Competitive Global Optimization Codes

Some Branching Codes Using Function Values Only

DIRECT, Divide Rectangles (in Fortran, by Jörg Gablonsky)
gblSolve, a Matlab 5 implementation of DIRECT
Implementations of a simple and efficient global optimization method by Jones, Perttunen and Stuckmann for bound constrained problems

  • DIRECT is based on branching and a Pareto principle for box selection

    MCS, Multilevel Coordinate Search (by Huyer and Neumaier)
    A Matlab program for bound constrained global optimization using function values only

  • MCS is based on branching and sequential quadratic programming

    LGO, Lipschitz Global Optimization (commercial, by Janos Pinter)
    An integrated development environment for global optimization problems with Lipschitz continuous objective and constraints

  • LGO integrates a suite of global and local scope solvers. These include branch-and-bound, adaptive random search, statistical estimation techniques, (penalty-based) unconstrained and (exact) constrained local optimization methods. See the LGO tutorial Computational Global Optimization in Nonlinear Systems.
    Only function values are used; the computed bounds are probabilistic only.

    Some Branch and Bound Codes

    BARON, Branch-And-Reduce Optimization Navigator in Fortran (by Nikos Sahinidis)
    ``A general purpose solver for optimization problems with nonlinear constraints and/or integer variables. Fast specialized solvers for many linearly constrained problems. Easy to use GAMS/AMPL-like interface to the general purpose and specialized solvers.''

  • BARON is based on branching and box reduction using convex relaxation and Lagrange multiplier techniques

    alphaBB (by Adjiman, Androulakis, Maranas and Floudas)
    Branch and bound code for nonlinear programs The site has currently the description only; no code

  • alphaBB is based on branching and bound by convex underestimation, using interval analysis to write nonlinearities in DC (difference of convexc function) form

    INTOPT_90 ands its sequel GLOBSOL in Fortran 90 (by Baker Kearfott)
    Branch and bound code for global optimization with general factorable constraints, with rigorously guaranteed results (even roundoff is accounted for correctly)

  • GLobSol is based on branching and box reduction using interval analysis to verify that a global optimizer cannot be lost.

    MINLP (by Fletcher and Leyffer)
    Branch and bound code for mixed integer nonlinear programming; finding the global optimum is guaranteed only if all nonintegral constraints are convex.
    The site has currently the description only; no code. However, problems with AMPL input can be solved online via NEOS

  • MINLP uses standard mixed integer programming techniques and convex underestimation.

    GAMS/DICOPT (commercial, by Ignacio Grossmann)
    Solver for mixed Integer Nonlinear Programming (MINLP) problems.

  • No details available about methods used.

    ILOG Numerica (by Pascal van Hentenryck)
    Branch and bound code for constrained optimization (with mathematically rigorous results)

  • This code was based on branching and box reduction using interval analysis and constraint satisfaction techniques. ILOG Numerica is no longer a commercial product. The box reduction and interval analysis algorithms are now available in ILOG Solver.