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Is there any implementation, code or software, which can switch between search strategies in a B&B framework?

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In Cplex, try the following: run it once with a node or time limit, then change the search strategy, remove the node/time limit and rerun the solver. This should work also in command mode. The important thing is that you do not change the Mip model between the first and second run (otherwise Cplex will start a new run from the root node).

Using similar tricks you can also repeat several times the root node (to get more cuts), or you can use aggressive cuts only in the first 100 nodes (say), etc.

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    $\begingroup$ the folklore has it that a time limit changes the algorithmic behavior, so an effect observed for the changed rule may not only be attributed to the change of rule $\endgroup$ Jun 11 '19 at 5:12
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In open source codes you usually have more flexibility to change the parameter directly compared to commercial solvers.
Take SCIP for example where you can program your own node selector rules. You also have tons of parameters to adjust the node selection.
CBC offers similar features.

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    $\begingroup$ If one wants to program a custom rule, then commercial MIP solvers are very flexible as well—through callbacks. $\endgroup$ Jun 12 '19 at 8:07

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