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Constrained global optimization for wine blending

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Abstract

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.

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Notes

  1. Inverse operations of abs and max must be implemented for the constraint propagation (second phase of HC4-Revise [6]) and generalized gradients must be developed for the polyhedral relaxation.

  2. ε o b j -minimize f(X,Y) means minimize f(X,Y) with a precision ε o b j on the objective, i.e. find (X,Y) such that for all Z 1, Z 2 we have f(Z 1,Z 2)≥f(X,Y)−ε o b j .

  3. Another interval constraint programming operator, called 3B in [17, 23], is available in both solvers but is counterproductive in this application. It is based on a refutation reasoning that removes a sub-interval at a bound of a given domain if HC4 can prove that the corresponding sub-problem contains no solution.

  4. Wineblending1, Wineblending2, Wineblending1+2 and the six Wineblending3 instances can be downloaded from the web page of the first author.

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Authors and Affiliations

  1. LIRMM, UMR5506 Université de Montpellier - CNRS, Montpellier, France

    Philippe Vismara, Remi Coletta & Gilles Trombettoni

  2. MISTEA, UMR0729 Montpellier SupAgro - INRA, Montpellier, France

    Philippe Vismara

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  1. Philippe Vismara
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  2. Remi Coletta
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  3. Gilles Trombettoni
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Correspondence to Philippe Vismara.

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Vismara, P., Coletta, R. & Trombettoni, G. Constrained global optimization for wine blending. Constraints 21, 597–615 (2016). https://doi.org/10.1007/s10601-015-9235-5

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