Postdoctoral Position Offer
il y a 1 mois
kriging surrogates to save calls to the objective function, as embodied in the archetypal EGO algorithm [21]. The original optimization problem is translated into a series of other problems, that of the acquisition of new points where the costly function will be calculated. The acquisition criterion is based on the kriging model and it mitigates the optimization of the function and the learning of the kriging model [10]. BO has rapidly been extended to encompass constraints [20, 18][9, 11] or multi-objective functions [5].
In this post-doctoral work, we will focus on costly and general nonlinear constrained multi-objective optimization problems that are affected by uncertainties. We will consider the case where the uncertain parameters can be separated from the optimization variables and can be chosen during the simulations. Because of this separation and providing a probability of occurence of the uncertainties exists, a statistical modeling in the joint design × uncertain parameters space is possible. This will be the context of the work.
A key step when optimizing in the presence of uncertainties is the formulation of the problem, i.e., the choice of the robustness criteria. Considering
first unconstrained problems, relevant criteria are the expectation of the objective [12] or one of its (super-)quantiles [22, 23]. In Robust Optimization,
the uncertainties are handled in terms of specific compromises between the average performance and its dispersion [16, 4]. When there are constraints that depend on the uncertainties, the feasibility of the solutions is typically measured in probability. Probabilistic models of the constraints are called chance constraints [15] or reliability constraints [6]. The optimization problems are formulated in terms of statistical criteria such as probabilities of satisfying the constraints, expectations or (super-)quantiles or conditional quantiles of the objective function [22, 13, 19].
In the last decade, numerous contributions to the optimization of costly functions with uncertainties have relied on the learning of a metamodel of
the true functions, in particular Gaussian processes (GP) [8, 14]. In [12] and [2], the GP not only helps for the optimization (or for the inversion) of the
design variables, but it also serves to define an optimal sampling scheme. In [3], the problem of minimizing the mean of a stochastic function under
chance constraints is addressed. The objective function and the constraints are costly in the sense that they cannot be calculated more than a hundred times. The uncertainties, which can be described by parameters different from the optimization variables, can be chosen in the calculations. Generalizing [12], an optimization and sampling Bayesian procedure is proposed. It is based on the feasible improvement and the associated Stepwise Uncertainty Reduction (SUR) criterion to choose where to evaluate the uncertain parameters.
The goal of this work is to improve the ideas introduced in [3] by putting them in the context of multi-objective optimization under uncertainties. The
expected hyper-volume improvement must be adapted to take into account the uncertainties and a sampling SUR criterion must be devised to choose the value of the random parameter to be evaluated. As it is done in [17] a multi-output Gaussian process can be proposed to take into account the correlation between the objective functions. A wise choice of the correlation kernel should be done. The results wil be compared to others methods [7]. The methods developed will be applied to the design of energy efficient buildings, a major contemporary challenge. The criteria are the energy usage of the building, the thermal comfort and the cost. Important uncertainties affect the cost (through the cost of energy) and the external conditions through the climate change. The building models will be done with the opensource software Energy+ [1].
Required skills
- doctoral degree or equivalent in mathematics,
- proven strong background in uncertainty quantification or statistical
learning theory,
- substantial experience in numerical programming.
Dates Renewable 12 months contract. The envisaged start date is flexible between january and june 2024.
Location Institut Camille Jordan (ICJ), Campus of l’Ecole Centrale de Lyon, Ecully
Stays will be expected at Laboratoire d’Informatique, de Modélisation et d’Optimisation des Système (LIMOS), Campus des Cézeaux de l’université
de Clermont.
Salary : between 35k euros and 36k euros brut
References
[2] Reda El Amri, C´eline Helbert, Miguel Munoz Zuniga, Cl´ementine Prieur, and Delphine Sinoquet. Set inversion under functional uncertainties
[3] Reda El Amri, Rodolphe Le Riche, C´eline Helbert, Christophette Blanchet-Scalliet, and S´ebastien Da Veiga. A sampling criterion for constrained bayesian optimization with uncertainties, 2021.
[4] Hans-Georg Beyer and Bernhard Sendhoff. Robust optimization-a comprehensive survey. Co
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