Synthesizing MILP Constraints for Efficient and Robust Optimization

Jingbo Wang, Aarti Gupta, Chao Wang

Research output: Contribution to journalArticlepeer-review


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

Original languageEnglish (US)
Article number184
JournalProceedings of the ACM on Programming Languages
StatePublished - Jun 6 2023

All Science Journal Classification (ASJC) codes

  • Software
  • Safety, Risk, Reliability and Quality


  • Data Science
  • Machine Learning
  • Statistics
  • Syntax Guided Synthesis


Dive into the research topics of 'Synthesizing MILP Constraints for Efficient and Robust Optimization'. Together they form a unique fingerprint.

Cite this