Originally posted by: SystemAdmin
[jgregory said:]
I believe you have the right idea. MIP is the general model type whenever discrete variables (general integer, binary, SOS, etc) are present. For any such problem, Branch & Cut is the algorithm used, solving a sequence of subproblems organized in a tree structure.
For more detailed algorithmic purposes, we further divide the MIP type into MILP, MIQP, or MIQCP, depending on the nature of those subproblems. For MILP and MIQP problems there are both Simplex and Barrier implementations to handle the subproblems; for MIQCP the Barrier algorithm is the only choice (with a slightly obscure exception that I won't go into here). It is possible to make independent choices of the algorithm used at the top (root node) of the tree, and the rest of the nodes. The design of CPLEX's Branch & Cut solver is intended to make this distinction unimportant to users most of the time, with automatic strategies in place to handle details like these.
#CPLEXOptimizers#DecisionOptimization