Non-convex multiobjective optimization under uncertainty: a descent algorithm. Application to sandwich plate design and reliability

In this paper a novel algorithm for solving multiobjective design optimization problems with non-smooth objective functions and uncertain parameters is presented. The algorithm is based on the existence of a common descent vector for each sample of the random objective functions and on an extension...

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Vydáno v:Engineering optimization Ročník 51; číslo 5; s. 733 - 752
Hlavní autoři: Mercier, Q., Poirion, F., Désidéri, J. A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Abingdon Taylor & Francis 04.05.2019
Taylor & Francis Ltd
Témata:
Algorithms
Computer Science
Data Structures and Algorithms
Descent
Design optimization
Engineering Sciences
Genetic algorithms
Materials
Multiobjective optimization
Multiple objective analysis
Parallel processing
Parameter uncertainty
Reliability
stochastic algorithm
uncertainty
INCERTITUDE
ALGORITHME STOCHASTIQUE
FIABILITE
OPTIMISATION MULTIDISCIPLINAIRE
ISSN:0305-215X, 1029-0273
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Abstract In this paper a novel algorithm for solving multiobjective design optimization problems with non-smooth objective functions and uncertain parameters is presented. The algorithm is based on the existence of a common descent vector for each sample of the random objective functions and on an extension of the stochastic gradient algorithm. The proposed algorithm is applied to the optimal design of sandwich material. Comparisons with the genetic algorithm NSGA-II and the DMS solver are given and show that it is numerically more efficient due to the fact that it does not necessitate the objective function expectation evaluation. It can moreover be entirely parallelizable. Another simple illustration highlights its potential for solving general reliability problems, replacing each probability constraint by a new objective written in terms of an expectation. Moreover, for this last application, the proposed algorithm does not necessitate the computation of the (small) probability of failure.
AbstractList In this paper a novel algorithm for solving multiobjective design optimization problems with non-smooth objective functions and uncertain parameters is presented. The algorithm is based on the existence of a common descent vector for each sample of the random objective functions and on an extension of the stochastic gradient algorithm. The proposed algorithm is applied to the optimal design of sandwich material. Comparisons with the genetic algorithm NSGA-II and the DMS solver are given and show that it is numerically more efficient due to the fact that it does not necessitate the objective function expectation evaluation. It can moreover be entirely parallelizable. Another simple illustration highlights its potential for solving general reliability problems, replacing each probability constraint by a new objective written in terms of an expectation. Moreover, for this last application, the proposed algorithm does not necessitate the computation of the (small) probability of failure.
In this paper a novel algorithm for solving multiobjective design optimization problems with non-smooth objective functions and uncertain parameters is presented. The algorithm is based on the existence of a common descent vector for each sample of the random objective functions and on an extension of the stochastic gradient algorithm. The proposed algorithm is applied to the optimal design of sandwich material. Comparisons with the genetic algorithm NSGA-II and the DMS solver are given and show that it is numerically more efficient due to the fact that it does not necessitate the objective function expectation evaluation. It can moreover be entirely parallelizable. Another simple illustration highlights its potential for solving general reliability problems, replacing each probability constraint by a new objective written in terms of an expectation. Moreover, for this last application, the proposed algorithm does not necessitate the computation of the (small) probability of failure. Nous présentons un algorithme de descente pour résoudre numériquement les problèmes d’optimisation multi-critères sous incertitudes lorsque les fonctions objectifs sont non régulières ni convexes mais localement lipchitziennes. L'algorithme repose sur l'existence d'une direction de descente commune à l'ensemble des objectifs. Il est illustré sur un problème de conception optimale d'un matériau sandwich. La comparaison avec les algorithmes NSGA-II et DMS montrent les gains numériques importants de cette approche . Une seconde illustration montre également les apports de cet algorithme pour résoudre les problèmes d'optimisation fiabilistes.
Author Mercier, Q.
Poirion, F.
Désidéri, J. A.
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  surname: Poirion
  fullname: Poirion, F.
  email: fabrice.poirion@onera.fr
  organization: ONERA, The French Aerospace Lab
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  surname: Désidéri
  fullname: Désidéri, J. A.
  organization: INRIA
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Snippet In this paper a novel algorithm for solving multiobjective design optimization problems with non-smooth objective functions and uncertain parameters is...
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SubjectTerms Algorithms
Computer Science
Data Structures and Algorithms
Descent
Design optimization
Engineering Sciences
Genetic algorithms
Materials
Multiobjective optimization
Multiple objective analysis
Parallel processing
Parameter uncertainty
Reliability
stochastic algorithm
uncertainty
Title Non-convex multiobjective optimization under uncertainty: a descent algorithm. Application to sandwich plate design and reliability
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