Synthesizing MILP Constraints for Efficient and Robust Optimization

While mixed integer linear programming (MILP) solvers are routinely used to solve a wide range of important science and engineering problems, it remains challenging task for end users write correct efficient MILP constraints, especially problems specified using the inherently non-linear Boolean logic operations. To overcome this challenge, we propose syntax guided synthesis (SyGuS) method capable generating high-quality constraints from specifications expressed arbitrary combinations At center our is an extensible domain specification language (DSL) whose expressiveness may be improved by adding new variables as decision variables, together with iterative procedure synthesizing operations these variables. make efficient, also over-approximation technique soundly proving correctness synthesized under-approximation safely pruning away incorrect constraints. We have implemented evaluated on benchmark statistics, machine learning, data applications. The experimental results show that in handling benchmarks, quality close to, or higher than, manually-written terms both compactness solving time.