The parameter IloCplex::MipEmphasis / CPX_PARAM_MIPEMPHASIS (set mip emphasis in the Interactive Optimizer) specifies whether CPLEX should emphasize feasibility or optimality as it solves the problem.

At the default setting of 0, CPLEX uses tactics designed to find a proved optimal solution most quickly, with less regard for the speed at which feasible solutions are produced along the way. With a setting of 1, CPLEX uses tactics designed to find the first and subsequent feasible solutions more quickly, at the likely expense of prolonging the time required to find a proven optimal solution.

Either setting will deliver a proved optimum, will produce feasible solutions during the course of computation, and will honor other parameter settings (such as time limits or branching strategies); the difference is in the trade-offs the MIP algorithm makes between the competing aims. Since proving optimality is often far more difficult than finding feasible solutions, setting this parameter to 1 is useful in situations (for example) where obtaining a good solution within a time limit is more important than arriving at a proved optimum.