Handling constraints using multiobjective optimization concepts

International Journal for Numerical Methods in Engineering

Volumn 59, Issue 15, 2004, Pages 1989-2017

  Aguirre, Arturo Hernández ^a   Rionda, Salvador Botello ^a   Coello Coello, Carlos A ^b   Lizárraga, Giovanni Lizárraga ^a   Montes, Efrén Mezura ^b  

^a CENTRO DE INVESTIGACIÓN EN MATEMÁTICAS   (Mexico)

^b DEPARTAMENTO DE FÍSICA   (Mexico)

Author keywords

Constraint handling; Evolutionary algorithms; Evolutionary multiobjective optimization; Evolutionary optimization

Indexed keywords

EVOLUTIONARY ALGORITHMS; OPTIMIZATION; RANDOM PROCESSES; SHRINKAGE;

MULTIOBJECTIVE OPTIMIZATION; STOCHASTIC RANKING METHODS;

ENGINEERING;

MATHEMATICAL METHOD;

EID: 2442454689     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.947     Document Type: Article

References (35)

1. Goldberg DE. Genetic Algorithms in Search. Optimization and Machine Learning. Addison-Wesley: Reading, MA, 1989.
2. Schwefel H-P. Evolution and Optimum Seeking. Wiley: New York, 1995.
3. Fogel LJ. Intelligence Through Simulated Evolution. Forty Years of Evolutionary Programming. Wiley: New York, 1999.
4. Coello Coello CA, Mezura-Montes E. Handling constraints in genetic algorithms using dominance-based tournaments. In Proceedings of the Fifth International Conference on Adaptive Computing Design and Manufacture (ACDM 2002). vol. 5. University of Exeter, Devon. UK. Parmee IC (ed.). Springer: Berlin, April 2002: 273-284.
5. Michalewicz Z, Schoenauer M. Evolutionary algorithms for constrained parameter optimization problems. Evolutionary Computation 1996: 4(1):1-32.
6. Richardson JT, Palmer MR, Liepins G, Hilliard M. Some guidelines for genetic algorithms with penalty functions. In Proceedings of the Third International Conference on Genetic Algorithms (ICGA-89), San Mateo. CA, Schaffer JD (ed.). George Mason University, Morgan Kaufmann: Los Altos, CA, June 1989: 191-197.
7. Smith AE, Coit DW. Constraint handling techniques-penalty functions. In Handbook of Evolutionary Computation Bäck T. Fogel DB, Michalewicz Z (eds). Chapter C 5.2. Oxford University Press and Institute of Physics Publishing: Bristol, UK, 1997.
8. Rao SS. Engineering Optimization. Theory and Practice (3rd edn). Wiley: New York, 1996.
9. Knowles JD, Corne DW. Approximating the nondominated front using the Pareto archived evolution strategy. Evolutionary Computation 2000: 8(2):149-172.
10. Edgeworth FY. Mathematical Physics. P. Keagan: London, England, 1881.
11. Pareto V. Cours D'Economie Politique, vols. I and II. F. Rouge: Lausanne, 1896.
12. Stadler W. Fundamentals of multicriteria optimization. In Multicriteria Optimization in Engineering and the Sciences, Stadler W (ed.). Plenum Press: New York, 1988; 1-25.
13. Coello Coello CA, David A. Van Veldhuizen, Lamont GB. Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers: New York, May 2002. ISBN 0-3064-6762-3.
14. Camponogara E, Talukdar SN. A genetic algorithm for constrained and multiobjective optimization. In 3rd Nordic Workshop on Genetic Algorithms and Their Applications (3NWGA), Alander JT (ed.). University of Vaasa. Vaasa, Finland, August 1997; 49-62.
15. Jiménez F, Gómez-Skarmeta AF, Sánchez G. How evolutionary multi-objective optimization can be used for goals and priorities based optimization. In Primer Congreso Español de Algoritmos Evolutivos y Bioinspirados (AEB'02). Alba E. Fernández F. Gómez JA, Herrera F, Hidalgo JI, Lanchares J, Merelo JJ, Sánchez JM (eds). Mérida España, Universidad de la Extremadura, España, 2002; 460-465.
16. Coello Coello CA. Constraint-handling using an evolutionary multiobjective optimization technique. Civil Engineering and Environmental Systems 2000; 17:319-346.
17. Ray T, Kang T, Chye SK. An evolutionary algorithm for constrained optimization. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO'2000), San Francisco. CA. Whitley D et al. (eds). Morgan Kaufmann: Los Altos, CA, 2000: 771-777.
18. Ray T, Liew KM. A swarm metaphor for multiobjective design optimization. Engineering Optimization 2002; 34(2):141-153.
19. Schaffer JD. Multiple objective optimization with vector evaluated genetic algorithms. In Genetic Algorithms and their Applications: Proceedings of the First International Conference on Genetic Algorithms, Lawrence Erlbaum: London, 1985; 93-100.
20. Surry PD, Radcliffe NJ. The COMOGA method: constrained optimisation by multiobjective genetic algorithms. Control and Cybernetics 1997; 26(3):391-412.
21. Parmee IC. Purchase G. The development of a directed genetic search technique for heavily constrained design spaces. In Adaptive Computing in Engineering Design and Control-'94. Plymouth, UK, Parmee IC (ed.). University of Plymouth: Plymouth, 1994; 97-102.
22. Coello Coello CA. Treating constraints as objectives for single-objective evolutionary optimization. Engineering Optimization 2000; 32(3):275-308.
23. Mezura-Montes E, Coello Coello CA. A numerical comparison of some multiobjective-based techniques to handle constraints in genetic algorithms. Technical Report EVOCINV-03-2002. Evolutionary Computation Group at CINVESTAV-IPN, México, D.F. 07300. September 2002. Available at: http://www.cs.cinvestav.mx/-EVOCINV/
24. Bäck T. Evolutionary Algorithms in Theory and Practice. Oxford University Press: New York, 1996.
25. Runarsson TP, Yao X. Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation 2000; 4(3):284-294.
26. Koziel S, Michalewicz Z. Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evolutionary Computation 1999: 7(1):19-44.
27. Fonseca CM, Fleming PJ. Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In Proceedings of the Fifth International Conference on Genetic Algorithms, San Mateo, CA, Forrest S (ed.). University of Illinois at Urbana-Champaign, Morgan Kaufmann: Los Altos, CA, 1993; 416-423.
28. Horn J, Nafpliotis N, Goldberg DE. A niched Pareto genetic algorithm for multiobjective optimization. In Proceedings of the First IEEE Conference on Evolutionary Computation, IEEE World Congress on Computational Intelligence, vol. 1. Piscataway, New Jersey. IEEE Service Center: June 1994; 82-87.
29. Deb K. Goldberg DE. An investigation of niche and species formation in genetic function optimization. In Proceedings of the Third International Conference on Genetic Algorithms, San Mateo, CA. Schaffer JD (ed.). George Mason University, Morgan Kaufmann: Los Altos, CA, June 1989; 42-50.
30. Botello S, Marroquín JL, Onate E, Horebeek JV. Solving structural optimization problems with genetic algorithms and simulated annealing. International Journal for Numerical Methods in Engineering 1999; 45(8):1069-1084.
31. Rajeev S, Krishnamoorthy CS. Genetic algorithms-based methodologies for design optimization of trusses. Journal of Structural Engineering 1997; 123(3):350-358.
32. Elperin T. Monte-Carlo structural optimization in discrete variables with annealing algorithm. International Journal for Numerical Methods in Engineering 1988: 26:815-821.
33. Tzan S, Pantelides CP. Annealing strategy for optimal structural design. Journal of Structural Engineering 1996; 122(7):815-827.
34. Ackley D. An empirical study of bit vector function optimization. In Genetic Algorithms and Simulated Annealing, Davis L (ed.). Morgan Kaufmann: Los Altos, CA, 1987; 170-271.
35. Haug EJ, Arora JS. Applied Optimal Design: Mechanical and Structural Systems. Wiley: New York, 1979.