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2018 | OriginalPaper | Buchkapitel

2. Possibilistic Framework for Multi-Objective Optimization Under Uncertainty

verfasst von : Oumayma Bahri, Nahla Ben Amor, El-Ghazali Talbi

Erschienen in: Recent Developments in Metaheuristics

Verlag: Springer International Publishing

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Abstract

Optimization under uncertainty is an important line of research having today many successful real applications in different areas. Despite its importance, few works on multi-objective optimization under uncertainty exist today. In our study, we address combinatorial multi-objective problem under uncertainty using the possibilistic framework. To this end, we firstly propose new Pareto relations for ranking the generated uncertain solutions in both mono-objective and multi-objective cases. Secondly, we suggest an extension of two well-known Pareto-base evolutionary algorithms namely, SPEA2 and NSGAII. Finally, the extended algorithms are applied to solve a multi-objective Vehicle Routing Problem (VRP) with uncertain demands.

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Literatur
1.
Zurück zum Zitat S. Asma, E.-G. Talbi, M. Aider, A. Liefooghe, Multi-objective local search with epistemic uncertainty: application to multi-objective vehicle routing problem with uncertain demands, in ISOR’11 (2011), pp. 1–22 S. Asma, E.-G. Talbi, M. Aider, A. Liefooghe, Multi-objective local search with epistemic uncertainty: application to multi-objective vehicle routing problem with uncertain demands, in ISOR’11 (2011), pp. 1–22
2.
Zurück zum Zitat M. Babbar, A. Lakshmikantha, D.E. Goldberg, A modified NSGA-II to solve noisy multiobjective problems, in Genetic and Evolutionary Computation Conference (GECCO’03). Lecture Notes in Computer Science, Chicago, IL (Springer, Berlin, 2003), pp. 2723–2727 M. Babbar, A. Lakshmikantha, D.E. Goldberg, A modified NSGA-II to solve noisy multiobjective problems, in Genetic and Evolutionary Computation Conference (GECCO’03). Lecture Notes in Computer Science, Chicago, IL (Springer, Berlin, 2003), pp. 2723–2727
3.
Zurück zum Zitat M. Basseur, A. Liefooghe, L. Jourdan, E.-G. Talbi, ParadisEO-MOEO: a framework for evolutionary multi-objective optimization, in Evolutionary Multi-Criterion Optimization (Springer, Berlin, 2007), pp. 386–400 M. Basseur, A. Liefooghe, L. Jourdan, E.-G. Talbi, ParadisEO-MOEO: a framework for evolutionary multi-objective optimization, in Evolutionary Multi-Criterion Optimization (Springer, Berlin, 2007), pp. 386–400
4.
Zurück zum Zitat J. Brito, J.A. Morino, J.L. Verdegay, Fuzzy optimization in vehicle routing problems, in IFSA-EUSFLAT (2009) J. Brito, J.A. Morino, J.L. Verdegay, Fuzzy optimization in vehicle routing problems, in IFSA-EUSFLAT (2009)
5.
Zurück zum Zitat C.A.C. Coello, G.B. Lamont, Applications of Multi-objective Evolutionary Algorithms (World Scientific, Singapore, 2004)CrossRef C.A.C. Coello, G.B. Lamont, Applications of Multi-objective Evolutionary Algorithms (World Scientific, Singapore, 2004)CrossRef
6.
Zurück zum Zitat C.A.C. Coello, G.B. Lamont, D.A. Van Veldhuisen, Evolutionary Algorithms for Solving Multi-objective Problems (Springer, New York, 2007) C.A.C. Coello, G.B. Lamont, D.A. Van Veldhuisen, Evolutionary Algorithms for Solving Multi-objective Problems (Springer, New York, 2007)
7.
Zurück zum Zitat K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms (Wiley, New York, 2001) K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms (Wiley, New York, 2001)
8.
Zurück zum Zitat K. Deb, N. Srinivas, Multiobjective optimization using nondominated sorting in genetic algorithms. IEEE Trans. Evol. Comput. 2(3), 221–248 (1994) K. Deb, N. Srinivas, Multiobjective optimization using nondominated sorting in genetic algorithms. IEEE Trans. Evol. Comput. 2(3), 221–248 (1994)
9.
Zurück zum Zitat K. Deb, S. Agrawal, A. Pratap, T. Meyarivan, A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2000)CrossRef K. Deb, S. Agrawal, A. Pratap, T. Meyarivan, A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2000)CrossRef
10.
Zurück zum Zitat D. Dubois, H. Prade, An introductory survey of possibility theory and its recent developments. J. Jpn. Soc. Fuzzy Theory Syst. 10, 21–42 (1998) D. Dubois, H. Prade, An introductory survey of possibility theory and its recent developments. J. Jpn. Soc. Fuzzy Theory Syst. 10, 21–42 (1998)
11.
Zurück zum Zitat C.M. Fonseca, P.J. Fleming, Genetic algorithms for multiobjective optimization: formulation, discussion and generalization, in Proceedings of the Fifth International Conference on Genetic Algorithms (1993), pp. 416–423 C.M. Fonseca, P.J. Fleming, Genetic algorithms for multiobjective optimization: formulation, discussion and generalization, in Proceedings of the Fifth International Conference on Genetic Algorithms (1993), pp. 416–423
12.
Zurück zum Zitat C.K. Goh, K.C. Tan, Evolutionary Multi-objective Optimization in Uncertain Environments: Issues and Algorithms (Springer, Heidelberg, 2009) C.K. Goh, K.C. Tan, Evolutionary Multi-objective Optimization in Uncertain Environments: Issues and Algorithms (Springer, Heidelberg, 2009)
13.
Zurück zum Zitat G. Goncalves, T. Hsu, J. Xu, Vehicle routing problem with time windows and fuzzy demands: an approach based on the possibility theory. Int. J. Adv. Oper. Manage. Inderscience 4, 312–330 (2009) G. Goncalves, T. Hsu, J. Xu, Vehicle routing problem with time windows and fuzzy demands: an approach based on the possibility theory. Int. J. Adv. Oper. Manage. Inderscience 4, 312–330 (2009)
14.
Zurück zum Zitat J. Horn, N. Nafpliotis, D.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, vol. 1 (1994), pp. 82–87 J. Horn, N. Nafpliotis, D.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, vol. 1 (1994), pp. 82–87
15.
Zurück zum Zitat E. Hughes, Evolutionary multi-objective ranking with uncertainty and noise, in Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization, London (Springer, Berlin, 2001), pp. 329–343 E. Hughes, Evolutionary multi-objective ranking with uncertainty and noise, in Proceedings of the First International Conference on Evolutionary Multi-Criterion Optimization, London (Springer, Berlin, 2001), pp. 329–343
16.
Zurück zum Zitat E.J. Hughes, Constraint handling with uncertain and noisy multi-objective evolution, in Proceedings of the 2001 Congress on Evolutionary Computation, Seoul (2001) E.J. Hughes, Constraint handling with uncertain and noisy multi-objective evolution, in Proceedings of the 2001 Congress on Evolutionary Computation, Seoul (2001)
17.
Zurück zum Zitat Y. Jin, J. Branke, Evolutionary optimization in uncertain environments: a survey. IEEE Trans. Evol. Comput. 9(3), 303–317 (2005)CrossRef Y. Jin, J. Branke, Evolutionary optimization in uncertain environments: a survey. IEEE Trans. Evol. Comput. 9(3), 303–317 (2005)CrossRef
18.
Zurück zum Zitat J.D. Knowles, D.W. Corne, Approximating the nondominated front using the Pareto archived evolution strategy. IEEE Trans. Evol. Comput. 8(2), 149–172 (2000) J.D. Knowles, D.W. Corne, Approximating the nondominated front using the Pareto archived evolution strategy. IEEE Trans. Evol. Comput. 8(2), 149–172 (2000)
19.
Zurück zum Zitat A.N. Kolmogorov, Foundations of the Theory of Probability, 2nd edn. (Chelsea Pub Co., New York, 1960) A.N. Kolmogorov, Foundations of the Theory of Probability, 2nd edn. (Chelsea Pub Co., New York, 1960)
20.
Zurück zum Zitat M.H. Laarabi, R. Sacile, A. Boulmakoul, E. Garbolino, Ranking triangular fuzzy numbers using fuzzy set inclusion index, in Fuzzy Logic and Applications (Springer, Cham, 2013), pp. 100–108 M.H. Laarabi, R. Sacile, A. Boulmakoul, E. Garbolino, Ranking triangular fuzzy numbers using fuzzy set inclusion index, in Fuzzy Logic and Applications (Springer, Cham, 2013), pp. 100–108
21.
Zurück zum Zitat P. Limbourg, Multi-objective optimization of problems with epistemic uncertainty, in Evolutionary Multi-Criterion Optimization (Springer, Berlin, 2005), pp. 413–427 P. Limbourg, Multi-objective optimization of problems with epistemic uncertainty, in Evolutionary Multi-Criterion Optimization (Springer, Berlin, 2005), pp. 413–427
22.
Zurück zum Zitat P. Limbourg, E.S. Daniel, An optimization algorithm for imprecise multi-objective problem functions. Evol. Comput. 1, 459–466 (2005) P. Limbourg, E.S. Daniel, An optimization algorithm for imprecise multi-objective problem functions. Evol. Comput. 1, 459–466 (2005)
23.
Zurück zum Zitat B. Oumayma, B.A. Nahla, E.-G. Talbi, A possibilistic framework for solving multi-objective problems under uncertainty: definition of new Pareto optimality, in IPDPSW 2013 (2013), pp. 405–414 B. Oumayma, B.A. Nahla, E.-G. Talbi, A possibilistic framework for solving multi-objective problems under uncertainty: definition of new Pareto optimality, in IPDPSW 2013 (2013), pp. 405–414
24.
Zurück zum Zitat L.F. Paquete, T. Stutzle, Stochastic local search algorithms for multiobjective combinatorial optimization: methods and analysis, in Handbook of Approximation Algorithms and Metaheuristics, vol. 13 (Chapman & Hall/CRC Boca Raton, 2007) L.F. Paquete, T. Stutzle, Stochastic local search algorithms for multiobjective combinatorial optimization: methods and analysis, in Handbook of Approximation Algorithms and Metaheuristics, vol. 13 (Chapman & Hall/CRC Boca Raton, 2007)
25.
Zurück zum Zitat G. Shafer, A Mathematical Theory of Evidence (Princeton University Press, Princeton, 1976) G. Shafer, A Mathematical Theory of Evidence (Princeton University Press, Princeton, 1976)
26.
Zurück zum Zitat P. Smets, Constructing the pignistic probability function in a context of uncertainty, in Proceeding 5th Conference on Uncertainty in Artificial intelligence, Windsor (1989), pp. 29–40 P. Smets, Constructing the pignistic probability function in a context of uncertainty, in Proceeding 5th Conference on Uncertainty in Artificial intelligence, Windsor (1989), pp. 29–40
27.
Zurück zum Zitat M.M. Solomon, Algorithms for the vehicle routing and scheduling problem with time window constraints. Oper. Res. 35(2), 254–265 (1987)CrossRef M.M. Solomon, Algorithms for the vehicle routing and scheduling problem with time window constraints. Oper. Res. 35(2), 254–265 (1987)CrossRef
28.
Zurück zum Zitat D. Sulieman, L. Jourdan, E.-G. Talbi, Using multiobjective metaheuristics to solve VRP with uncertain demands, in IEEE Congress on Evolutionary Computation (2010), pp. 1–8 D. Sulieman, L. Jourdan, E.-G. Talbi, Using multiobjective metaheuristics to solve VRP with uncertain demands, in IEEE Congress on Evolutionary Computation (2010), pp. 1–8
29.
Zurück zum Zitat E.-G. Talbi, Metaheuristics: From Design to Implementation (Wiley, New York, 2009)CrossRef E.-G. Talbi, Metaheuristics: From Design to Implementation (Wiley, New York, 2009)CrossRef
30.
Zurück zum Zitat J. Teich, Pareto-front exploration with uncertain objectives, in Evolutionary Multi-Criterion Optimization (EMO2001). Lecture Notes in Computer Science, vol. 1993 (2001), pp. 314–328 J. Teich, Pareto-front exploration with uncertain objectives, in Evolutionary Multi-Criterion Optimization (EMO2001). Lecture Notes in Computer Science, vol. 1993 (2001), pp. 314–328
31.
Zurück zum Zitat P. Toth, D. Vigo, The Vehicle Routing Problem (SIAM, Philadelphia, 2002)CrossRef P. Toth, D. Vigo, The Vehicle Routing Problem (SIAM, Philadelphia, 2002)CrossRef
32.
Zurück zum Zitat Z. Wang, F. Tian, A note of the expected value and variance of fuzzy variables. Int. J. Nonlinear Sci. 9(4), 486–492 (2010) Z. Wang, F. Tian, A note of the expected value and variance of fuzzy variables. Int. J. Nonlinear Sci. 9(4), 486–492 (2010)
33.
34.
Zurück zum Zitat L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 100, 9–34 (1999)CrossRef L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst. 100, 9–34 (1999)CrossRef
35.
Zurück zum Zitat E. Zitzler, L. Thiele, Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)CrossRef E. Zitzler, L. Thiele, Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Trans. Evol. Comput. 3(4), 257–271 (1999)CrossRef
36.
Zurück zum Zitat E. Zitzler, M. Laumans, L. Thiele, SPEA2: improving the strength Pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Zurich, May 2001 E. Zitzler, M. Laumans, L. Thiele, SPEA2: improving the strength Pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich, Zurich, May 2001
37.
Zurück zum Zitat E. Zitzler, L. Thiele, M. Laumanns, C.M. Foneseca, D. Grunert, Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7, 117–132 (2003)CrossRef E. Zitzler, L. Thiele, M. Laumanns, C.M. Foneseca, D. Grunert, Performance assessment of multiobjective optimizers: an analysis and review. IEEE Trans. Evol. Comput. 7, 117–132 (2003)CrossRef
38.
Zurück zum Zitat E. Zitzler, L. Thiele, J.D Knowles, A tutorial on the performance assessment of stochastic multiobjective optimizers, in Proceeding of the Third International Conference on Evolutionary Multi-Criterion Optimization (2005) E. Zitzler, L. Thiele, J.D Knowles, A tutorial on the performance assessment of stochastic multiobjective optimizers, in Proceeding of the Third International Conference on Evolutionary Multi-Criterion Optimization (2005)
Metadaten
Titel
Possibilistic Framework for Multi-Objective Optimization Under Uncertainty
verfasst von
Oumayma Bahri
Nahla Ben Amor
El-Ghazali Talbi
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-58253-5_2

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