Hi, I would like to defend the use of Gurobi in an academic setting and would very much appreciate any advice and help in doing so.
I have formed a MIQP (for a rich variant of the VRP) and two MIQCP problems (for rich variants of the Vehicle Scheduling Problem) and sought to compare the outcomes and associated decision variables adopted for a variety of scenarios analysed. The problems are NP hard and as a result, I get optimality gaps of <10% for the MIQP problem and 20-40% for the MIQCP problems.
I ultimately want to answer the question: Are the solutions for different scenarios comparable (despite the optimality gaps)?
- Specifically, I think this means: How can I demonstrate that the solution techniques used by Gurobi are appropriate and that the uncertainty that remains to optimality is not subject to structural or hidden biases which might favour one or another scenario? (scenarios vary in input values, but not the objective function or constraints)
- As a follow up, is there a way to get Gurobi to implement simple, well known solution approaches without all of the fancy/sophisticated, but less transparent heuristics? Even if it means less-optimal answers?
I believe I have also managed to convert the problems to MILPs, however this doesn’t appear to have improved the solutions or optimality gaps. Is it possible to get more detail on how the quadratic problems are solved and why I don't get better results if I convert to MILPs?
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