FilMINT: An Outer-Approximation-Based Solver for Nonlinear Mixed Integer Programs

We describe a new solver for mixed integer nonlinear programs (MINLPs) that implements a linearization-based algorithm. The solver is based on the algorithm by Quesada and Grossmann, and avoids the complete solution of master mixed integer linear programs (MILPs) by adding new linearizations at open nodes of the branch-and-bound tree whenever an integer solution is found. The new solver, FilMINT, combines the MINTO branch-and-cut framework for MILP with filterSQP used to solve the nonlinear programs that arise as subproblems in the algorithm. The MINTO framework allows us to easily extend cutting planes, primal heuristics, and other well-known MILP enhancements to MINLPs. We present detailed computational experiments that show the benefit of such advanced MILP techniques. We offer new suggestions for generating and managing linearizations that are shown to be efficient on a wide range of MINLPs. Comparisons to existing MINLP solvers are presented, that highlight the effectiveness of FilMINT.