The MOSEK command line tool Version 7.0 (Revision 141)

52 CHAPTER 6. THE OPTIMIZERS FOR MIXED-INTEGER PROBLEMS
6.3.3 The optimization phase
This phase solves the problem using the branch and cut algorithm.
6.3.4 Caveats
The mixed-integer conic optimizer ignores the parameter
MSK IPAR MIO CONT SOL:
The user should fix all the integer variables at their optimal value and reoptimize instead of
relying in this option.
6.4 The mixed-integer optimizer
The mixed-integer optimizer is employed by setting the parameter MSK IPAR OPTIMIZER to MSK OPTIMIZER MIXED INT.
In the following it is briefly described how the optimizer works.
The process of solving an integer optimization problem can be split in three phases:
Presolve:
In this phase the optimizer tries to reduce the size of the problem using preprocessing techniques.
Moreover, it strengthens the continuous relaxation, if possible.
Heuristic:
Using heuristics the optimizer tries to guess a good feasible solution.
Optimization:
The optimal solution is located using a variant of the branch-and-cut method.
6.4.1 Presolve
In the preprocessing stage redundant variables and constraints are removed. The presolve stage can
be turned off using the MSK IPAR MIO PRESOLVE USE parameter.
6.4.2 Heuristic
Initially, the integer optimizer tries to guess a good feasible solution using different heuristics:
• First a very simple rounding heuristic is employed.
• Next, if deemed worthwhile, the feasibility pump heuristic is used.
• Finally, if the two previous stages did not produce a good initial solution, more sophisticated
heuristics are used.