• About Mixed integer linear programming and linear programming..

    From Wisdom90@21:1/5 to All on Wed Mar 18 17:58:41 2020

    About Mixed integer linear programming and linear programming..

    Mixed integer linear programming problems are much harder to solve than
    linear programming problems. In terms of computational complexity, LP's
    can be solved in polynomial time while solving MILP is an NP-Hard
    problem. The known algorithms for solving MILP's have exponential worst
    case complexity.

    And read about a comparison of Open-Source Linear Programming Solvers
    from Sandia National Laboratories:


    And i think that Symphony is the best non-commercial MILP solver with an ECLIPSE PUBLIC LICENSE here:


    I think Symphony MILP solver has a decent performance, read here to
    notice it:


    But i have noticed that the sensitivity analysis in Symphony MILP solver
    is part of the callable library and is not part of the command-line
    Symphony MILP solver.

    Also i think that CLP is the best non-commercial linear programming solver.

    About my linear programming modeling examples in Object Pascal..

    I have just updated my Linear programming modeling examples in Object
    Pascal, and i have just included the last stable version of 64bit
    Symphony MILP solver inside the zip file, so just pass it the MPS output
    file from the object pascal example.

    You can download it from:


    And about optimization..

    Advances in integer optimization from 1988 to 2017:

    – Improved algorithms and methods: 147,650 times faster

    – Improved computing power: 17,120 times faster

    – Overall improvement: 2,527,768,000 times faster

    In practice, this means that solving a typical MILP problem would have
    taken 80 years back in 1988, whereas today it only takes one second.
    However, while MILP problem solving is nowadays standard technology,
    MINLP problems still pose a challenge.This is motivating and inspiring researchers in the field.

    Read more here:

    The world’s fastest


    Optimization is a special area within Mathematics and Engineering. The
    idea of optimization is to find the best possible – or a sufficiently
    good – solution to a problem given in the form of a mathematical
    description of a system or process.

    And about optimization, i have just included the 64 bit SYMPHONY solver
    for mixed-integer linear programs (MILPs), with a batch file that
    executes the MPS file, inside the zip file that you can download from here:


    And read my following webpage about my Linear programming formulation of
    the Shortest-Route problem in object pascal to understand more:


    Thank you,
    Amine Moulay Ramdane.

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