Genetic Algorithms. Control and Cybernetics, 26(3):391–412, 1997.
52. Sangameswar Venkatraman and Gary G. Yen. A Generic Framework for Constrained Optimization Using Genetic Algorithms. IEEE Transactions on Evolutionary Computation, 9(4), August 2005.
53. Yuping Wang, Dalian Liu, and Yiu-Ming Cheung. Preference bi-objective evolutionary algorithm for constrained optimization. In Yue Hao et al., editor, Computational Intelligence and Security. International Conference, CIS 2005, volume 3801, pages 184–191, Xi’an, China, December 2005. Springer-Verlag. Lecture Notes in Artificial Intelligence.
54. Wang Yong and Cai Zixing. A Constrained Optimization Evolutionary Algorithm Based on Multiobjective Optimization Techniques. In 2005 IEEE Congress on Evolutionary Computation (CEC’2005), volume 2, pages 1081– 1087, Edinburgh, Scotland, September 2005. IEEE Service Center.
55. Yuren Zhou, Yuanxiang Li, Jun He, and Lishan Kang. Multi-objective and MGG Evolutionary Algorithm for Constrained Optimization. In Proceedings of the Congress on Evolutionary Computation 2003 (CEC’2003), volume 1, pages 1–5, Piscataway, New Jersey, December 2003. Canberra, Australia, IEEE Service Center.
56. E. Zitzler and L. Thiele. Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation, 3(4):257–271, 1999.