A framework for parallel large-scale global optimization

  • Yuri Evtushenko
  • Mikhail PosypkinEmail author
  • Israel Sigal
Special Issue Paper


The paper describes the design and implementation of BNB-Solver, an object-oriented framework for discrete and continuous parallel global optimization. The framework supports exact branch-and-bound algorithms, heuristic methods and hybrid approaches. BNB-Solver provides a support for distributed and shared memory architectures. The implementation for distributed memory machines is based on MPI and thus can run on almost any computational cluster. In order to take advantages of multicore processors we provide a separate multi-threaded implementation for shared memory platforms. We introduce a novel collaborative scheme for combining exact and heuristic search methods that provides the support for sophisticated parallel heuristics and convenient balancing between exact and heuristic methods. In the experimental results section we discuss a nonlinear programming solver and a highly efficient knapsack solver that significantly outperforms existing parallel implementations.


Parallel global optimization   Branch-and-bound methods   Heuristic methods, knapsack problems   Nonlinear programming 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alba E, Almeida F, Blesa M et al (2006) Efficient parallel LAN/WAN algorithms for optimization. The MALLBA project. Parall Comput 32(5-6):415–440CrossRefGoogle Scholar
  2. 2.
    Ananth G, Kumar V, Pardalos P (1993) Parallel processing of discrete optimization problems. Encycl Microcomput 13:129–147Google Scholar
  3. 3.
    Casado L, Martínez J, García I et al (2008) Branch-and-Bound interval global optimization on shared memory multiprocessors. Optim Methods Softw 23(5):689–701zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Crainic TG, Le Cun B, Roucairol C (2006) Parallel branch and bound algorithms. In: Parallel Combinatorial Optimization, Chap 1, John Wiley & Sons, Hoboken, NJ, pp 1–28Google Scholar
  5. 5.
    Crainic TG, Toulouse M (2002) Parallel Strategies for Metaheuristics. In: Glover F, Kochenberger G (eds) State-of-the-Art Hand-book in Metaheuristics, Kluwer Academic Publishers, Dordrecht, pp 475–513Google Scholar
  6. 6.
    Coello Coello CA, Mezura-Montes E (2002) Constraint-handling in genetic algorithms through the use of dominance-based tournament selection. Adv Eng Inf 16(3):193–203CrossRefGoogle Scholar
  7. 7.
    Drepper U, Molnar I (2005) The Native POSIX Thread Library for Linux. Last access: 13 May 2009Google Scholar
  8. 8.
    Eckstein J, Philips C, Hart W (2006) PEBBL 1.0 User Guide. RUTCOR Research Report RRR 19-2006. Last access: 13 May 2009Google Scholar
  9. 9.
    Evtushenko Y (1971) Numerical methods for finding global extreme (case of a non-uniform mesh). USSR Comput Maths Math Phys 11(6):38–54CrossRefGoogle Scholar
  10. 10.
    Kellerer H, Pferschy U, Pisinger D (2004) Knapsack Problems. Springer, BerlinzbMATHGoogle Scholar
  11. 11.
    Posypkin M, Sigal I (2008) A combined parallel algorithm for solving the knapsack problem. J Comput Syst Sci Int 47(4):543–551CrossRefGoogle Scholar
  12. 12.
    Ralphs T (2006) Parallel branch and cut. In: Parallel Combinatorial Optimization. John Wiley & Sons, Hoboken, NJ, pp 53–103CrossRefGoogle Scholar
  13. 13.
    Snir M, Otto S, Huss-Lederman S, Walker D, Dongarra J (1996) MPI: The Complete Reference. MIT Press, BostonGoogle Scholar
  14. 14.
    Tschöke S, Holthöfer N (1995) A new parallel approach to the constrained two-dimensional cutting stock problem. In: Parallel Algorithms for Irregularly Structured Problems, LNCS 980, pp 285–300, Springer, LondonGoogle Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Yuri Evtushenko
    • 1
  • Mikhail Posypkin
    • 2
    Email author
  • Israel Sigal
    • 1
  1. 1.Dorodnicyn Computing Centre of the Russian Academy of SciencesMoscowRussia
  2. 2.Institute for System Analysis of Russian Academy of SciencesMoscowRussia

Personalised recommendations