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What are the ways to improve lower bounds while solving a minimization problem (MILP)?

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    $\begingroup$ Welcome to OR.SE. Your question is broad. I recommended you explain your question in the detailed. It gives more chance to answer by the community. :) $\endgroup$
    – A.Omidi
    Commented May 20, 2020 at 3:55
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    $\begingroup$ One way is to use a very aggressive cut generation strategy. $\endgroup$
    – T_O
    Commented May 20, 2020 at 5:09
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    $\begingroup$ Not sure what you mean by "while". Here is a now somewhat old paper on presolve, very pertinent to bound tightening techniques ampl.com/REFS/pripre.pdf .Or are you asking about getting better continuous relaxations during the solution process? $\endgroup$ Commented May 20, 2020 at 14:52
  • $\begingroup$ In addition to what was said above, also strong branching comes to mind. Note that some solvers provide a way to focus on raising that bound (for CPLEX see the MIP emphasis parameter). $\endgroup$ Commented May 26, 2020 at 5:03

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There are serveral strategies. I recomend Lagrangian and Surrogate relaxation.

Look for James Davis video "2.6 lagrangian relaxation". I guess it would help.

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