In this article, we propose an interval constraint programming method for globally solving catalog-based categorical optimization problems. It supports catalogs of arbitrary size and properties of arbitrary dimension,...
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In this article, we propose an interval constraint programming method for globally solving catalog-based categorical optimization problems. It supports catalogs of arbitrary size and properties of arbitrary dimension, and does not require any modeling effort from the user. A novel catalog-based contractor (or filtering operator) guarantees consistency between the categorical properties and the existing catalog items. This results in an intuitive and generic approach that is exact, rigorous (robust to roundoff errors) and can be easily implemented in an off-the-shelf interval-based continuous solver that interleaves branching and constraint propagation. We demonstrate the validity of the approach on a numerical problem in which a categorical variable is described by a two-dimensional property space. A Julia prototype is available as open-source software under the MIT license at https://***/cvanaret/***.
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 po...
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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 intervalconstraint 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.
An operator called CID and an efficient variant 3BCID were proposed in 2007. For numerical CSPs handled by interval methods, these operators compute a partial consistency equivalent to Partition-1-AC for discrete CSPs...
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ISBN:
(纸本)9781479929719
An operator called CID and an efficient variant 3BCID were proposed in 2007. For numerical CSPs handled by interval methods, these operators compute a partial consistency equivalent to Partition-1-AC for discrete CSPs. The two main parameters of CID are the number of times the main CID procedure is called and the maximum number of sub-intervals treated by the procedure. The 3BCID operator is state-of-the-art in numerical CSP solving, but not in constrained global optimization. This paper proposes an adaptive variant of 3BCID. The number of variables handled is auto-adapted during the search, the other parameters are fixed and robust to modifications. On a representative sample of instances, ACID appears to be the best approach in solving and optimization, and has been added to the default strategies of the Ibex interval solver.
This paper considers the use of cooperative solvers for solving global optimization problems. We present the cooperative solver Sib-calc and show how it can be used in solution of different optimization problems. Seve...
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ISBN:
(纸本)354026003X
This paper considers the use of cooperative solvers for solving global optimization problems. We present the cooperative solver Sib-calc and show how it can be used in solution of different optimization problems. Several examples of applying the Sibcalc solver for solving optimization problems are given.
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