A non-dominance-based online stopping criterion for multi-objective evolutionary algorithms

International Journal for Numerical Methods in Engineering

Volumn 84, Issue 6, 2010, Pages 661-684

  Goel, Tushar ^a   Stander, Nielen ^a  

^a LIVERMORE SOFTWARE TECHNOLOGY CORPORATION   (United States)

Author keywords

Convergence; Crashworthiness; Evolutionary algorithm; Genetic algorithms; Multi objective; Stopping criterion

Indexed keywords

COMPUTATIONAL COSTS; CONVERGENCE; CRASHWORTHINESS OPTIMIZATION; DOMINANCE CRITERIA; MULTI OBJECTIVE EVOLUTIONARY ALGORITHMS; MULTI-OBJECTIVE; NONDOMINATED SOLUTIONS; PARETO-OPTIMAL FRONT; SINGLE OBJECTIVE OPTIMIZATION; STOPPING CRITERIA; STOPPING CRITERION;

CRASHWORTHINESS; GENETIC ALGORITHMS; MULTIOBJECTIVE OPTIMIZATION;

CONVERGENCE OF NUMERICAL METHODS;

EID: 77958559728     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2909     Document Type: Article

References (48)

1. Miettenen K. Non-Linear Multi-Objective Optimization. Kluwer: Dordrecht, 1999.
2. Deb K. Multi-Objective Optimization Using Evolutionary Algorithms. Wiley: New York, 2001.
3. Rao SS. Engineering Optimization: Theory and Practice. Wiley: New York, 1996.
4. Harrington J. The desirability function. Industrial Quality Control 1965; 21(10):494-498.
5. Trautmann H, Weihs C. On the distribution of the desirability index using Harrington's desirability function. Metrika 2006; 63(2):207-213.
6. Goel T, Stander N, Lin Y-Y. Efficient resource allocation for genetic algorithm based multi-objective optimization with 1000 simulations. Structural and Multi-Disciplinary Optimization 2009; DOI: 10.1007/s00158-009-0426-9.
7. ® User's Manual, Version 971, May 2007.
8. Venkataraman S, Haftka RT. Structural optimization: what has Moore's law done for US? Structural and Multi-Disciplinary Optimization 2004; 28(6):375-387.
9. Coello CAC, Pulido GT. Multiobjective optimization using a micro genetic algorithm. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2001), San Francisco, CA, 2001.
10. Knowles J. ParEGO: a hybrid algorithm with on-line landscape approximation for expensive multi-objective problems. IEEE Transactions on Evolutionary Computation 2006; 10(1):50-66.
11. Jensen MT. Reducing the run-time complexity of multiobjective EAs: the NSGA-II and other algorithms. IEEE Transactions on Evolutionary Computation 2003; 7(5):503-515.
12. Isibuchi M, Murata T. A multi-objective genetic local search algorithm and its application to flowshop scheduling. IEEE Transactions on Systems, Man and Cybernetics-Part C: Applications and Reviews 1998; 28(3):392-403.
13. Deb K, Goel T. A hybrid multi-objective evolutionary approach to engineering shape design. Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization (EMO'01), Zurich, Switzerland, March 2001; 385-399.
14. Goel T, Deb K. Hybrid methods for multi-objective evolutionary algorithms. Proceedings of the 4th Asia-Pacific Conference on Simulated Evolution And Learning (SEAL-01), Singapore, November 2001; 188-192.
15. El-Beltagy MA, Nair PB, Keane AJ. Metamodeling techniques for evolutionary optimization of computationally expensive problems: promises and limitations. Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-1999), Orlando, FL, 1999.
16. Wilson B, Cappalleri D, Simpson TW, Frecker M. Efficient pareto frontier approximation using surrogate approximations. Optimization and Engineering 2001; 2(1):31-50.
17. Giannakoglou KC. Design of optimal aerodynamic shapes using stochastic optimization methods and computational intelligence. Progress in Aerospace Sciences 2001; 38(1):43-76.
18. Goel T, Vaidyanathan R, Haftka RT, Shyy W. Response surface approximation of pareto optimal front in multiobjective optimization. Computer Methods in Applied Mechanics and Engineering 2007; 196(4-6):879-893. Also presented at the 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (MAO, Sep-2004).
19. Voutchkov I, Keane AJ. Multi-objective optimization using surrogates. Proceedings of the 7th International Conference on Adaptive Computing in Design and Manufacture, Bristol, U.K., April 2006.
20. Ray T, Smith W. A surrogate assisted parallel multi-objective evolutionary algorithm for robust engineering design. Engineering Optimization 2006; 38(8):997-1011.
21. Emmerich MTM, Giannakoglou KC, Naujoks B. Single- and multi-objective evolutionary optimization assisted by gaussian random field metamodels. IEEE Transactions on Evolutionary Computation 2006; 10(4):421-439.
22. Goel T, Dorney DJ, Haftka RT, Shyy W. Improving the hydrodynamic performance of diffuser vanes via shape optimization. Computers and Fluids 2008; 37(6):705-723.
23. Aytug H, Koehler GJ. Stopping criteria for finite length genetic algorithms. ORSA Journal of Computing 1996; 8(2):181-193.
24. Aytug H, Koehler GJ. New stopping criteria for genetic algorithms. European Journal of Operations Research 1996; 126:662-674.
25. Pendharkar P, Koehler GJ. A general steady state distribution based stopping criteria for finite length genetic algorithms. European Journal of Operations Research 2007; 176:1436-1451.
26. van Veldhuizen DA, Lamont GB. Evolutionary computation and convergence to a pareto front. Proceedings of the 3rd Annual Conference on Genetic Programming, San Francisco, CA, August 1998; 221-228.
27. Hanne T. On the convergence of multiobjective evolutionary algorithms. European Journal of Operational Research 1999; 117(3):553-564.
28. Rudolph G, Agapie A. Convergence properties of some multi-objective evolutionary algorithms. Proceedings of the IEEE Congress on Evolutionary Computation (CEC-2000), San Diego, CA, 2000; 1010-1016.
29. Rudolph G. Self-adaptive mutations lead to premature convergence. IEEE Transactions on Evolutionary Computation 2001; 5(4):410-414.
30. ® User's Conference, Detroit, MI, 8-10 June 2008.
31. Rudenko O, Schoenauer M. A steady performance stopping criterion for pareto-based evolutionary algorithm. Proceedings of the 6th International Conference on Multi-Objective Programming and Goal Programming, Hammamet, Tunisia, 2004.
32. Marti L, Garcia J, Berlanga A, Molina JM. A cumulative evidential stopping criterion for multi-objective optimization evolutionary algorithms. Proceedings of the 9th Genetic And Evolutionary Computation Conference (GECCO-07), London, U.K., July 2007; 2835-2842.
33. Trautmann H, Ligges U, Mehnen J, Preuss M. A convergence criterion for multi-objective evolutionary algorithm based on systematic statistical testing. Proceedings of the 10th Parallel Problem Solving From Nature (PPSN-X), Dortmund, Germany, September 2008; 825-836.
34. Wagner T, Trautmann H, Naujoks B. OCD: online convergence detection for evolutionary multi-objective algorithms based on statistical testing. Proceedings of the 5th International Conference on Multi-Criterion Optimization (EMO-09), Nantes, France, April 2009; 198-215.
35. Naujoks B, Trautmann H. Online convergence detection for multiobjective aerodynamics applications. Proceedings of the IEEE Congress on Evolutionary Computation (CEC-2009), Trondheim, Norway, May 2009.
36. Trautmann H, Wagner T, Naujoks B, Preuss M, Mehnen J. Statistical methods for convergence detection of multiobjective evolutionary algorithms. Evolutionary Computation Journal 2009; 17(4):493-509.
37. Martí L, García J, Berlanga A, Molina JM. An approach to stopping criteria for multi-objective optimization evolutionary algorithms: the MGBM criterion. 2009 IEEE Conference on Evolutionary Computation (CEC 2009), Trondheim, Norway, May 2009.
38. Van Veldhuizen DA. Multiobjective evolutionary algorithms: classifications, analyses, and new innovations. Ph.D. Thesis, Department of Electrical and Computer Engineering, Air Force Institute of Technology, Wright Patterson Air Force Base, OH, 1999.
39. Zitzler E, Thiele L. Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach. IEEE Transactions on Evolutionary Computation 1999; 3(4):257-271.
40. Deb K, Jain S. Running performance metrics for evolutionary multi-objective optimization. Proceedings of the Fourth Asia-Pacific Conference on Simulated Evolution and Learning (SEAL-02), Singapore, 2002; 13-20.
41. Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 2002; 6(2):182-197.
42. Tanaka M, Watanabe H, Furukawa Y, Tanino T. GA-based decision support system for multi-criteria optimization. Proceedings of the International Conference on Systems, Man, and Cybernetics, Vancouver, BC, Canada, vol. 2, 1995; 1556-1561.
43. Osyczka A, Kundu S. A new method to solve generalized multicriteria optimization using the simple genetic algorithm. Structural Optimization 1995; 10(2):94-99.
44. Akkerman A, Thyagarajan R, Stander N, Burger M, Kuhm R, Rajic H. Shape optimization for crashworthiness design using response surfaces. Proceedings of the International Workshop on Multidisciplinary Design Optimization, Pretoria, South Africa, 2000; 270-279.
45. Craig KJ, Stander N, Dooge DA, Varadappa S. Automotive crashworthiness design using response surface-based variable screening and optimization. Engineering Computations 2005; 22:38-61.
46. ® Version 4.0 User's Manual, Livermore Software Technology Corporation, April 2009.
47. Schott JR. Fault tolerance design using single and multi-criteria genetic algorithms. Master's Thesis, Department of Aeronautics and Astronautics, MIT, Boston, MA, 1995.
48. Hansen MP, Jaskiewicz A. Evaluating the quality of approximation to the non-dominated set. Technical Report IMM-REP-1998-7, Institute of Mathematical Modeling, Technical University of Denmark, Lygnby, 1998.