The Journal of Supercomputing

, Volume 64, Issue 1, pp 38-48

First online:

Open Access This content is freely available online to anyone, anywhere at any time.

A threaded approach of the quadratic bi-blending algorithm

  • Juan F. R. HerreraAffiliated withDpt. of Comput. Archit. and Electron., Univ. of Almería Email author 
  • , Leocadio G. CasadoAffiliated withDpt. of Comput. Archit. and Electron., Univ. of Almería
  • , Eligius M. T. HendrixAffiliated withComputer Architecture, Málaga UniversityOperations Research and Logistics, Wageningen University
  • , Inmaculada GarcíaAffiliated withComputer Architecture, Málaga University


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.


Shared memory Parallel processors Multithreaded Branch-and-bound Global optimization