Additional Details
Note that the optimality criteria for each optimization pass of a multiple-objective problem are defined as usual by the global parameters MIPGap and MIPGapAbs. This means that you can not set different optimality criteria for different objective functions.
We haven't attempted to generalize the notions of dual solutions or simplex bases for continuous multi-objective models, so you can't query attributes such as Pi, RC, VBasis, or CBasis for multi-objective solutions. Because of this, we've concluded that the most consistent result to return for attribute IsMIP is 1.
Gurobi will only solve multi-objective models with strictly linear objectives. If the primary objective is quadratic or piecewise linear, the solve call will return an error.
When solving a continuous multi-objective model using a hierarchical approach, you have a choice of which optimization algorithm to use for the different steps (primal simplex, dual simplex, or barrier). The first step will always use the algorithm specified in the Method parameter. The algorithm for subsequent steps is controlled by the MultiObjMethod parameter. This parameter has no effect for multi-objective MIP models.
For the hierarchical approach, Gurobi will perform a conservative presolve step at the beginning of the multi-objective optimization, and a more aggressive presolve step at the beginning of each step (assuming presolve hasn't been turned off). You can optionally perform a more aggressive presolve step at the beginning of the multi-objective optimization by setting parameter MultiObjPre to value 2. This can help performance, but it makes a few simplifying assumptions that could lead to small degradations in the values achieved for lower-priority objectives.
The log file when using a hierarchical approach will show optimization progress for each step of the process. You'll see log lines that look like this:
Multi-objectives: optimize objective 1 (Obj1Name) ... ... Multi-objectives: optimize objective 2 (weighted) ... ...For further details, please see section Multi-Objective Logging.
