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Comparing suboptimal solutions for different scenarios and defending the use of Gurobi as a solver in an academic setting,

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  • Mario Ruthmair
    Gurobi Staff Gurobi Staff

    Hi Garrett,

    Just to understand your situation a bit better, you have 3 VRP models and for each model you have several instances (=scenarios), right?

    For each model you want to compare the solutions for the different scenarios. What exactly do you want to compare? The runtime to solve them, the obtained objective values, or the solution structure itself? The latter two aspects are independent of your solution method, this depends only on the model and the input values.

    In general, the current state-of-the-art methodology to solve MIQPs, MILPs, etc. based on branch-and-bound is subject to high variability, i.e., the same mathematical model with different input values can potentially lead to significantly different runtimes. Many random decisions are taken throughout the optimization process (in branching, cutting, heuristics, etc.) that finally lead to a provably optimal solution, but potentially over different solution paths. The runtime can therefore be hardly predicted.

    I am not sure if I understand your second question. Do you want to switch off some components of Gurobi, e.g., built-in heuristics, cuts, presolving, etc.? Even if you would do that (I do not recommend this), the algorithm stays a black-box, the millions of decisions taken will not be transparent.

    Regarding the linearizations to MILP, it depends on the way you did it whether it pays off or not. Gurobi can re-solve quadratic terms in different ways, there are also parameters that control this, e.g., MIQCPMethod, PreMIQCPForm. We have a webinar that describes more details how Gurobi considers quadratic constraints.


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