The incumbent callback is used to reject integer feasible solutions that do not meet additional restrictions the user may wish to impose. The user callback routine will be called each time a new incumbent solution has been found, including when solutions are provided by the user's heuristic callback routine. The user callback routine is called with the new solution as input. Depending on the API, the callback function changes an argument or invokes a method to indicate whether or not the new solution should replace the incumbent solution.
For the object-oriented callback classes of the C++, Java, and .NET APIs, all callback information about the model and solution vector pertains to the original, unpresolved model. For the C API, the CPX_PARAM_MIPCBREDLP parameter influences the arguments to the user callback routine. If this parameter is set to its default value of CPX_ON (1), the solution vector that is input to the callback is a presolved vector. It contains one value for each variable in the presolved problem. The same is true of the various callback support routines (CPXcallbackglobalub, and so forth.). If the parameter is set to CPX_OFF (0), all these vectors relate to the variables of the original problem. Note that this parameter should not be changed in the middle of an optimization.
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