Section: Software and Platforms

IBEX

Participants : Ignacio Salas Donoso, Anthony Baire, Gilles Chabert [correspondant] , Rémi Douence, Bertrand Neveu, Gilles Trombettoni.

IBEX (Interval-Based EXplorer) is a C++ library for solving nonlinear constraints over real numbers (25000 lines of source code). The main feature of Ibex is its ability to build solver/paver strategies declaratively through the contractor programming paradigm.

In 2013 the work on IBEX has focussed on the following points.

• Continuing last year work on the redesign of the architecture, the IBEX library has been augmented with new features. First, affine forms (with the help of Jordan Ninin ) have been introduced in core calculations as an alternative to interval arithmetic. Five different implementations are under testing. A symbolic differentiation module has been developed and used for applying first-order conditions in global optimization (an interval variant of Khun-Tucker conditions). We have started a redesign of the global optimizer to integrate properly first-order conditions and exact equality constraints (not relaxed to inequalities). This work will be pursued in early 2014.

• In deterministic continuous constrained global optimization, upper bounding the objective function generally resorts to local minimization at several nodes of the branch and bound. We have proposed an alternative approach when the constraints are inequalities and the feasible space has a non-null volume. First, we extract an inner region, i.e., an entirely feasible convex polyhedron or box in which all points satisfy the constraints. Second, we select a point inside the extracted inner region and update the upper bound with its cost. We have implemented this principle with two inner region extraction algorithms, once being based on the algorithm published in CP'10 by G. Chabert & N. Beldiceanu for sweeping with continuous domains. The corresponding paper is Upper Bounding in Inner Regions for Global Optimization under Inequality Constraints that has been accepted for publication in JOGO (Journal of Global Optimization).

• The packaging of IBEX has also been considerably enhanced with the integration of a 3rd interval library (Filib++) and a 2nd LP solver (CPlex) and by making the library compatible with 64-bits platforms. The writing of documentation and tutorials has continued. A document of specifications has also been written for an automatic benchmarking tool.