Constrained global optimization for wine blending

Assemblage consists in blending base wines in order to create target wines. Recent developments in aroma analysis allow us to measure chemical compounds impacting the taste of wines. This chemical analysis makes it possible to design a decision tool for the following problem: given a set of target wines, determine which volumes must be extracted from each base wine to produce wines that satisfy constraints on aroma concentration, volumes, alcohol contents and price. This paper describes the modeling of wine assemblage as a mixed constrained optimization problem, where the main goal is to minimize the gap to the desired concentrations for every aromatic criterion. The deterministic branch and bound solvers Couenne and IbexOpt behave well on the wine blending problem thanks to their interval constraint propagation/programming and polyhedral relaxation methods. We also study the performance of other optimization goals that could be embedded in a configuration tool, where the different possible interactions amount to solving the same constraints with different objective functions. We finally show on a recent generic wine blending instance that the proposed optimization process scales up well with the number of base wines.

[1]  Gilles Trombettoni,et al.  A Contractor Based on Convex Interval Taylor , 2012, CPAIOR.

[2]  Frédéric Messine,et al.  Enclosure Methods for Multivariate Differentiable Functions and Application to Global Optimization , 1998, J. Univers. Comput. Sci..

[3]  Olivier Lhomme,et al.  Consistency Techniques for Numeric CSPs , 1993, IJCAI.

[4]  Garth P. McCormick,et al.  Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems , 1976, Math. Program..

[5]  Luc Jaulin,et al.  Contractor programming , 2009, Artif. Intell..

[6]  Computer‐aided Optimization of Wine Blending , 1992 .

[7]  David E. Block,et al.  Neural-Network-Assisted Optimization of Wine Blending Based on Sensory Analysis , 2001, American Journal of Enology and Viticulture.

[8]  Frédéric Goualard,et al.  Revising Hull and Box Consistency , 1999, ICLP.

[9]  Pierre Hansen,et al.  A reliable affine relaxation method for global optimization , 2010, 4OR.

[10]  Laurent Dagan.  Potentiel aromatique des raisins de Vitis vinifera L. Cv. Petit Manseng et Gros Manseng. Contribution à l’arôme des vins de pays Côtes de Gascogne , 2006 .

[11]  Gilles Trombettoni,et al.  Constructive Interval Disjunction , 2007, CP.

[12]  Jorge Stolfi,et al.  Affine Arithmetic: Concepts and Applications , 2004, Numerical Algorithms.

[13]  Frédéric Messine.  Méthodes d'optimisation globale basées sur l'analyse d'intervalle pour la résolution de problèmes avec contraintes , 1997 .

[14]  Gilles Trombettoni,et al.  Inner Regions and Interval Linearizations for Global Optimization , 2011, AAAI.

[15]  Gilles Trombettoni,et al.  Constrained Wine Blending , 2013, CP.

[16]  Leo Liberti,et al.  Branching and bounds tighteningtechniques for non-convex MINLP , 2009, Optim. Methods Softw..

[17]  Gilles Trombettoni,et al.  Upper bounding in inner regions for global optimization under inequality constraints , 2014, J. Glob. Optim..

[18]  Walter Krämer,et al.  FILIB++, a fast interval library supporting containment computations , 2006, TOMS.

[19]  Byung-sun Kang,et al.  Blending of different domestic grape wines using mixture design and optimization technique , 2010 .

[20]  Sylvain Bouveret,et al.  Computing leximin-optimal solutions in constraint networks , 2009, Artif. Intell..

[21]  O. Knüppel,et al.  PROFIL/BIAS—A fast interval library , 1994, Computing.

[22]  Laurent Granvilliers,et al.  Some Interval Approximation Techniques for MINLP , 2009, SARA.