The Automatic Dynamic Penalisation method (ADP) for handling constraints with genetic algorithms

Computer Methods in Applied Mechanics and Engineering

Volumn 256, Issue , 2013, Pages 70-87

  Montemurro, Marco ^a,b,c   Vincenti, Angela ^a   Vannucci, Paolo ^d  

^a INSTITUT JEAN LE ROND D ALEMBERT   (France)

^b LUXEMBOURG INSTITUTE OF SCIENCE AND TECHNOLOGY   (Luxembourg)

^c UNIVERSITÉ DE LORRAINE   (France)

^d LABORATOIRE DES SCIENCES DU CLIMAT ET DE L ENVIRONNEMENT   (France)

Author keywords

Constrained optimisation; Constraint handling techniques; Exterior penalty function; Genetic algorithms

Indexed keywords

BENCH-MARK PROBLEMS; BUCKLING LOADS; COMPOSITE LAMINATE; CONSTRAINT-HANDLING TECHNIQUES; CURRENT GENERATION; DAMPING PROPERTY; DEFINITION DOMAIN; ELASTIC SYMMETRY; ENGINEERING APPLICATIONS; HANDLING CONSTRAINTS; OPTIMAL DESIGN; OPTIMISATIONS; PENALISATION METHOD; PENALTY COEFFICIENT; PENALTY FUNCTION;

BUCKLING; GENETIC ALGORITHMS;

OPTIMIZATION;

EID: 84872953305     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2012.12.009     Document Type: Article

References (49)

1. Rechenberg I. Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der Biologischen Evolution 1973, Frommann-Holzboog Verlag, Stuttgart, (in German).
2. Schwefel H.P. Numerical Optimization for Computer Models 1981, John Wiley, Chichester.
3. Michalewicz Z. Genetic Algorithms+Data Structures=Evolution Programs 1994, Springer, Berlin.
4. Fogel L.J., Owens A.J., Walsh M.J. Artificial Intelligence Through Simulated Evolution 1966, John Wiley, Chichester.
5. Glover F. Heuristics for integer programming using surrogate constraints. Decis. Sci. 1977, 8(1):156-166.
6. Holland J.H. Adaptation in Natural and Artificial Systems 1975, University of Michigan Press, Ann Arbor.
7. Goldberg D.E. Genetic Algorithms 1994, Addison and Wesley, New York.
8. Dasgupta D., Michalewicz Z. Evolutionary Algorithms in Engineering Applications 1997, Springer, Berlin.
9. Michalewicz Z., Schoenauer M. Evolutionary algorithms for constrained parameter optimization problems. Evolut. Comput. 1996, 4(1):1-32.
10. Coello Coello C.A. Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput. Methods Appl. Mech. Engrg. 2002, 191:1245-1287.
11. Courant R. Variational methods for the solution of problems of equilibrium and vibrations. Bull. Am. Math. Soc. 1943, 49:1-23.
12. Carroll C.W. The created response surface technique for optimizing nonlinear restrained systems. Oper. Res. 1961, 9:169-184.
13. Fiacco A.V., McCormick G.P. Extensions of SUMT for nonlinear programming: equality constraints and extrapolation. Manage. Sci. 1968, 12(11):816-828.
14. Runarsson T.P., Yao X. Stochastic ranking for constrained evolutionary optimization. IEEE Trans. Evolut. Comput. 2000, 4(3):284-294.
15. Farmani R., Wright J.A. Self-adaptive fitness formulation for constrained optimization. IEEE Trans. Evolut. Comput. 2003, 7(5):445-455.
16. Lin C.Y., Wu W.H. Self-organizing adaptive penalty strategy in constrained genetic search. Struct. Multidisciplin. Optim. 2004, 26(6):417-428.
17. Huang F.Z., Wang L., He Q. An effective co-evolutionary differential evolution for constrained optimization. Appl. Math. Comput. 2007, 186(1):340-356.
18. Orvosh D., Davis L. Shall we repair? genetic algorithms, combinatorial optimization and feasibility constraints. Proceedings of International Conference on Genetic Algorithms 1993, 650. Morgan Kaufmann, San Mateo.
19. Orvosh D., Davis L. Using a genetic algorithm to optimize problems with feasibility constraints. Proceedings of IEEE Conference on Evolutionary Computation 1994, 548-553. IEEE Press, New York.
20. Chootinan P., Chen A. Constraint handling in genetic algorithms using a gradient-based repair method. Comput. Oper. Res. 2006, 33(8):2263-2281.
21. T. Takahama, S. Sakai, Constrained optimization by the a constrained differential evolution with gradient-based mutation and feasible elites, in: Proceedings of the 2006 IEEE Congress on Evolutionary Computation, Vancouver, BC, 2006, pp. 308-315.
22. Deb K. An efficient constraint handling method for genetic algorithms. Comput. Methods Appl. Mech. Engrg. 2000, 186(2-4):311-338.
23. Wang Y., Cai Z.X., Zhou Y.R., Fan Z. Constrained optimization based on hybrid evolutionary algorithm and adaptive constraint handling technique. Struct. Multidisciplin. Optim. 2009, 37(4):395-413.
24. Wang L., Li L.P. An effective differential evolution with level comparison for constrained engineering design. Struct. Multidisciplin. Optim. 2010, 41(6):947-963.
25. Surry P.D., Radcliffe N.J. The COMOGA method: constrained optimisation by multi-objective genetic algorithms. Control Cybern. 1997, 26(3):391-412.
26. Venter G., Haftka R. Constrained particle swarm optimization using a biobjective formulation. Struct. Multidisciplin. Optim. 2010, 40(1-6):65-76.
27. Vincenti A., Ahmadian M.R., Vannucci P. BIANCA: a genetic algorithm to solve hard combinatorial optimisation problems in engineering. J. Global Optim. 2010, 48:399-421.
28. Montemurro M., Vincenti A., Vannucci P. A two-level procedure for the global optimum design of composite modular structures - application to the design of an aircraft wing. Part 1: Theoretical formulation. J. Optim. Theory Appl. 2012, 155(1):1-23. (Invited Paper).
29. Montemurro M., Vincenti A., Vannucci P. A two-level procedure for the global optimum design of composite modular structures - application to the design of an aircraft wing. Part 2: Numerical aspects and examples. J. Optim. Theory Appl. 2012, 155(1):24-53. (Invited Paper).
30. Davis L. Genetic Algorithms and Simulated Annealing 1987, Pitman, London.
31. Rao S.S. Engineering Optimization 1996, Wiley, New York. third ed.
32. Kannan B.K., Kramer S.N. An augmented lagrange multiplier based method for mixed integer discrete continuous optimization and its applications to mechanical design. Trans. ASME J. Mech. Des. 1994, 116:318-320.
33. Arora J.S. Introduction to Optimum Design 1989, McGraw-Hill, New York.
34. A.D. Belegundu, A study of mathematical programming methods for structural optimization, Department of Civil and Environmental Engineering, University of Iowa, Iowa City, Iowa.
35. Ragsdell K.M., Phillips D.T. Optimal design of a class of welded structures using geometric programming. ASME J. Engrg. Ind. 1976, 98(3):1021-1025.
36. Deb K. Optimal design of a welded beam via genetic algorithms. Engrg. Appl. Artif. Intell. 1991, 29(11):2013-2015.
37. Coello C.A.C., Montes E.M. Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv. Engrg. Inform. 2002, 16:193-203.
38. He Q., Wang L. An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Engrg. Appl. Artif. Intell. 2007, 20:89-99.
39. He Q., Wang L. A hybrid particle swarm optimization with a feasibility-based rule for constrained optimization. Appl. Math. Comput. 2007, 186(2):1407-1422.
40. Zhao J., Wang L., Zeng P., Fan W. An effective hybrid genetic algorithm with flexible allowance technique for constrained engineering design optimization. Expert Syst. Appl. 2012, 39:6041-6051.
41. Deb K. GeneAS: a robust optimal design technique for mechanical component design. Evolutionary Algorithms in Engineering Applications 1997, Springer, Berlin, pp. 497-514.
42. Montemurro M., Koutsawa Y., Belouettar S., Vincenti A., Vannucci P. Design of damping properties of hybrid laminates through a global optimisation strategy. Compos. Struct. 2012, 94:3309-3320.
43. Montemurro M., Nasser H., Koutsawa Y., Belouettar S., Vincenti A., Vannucci P. Identification of electromechanical properties of piezoelectric structures through evolutionary optimisation techniques. Int. J. Solids Struct. 2012, 49(13):1884-1892.
44. Berthelot J.M., Assarar M., Sefrani Y., Mahi A.E. Damping analysis of composite material and structures. Compos. Struct. 2008, 85:189-204.
45. Le Maoût N., Verron E., Bégué J. Simultaneous geometrical and material optimal design of hybrid elastomer/composite sandwich plates. Compos. Struct. 2011, 93:1153-1157.
46. Nakra B.C. Vibration control in machines and structures using viscoelastic damping. J. Sound Vib. 1998, 211(3):449-465.
47. Vannucci P. Designing the elastic properties of laminates as an optimisation problem: a unified approach based on polar tensor invariants. Struct. Multidisciplin. Optim. 2006, 31(5):378-387.
48. C. Julien, Conception optimale de l'anisotropie dans les structures stratifiées à rigidité variable par la mèthode polaire-génétiques, Ph.D. Thesis, Institut d'Alembert UMR7190 CNRS, Université Pierre et Marie Curie Paris 6, France, 2010 (in French).
49. Tsai S.W., Hahn T. Introduction to Composite Materials 1980, Technomic.