An informational approach to the global optimization of expensive-to-evaluate functions

In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each evaluation contributes to the localization of good candidates for the role of global minimizer, a sequential choice of evaluation points is usually carried out. In particular, when Kriging is used to interpolate past evaluations, the uncertainty associated with the lack of information on the function can be expressed and used to compute a number of criteria accounting for the interest of an additional evaluation at any given point. This paper introduces minimizer entropy as a new Kriging-based criterion for the sequential choice of points at which the function should be evaluated. Based on \emph{stepwise uncertainty reduction}, it accounts for the informational gain on the minimizer expected from a new evaluation. The criterion is approximated using conditional simulations of the Gaussian process model behind Kriging, and then inserted into an algorithm similar in spirit to the \emph{Efficient Global Optimization} (EGO) algorithm. An empirical comparison is carried out between our criterion and \emph{expected improvement}, one of the reference criteria in the literature. Experimental results indicate major evaluation savings over EGO. Finally, the method, which we call IAGO (for Informational Approach to Global Optimization) is extended to robust optimization problems, where both the factors to be tuned and the function evaluations are corrupted by noise.Comment: Accepted for publication in the Journal of Global Optimization (This is the revised version, with additional details on computational problems, and some grammatical changes

Bayesian optimization for parameter identification on a small simulation budget

International audienceBayesian optimization uses a probabilistic model of the objective function to guide the search for the optimum. It is particularly interesting for the optimization of expensive-to-evaluate functions. For the last decade, it has been increasingly used for industrial optimization problems and especially for numerical design involving complex computer simulations. We feel that Bayesian optimization should be considered with attention by anyone who has to identify the parameters of a model based on a very limited number of model simulations because of model complexity. In this paper, we wish to describe, as simply as possible, how Bayesian optimization can be used in parameter identification and to present a new application. We concentrate on two algorithms, namely EGO (for Efficient Global Optimization) and IAGO (for Informational Approach to Global Optimization), and describe how they can be used for parameter identification when the budget for evaluating the cost function is severely limited. Some open questions that must be addressed for theoretical and practical reasons are indicated

Olfactory proteins mediating chemical communication in the navel orangeworm moth, Amyelois transitella.

BackgroundThe navel orangeworm, Amyelois transitella Walker (Lepidoptera: Pyralidae), is the most serious insect pest of almonds and pistachios in California for which environmentally friendly alternative methods of control--like pheromone-based approaches--are highly desirable. Some constituents of the sex pheromone are unstable and could be replaced with parapheromones, which may be designed on the basis of molecular interaction of pheromones and pheromone-detecting olfactory proteins.MethodologyBy analyzing extracts from olfactory and non-olfactory tissues, we identified putative olfactory proteins, obtained their N-terminal amino acid sequences by Edman degradation, and used degenerate primers to clone the corresponding cDNAs by SMART RACE. Additionally, we used degenerate primers based on conserved sequences of known proteins to fish out other candidate olfactory genes. We expressed the gene encoding a newly identified pheromone-binding protein, which was analyzed by circular dichroism, fluorescence, and nuclear magnetic resonance, and used in a binding assay to assess affinity to pheromone components.ConclusionWe have cloned nine cDNAs encoding olfactory proteins from the navel orangeworm, including two pheromone-binding proteins, two general odorant-binding proteins, one chemosensory protein, one glutathione S-transferase, one antennal binding protein X, one sensory neuron membrane protein, and one odorant receptor. Of these, AtraPBP1 is highly enriched in male antennae. Fluorescence, CD and NMR studies suggest a dramatic pH-dependent conformational change, with high affinity to pheromone constituents at neutral pH and no binding at low pH

Worst-case global optimization of black-box functions through Kriging and relaxation

International audienceA new algorithm is proposed to deal with the worst-case optimization of black-box functions evaluated through costly computer simulations. The input variables of these computer experiments are assumed to be of two types. Control variables must be tuned while environmental variables have an undesirable effect, to which the design of the control variables should be robust. The algorithm to be proposed searches for a minimax solution, i.e., values of the control variables that minimize the maximum of the objective function with respect to the environmental variables. The problem is particularly difficult when the control and environmental variables live in continuous spaces. Combining a relaxation procedure with Kriging-based optimization makes it possible to deal with the continuity of the variables and the fact that no analytical expression of the objective function is available in most real-case problems. Numerical experiments are conducted to assess the accuracy and efficiency of the algorithm, both on analytical test functions with known results and on an engineering application

A new strategy for worst-case design from costly numerical simulations

International audienceWorst-case design is important whenever robustness to adverse environmental conditions should be ensured regardless of their probability. It leads to minimax optimization, which is most often considered assuming that a closed-form expression for the performance index is available. In this paper, we consider the important situation where this is not the case and where evaluation of the performance index is via costly numerical simulations. In this context, strategies to limit the number of these evaluations are of paramount importance. This paper describes one such strategy, which further improves the performance of an algorithm recently presented that combines the use of a relaxation procedure for minimax search and Kriging-based efficient global optimization. Test cases from the literature demonstrate the interest of the approach

Genome Analysis and Expression Patterns of Odorant-Binding Proteins from the Southern House Mosquito Culex pipiens quinquefasciatus

Olfactory-based behaviors in mosquitoes are mediated by odorant-binding proteins (OBPs). They form a multigenic family involved in the peripheral events in insect olfaction, specifically the transport of odorants to membrane-bound odorant receptors. OBPs contribute to the remarkable sensitivity of the insect's olfactory system and may be involved in the selective transport of odorants

Global optimization of expensive-to-evaluate functions: an empirical comparison of two sampling criteria

In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each of these evaluations usefully contributes to the localization of good candidates for the role of global minimizer, a stochastic model of the function can be built to conduct a sequential choice of evaluation points. Based on Gaussian processes and Kriging, the authors have recently introduced the informational approach to global optimization (IAGO) which provides a onestep optimal choice of evaluation points in terms of reduction of uncertainty on the location of the minimizers. To do so, the probability density of the minimizers is approximated using conditional simulations of the Gaussian process model behind Kriging. In this paper, an empirical comparison between the underlying sampling criterion called conditional minimizer entropy (CME) and the standard expected improvement sampling criterion (EI) is presented. Classical tests functions are used as well as sample paths of the Gaussian model and an actual industrial application. They show the interest of the CME sampling criterion in terms of evaluation savings

The influence of water/rock − water/clay interactions and mixing in the salinization processes of groundwater

Study region: Groundwater from the Precambrian Shield rock and Pleistocene deposit aquifers in Saguenay-Lac-Saint-Jean region ( >13 000 km2) in the province of Quebec, Canada. Study focus: Interpretations are based on the combination of hierarchical cluster analysis (HCA) results, principal component analysis (PCA), binary plots investigations ([Na+, Ca2+, Br−] vs. Cl−; Ca2+ vs. HCO3−; Ca2+ vs. Na+) and Piper diagram investigations. The HCA and PCA was applied on 321 samples to specifically enable the identification of two very distinct salinization paths that produce the brackish groundwater in the study area. New hydrological insights for the region: The results show that each of the two salinization paths exerts a major and different influence on the chemical signature of groundwater. Groundwater present in the crystalline bedrock naturally evolve from a recharge-type groundwater (Ca-HCO3-dominant) to a type of brackish groundwater (Ca-(Na)-Cl-dominant) due to water/rock interactions (plagioclase weathering and mixing with deep basement fluids). Groundwater evolution in confined aquifers is dominated by water/clay interactions. The term water/clay interactions was introduced in this paper to account for a combination of processes: ion exchange and/or leaching of salt water trapped in the regional aquitard. Mixing with fossil seawater might also increase the groundwater salinity. PCA revealed that Ca2+, Sr2+, Ba2+ are highly correlated with groundwater from bedrock aquifers, while Mg2+, SiO2, K+, SO42− and HCO3− are more representative of the regional confining conditions

Les eaux souterraines à salinité élevée autour du lac Saint-Jean, Québec : origines et incidences

Les eaux souterraines dans le socle cristallin grenviilien de la région du Saguenay- Lac-Saint-Jean sont l'objet d'une première étude géochimique et isotopique portant principalement sur des eaux de salinité élevée. Les objectifs de cette étude sont d'évaluer la qualité naturelle des eaux souterraines, d'évaluer la variabilité chimique dans le temps et dans S'espace, de corréler la géologie régionale avec l'hydrogéochimie identifiée et d'identifier les processus géochimiques contrôlant les caractéristiques chimiques des eaux souterraines et leur évolution. Au total 96 échantillons ont été prélevés lors de trois campagnes. Parmi les 46 stations sélectionnées, 18 ont été échantillonnées à trois reprises, soit aux mois de novembre et décembre 2004, février 2005 et mai 2005, 13 stations ont été échantillonnées lors de 2 campagnes et 16 stations ont été échantillonnées une seule fois. La majorité des échantillons proviennent du socle rocheux et la plupart ont été prélevés dans des puits privés alimentant une résidence; certains échantillons proviennent de puits publics (prises d'eau municipales) ou abandonnés. Les échantillons ont été analysés pour 25 composantes inorganiques majeures, mineures et traces, ainsi que pour les isotopes stables 2H et 18O. Les résultats montrent une importante variabilité de certains paramètres mesurés in situ, de même que des paramètres analysés en laboratoire; le plus variable étant les fluorures. Ces variations influencent directement le respect des normes de potabilité. Les résultats permettent de définir deux principaux faciès hydrochimiques sur les portions du territoire à l'étude : un type (Na-Ca)-HCO3 dont le TSD moyen est de 300 mg/L et un type (Na-Ca)-Ci dont le TSD moyen est de 4000 mg/L. Les corrélations ioniques avec les chlorures suggèrent une signature marine pour 30 échantillons parmi les 62 échantillons de type (Na-Ca)-CI. Ces échantillons sont tous du type Na-CI. Leur localisation aux endroits où sont présentes les argiles de la Mer de Laflamme (10 000 ans BP) tend à confirmer la participation de l'eau de mer à la salinité des échantillons. La relation entre le calcium et le strontium des 32 autres échantillons suggère une origine crustale des ions dissous; la salinité serait alors acquise par l'interaction entre l'eau et la roche, soit la dissolution. Une anomalie locale en bore et en lithium à Chambord suggère que la composante marine identifiée pour ces échantillons provient de l'interaction avec les roches sédimentaires paléozoïques d'origine marine (calcaires et shale) présentes à cet endroit. L'ensemble de ces observations corréiées à la géologie locale apporte des pistes de réflexion sur l'écoulement des eaux souterraines autour du lac Saint-Jean et permet d'expliquer en partie les variations dans la qualité naturelle des sources souterraines d'eau potable