Infeasibility spheres for finding robust solutions of blending problems with quadratic constraints
Journal of Global Optimization
Branch-and-Bound interval global optimization on shared memory multiprocessors
Optimization Methods & Software - THE JOINT EUROPT-OMS CONFERENCE ON OPTIMIZATION, 4-7 JULY, 2007, PRAGUE, CZECH REPUBLIC, PART I
PDP '11 Proceedings of the 2011 19th International Euromicro Conference on Parallel, Distributed and Network-Based Processing
On determining the cover of a simplex by spheres centered at its vertices
Journal of Global Optimization
Interval parallel global optimization with charm++
PARA'04 Proceedings of the 7th international conference on Applied Parallel Computing: state of the Art in Scientific Computing
A class of problems that can be solved using interval algorithms
Computing - Special Issue on GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (SCAN2010)
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Blending algorithms aim for solving the problem of determining the mixture of raw materials in order to obtain a cheap and feasible recipe with the smallest number of raw materials. An algorithm that solves this problem for two products, where available raw material is limited, has two phases. The first phase is a simplicial branch-and-bound algorithm which determines, for a given precision, a Pareto set of solutions of the bi-blending problem as well as a subspace of the initial space where better feasible solutions (with more precision) can be found. The second phase basically consists in an exhaustive reduction of the mentioned subspace by deleting simplicial subsets that do not contain solutions. This second phase is useful for future refinement of the solutions. Previous work only focused on the first phase neglecting the second phase due to computational burden. With this in mind, we study the parallelization of the different phases of the sequential bi-blending algorithm and focus on the most time consuming phase, analyzing the performance of several strategies.