Computing gap free Pareto front approximations with stochastic search algorithms

Evolutionary Computation

Volumn 18, Issue 1, 2010, Pages 65-96

  Schütze, Oliver ^a   Laumanns, Marco ^b   Tantar, Emilia ^c   Coello Coello, Carlos A ^a   Talbi, El Ghazali ^d,e  

^a DEPARTAMENTO DE FÍSICA   (Mexico)

^b ETH ZURICH   (Switzerland)

^c UNIVERSITÉ BORDEAUX 1   (France)

^d INRIA   (France)

^e KING SAUD UNIVERSITY   (Saudi Arabia)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77749286234     PISSN: 10636560     EISSN: 15309304     Source Type: Journal    
DOI: 10.1162/evco.2010.18.1.18103     Document Type: Article

References (37)

1. Bosman, P. A., and de Jong, E. D. (2005). Exploiting gradient information in numerical multi-objective evolutionary optimization. In Proceedings of the 2005 Genetic and Evolutionary Computation Conference (GECCO'2005), Vol. 1, pp. 755-762.
2. Brown, M., and Smith, R. E. (2005). Directed multi-objective optimization. International Journal on Computers, Systems, and Signals, 6(1):3-17.
3. Deb, K. (2001). Multi-objective optimization using evolutionary algorithms. New York: Wiley.
4. Deb, K., Mohan, M., and Mishra, S. (2005). Evaluating the ε-dominated based multi-objective evolutionary algorithm for a quick computation of Pareto-optimal solutions. Evolutionary Computation, 13(4):501-525.
5. Ehrgott, M. (2005). Multicriteria optimization. Berlin: Springer.
6. Fliege, J. (2004). Gap-free computation of Pareto-points by quadratic scalarizations. Mathematical Methods of Operations Research, 59:69-89.
7. Hanne, T. (1999). On the convergence of multiobjective evolutionary algorithms. European Journal of Operational Research, 117(3):553-564.
8. Harada, K., Sakuma, J., and Kobayashi, S. (2007). Uniform sampling of local Pareto-optimal solution curves by Pareto path following and its applications in multi-objective GA. In Proceedings of the 2007 Genetic and Evolutionary Computation Conference (GECCO'2007), vol. 1, pp. 813-820.
9. Hestermeyer, T., and Oberschelp, O. (2003). Selbstoptimierende Fahrzeugregelung-Verhaltensbasierte Adaption. In Intelligente mechatronische Systeme, vol. 122 of HNI-Verlagsschriftenreihe. Paderborn, Germany: Heinz Nixdorf Institut.
10. Hillermeier, C.(2001). Nonlinear multiobjective optimization-A generalizedhomotopy approach. Basel, Switzerland: Birkhäuser.
11. Knowles, J. D. (2002). Local-search and hybrid evolutionary algorithms for Pareto optimization. PhD thesis, The University of Reading, Department of Computer Science, Reading, UK.
12. Knowles, J. D., and Corne, D. W. (2000). Approximating the non-dominated front using the Pareto archived evolution strategy. Evolutionary Computation, 8(2):149-172.
13. Knowles, J. D., and Corne, D. (2003). Properties of an adaptive archiving algorithm for storing nondominated vectors. IEEE Transactions on Evolutionary Computation, 7(2):100-116.
14. Laumanns, M., Thiele, L., Deb, K., and Zitzler, E. (2002). Combining convergence and diversity in evolutionary multiobjective optimization. Evolutionary Computation, 10(3):263-282.
15. Loridan, P. (1984). ε-solutions in vector minimization problems. Journal of Optimization, Theory and Application, 42:265-276.
16. Pottharst, A., Baptist, K., Schütze, O., Böcker, J., Fröhlecke, N., and Dellnitz, M. (2004). Operating point assignment of a linear motor driven vehicle using multiobjective optimization methods. In Proceedings of the 11th International Conference EPE-PEMC 2004 (CD-ROM).
17. Rudolph, G. (1997a). Convergence rates of evolutionary algorithms for a class of convex objective functions. Control and Cybernetics, 26(3):275-390.
18. Rudolph, G. (1997b). Local convergence rates of simple evolutionary algorithms with Cauchy mutations. IEEE Transactions on Evolutionary Computation, 1(4):249-258.
19. Rudolph, G. (1998). Finite Markov chain results in evolutionary computation: A tour d'horizon. Fundamenta Informaticae, 35:67-89.
20. Rudolph, G., and Agapie, A. (2000). Convergence properties of some multi-objective evolutionary algorithms. In Proceedings of the 2000 Conference on Evolutionary Computation, vol. 2, pp. 1010-1016.
21. Rudolph, G., Naujoks, B., and Preuss, M. (2007). Capabilities of EMOA to detect and preserve equivalent Pareto subsets. In Proceedings of the 4th International Conference on Evolutionary Multi-Criterion Optimization, EMO 2007, pp. 36-50. Lecture Notes in Computer Science, Vol. 4403. Berlin: Springer.
22. Ruhe, G., and Fruhwirt, B. (1990). ε-optimality for bicriteria programs and its application to minimum cost flows. Computing, 44:21-34.
23. Sayin, S. (2000). Measuring the quality of discrete representations of efficient sets in multiple objective mathematical programming. Mathematical Programming, 87:543-560.
24. Schütze, O. (2004). Set oriented methods for global optimization. PhD thesis, University of Paderborn. Retrieved from http://ubdata.uni-paderborn.de/ediss/17/2004/schuetze/.
25. Schütze, O., Coello, C. A. C., Mostaghim, S., Talbi, E.-G., and Dellnitz, M. (2008a). Hybridizing evolutionary strategies with continuation methods for solving multi-objective problems. Engineering Optimization, 40(5):383-402.
26. Schütze, O., Coello, C. A. C., and Talbi, E.-G. (2007). Approximating the ε-efficient set of an MOP with stochastic search algorithms. In Proceedings of the Mexican International Conference on Artificial Intelligence (MICAI-2007), pp. 128-138.
27. Schütze, O., Coello, C. A. C., Tantar, E., and Talbi, E.-G. (2008b). Computing finite size representations of the set of approximate solutions of an MOP with stochastic search algorithms. In Proceedings of the 2008 Genetic and Evolutionary Computation Conference (GECCO'2008), pp. 713-720.
28. Schütze, O., Dell'Aere, A., and Dellnitz, M. (2005). On continuation methods for the numerical treatment of multi-objective optimization problems. In Branke, J., Deb, K., Miettinen, K., and Steuer, R. E., editors, Practical Approaches to Multi-Objective Optimization, number 04461 in Dagstuhl Seminar Proceedings. Internationales Begegnungsund Forschungszentrum (IBFI), Schloss Dagstuhl, Germany. Retrieved February 1, 2010 from http://drops.dagstuhl.de/opus/volltexte/2005/349.
29. Schütze, O., Laumanns, M., Tantar, E., Coello, C. A. C., and Talbi, E.-G. (2007). Convergence of stochastic search algorithms to gap-free Pareto front approximations. In Proceedings of the 2007 Genetic and Evolutionary Computation Conference (GECCO'2007), vol. 1, pp. 892-899.
30. Schütze, O., Laumanns, M., Coello, C. A. C., Dellnitz, M., and Talbi, E.-G. (2008c). Convergence of stochastic search algorithms to finite size Pareto set approximations. Journal of Global Optimization, 41(4):559-577.
31. Schütze, O., Vasile, M., and Coello Coello, C. A. (2008d). Approximate solutions in space mission design. In Parallel Problem Solving from Nature-PPSN X, pp. 805-814. Lecture Notes in Computer Science, Vol. 5199. Berlin: Springer.
32. Sharma, D., Kumar, A., Deb, K., and Sindhya, K. (2007). Hybridization of SBX based NSGA-II and sequential quadratic programming for solving multi-objective optimization problems. In Proceedings of the IEEE Congress on Evolutionary Computation, pp. 3003-3010.
33. Voigt, H.-M., Mühlenbein, H., and Cvetković, D. (1995). Fuzzy recombination for the breeder genetic algorithm. In Proceedings of the Sixth International Conference on Genetic Algorithms (ICGA'95), pp. 104-113.
34. White, D. J. (1998). Epsilon-dominating solutions in mean-variance portfolio analysis. European Journal of Operational Research, 105(3):457-466.
35. Witting, K., Schulz, B., Pottharst, A., Dellnitz, M., Böcker, J., and Fröhleke, N. (2008). A new approach for online multiobjective optimization of mechatronical systems. International Journal on Software Tools for Technology Transfer, 10:223-231.
36. Witting, K., and von Molo, M. H. (2006). Private communication. University of Paderborn, Germany.
37. Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C., and Fonseca, V. (2003). Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation, 7(2):117-132.