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

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.

KEYWORDS:

• Multiobjective optimization
• uncertainty
• stochastic algorithm
• reliability

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

F. Poirion http://orcid.org/0000-0002-3557-6144