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Autre Publication Scientifique Année : 2012

On feasibility based bounds tightening

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Résumé

Mathematical programming problems involving nonconvexities are usually solved to optimality using a (spatial) Branch-and-Bound algorithm. Algorithmic e?ciency depends on many factors, among which the widths of the bounding box for the problem variables at each Branch-and-Bound node naturally plays a critical role. The practically fastest box-tightening algorithm is known as FBBT (Feasibility-Based Bounds Tightening): an iterative procedure to tighten the variable ranges. Depending on the instance, FBBT may not converge ?nitely to its limit ranges, even in the case of linear constraints. Tolerance-based termination criteria yield ?nite termination, but not in worstcase polynomial-time. We model FBBT by using ?xed-point equations in terms of the variable bounding box, and we treat these equations as constraints of an auxiliary mathematical program. We demonstrate that the auxiliary mathematical problem is a linear program, which can of course be solved in polynomial time. We demonstrate the usefulness of our approach by improving an existing Branch-and-Bound implementation. global optimization, MINLP, spatial Branch-and-Bound, range reduction.
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Dates et versions

hal-00935464 , version 1 (08-04-2014)

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  • HAL Id : hal-00935464 , version 1

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Pietro Belotti, Sonia Cafieri, Jon Lee, Leo Liberti. On feasibility based bounds tightening. 2012. ⟨hal-00935464⟩
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