Mathematical Programming focuses on optimizing objective functions under a set of constraints, addressing a wide range of practical and theoretical challenges.
Our Research Focus
Pseudo-Boolean Optimization (PBO)
Investigate optimization over Boolean variables with linear constraints and objective functions:
- Cutting plane techniques
- Conflict analysis methods
- Preprocessing strategies
- Core-guided optimization
Mixed Integer Programming (MIP)
Study optimization involving both continuous and integer variables under linear constraints:
- Branch-and-bound techniques
- Cutting plane generation
- Preprocessing methods
- Heuristic approaches
- Parallel solving strategies
Integer Linear Programming (ILP)
Focus on optimization where all variables are integers, constrained by linear relationships:
- Branch-and-cut algorithms
- Symmetry breaking
- Decomposition methods
- Valid inequality generation
- Local search hybridization
Our group has developed several powerful optimization solvers:
Integer Programming
- Local-MIP: Efficient local search solver for Mixed Integer Programming
- ParaILP: Parallel local search solver for Integer Linear Programming
MaxSAT & PBO
- NuWLS: MaxSAT local search solver (2022 MaxSAT Competition champion)
- USW-LS: MaxSAT local search solver (2023 MaxSAT Competition champion)
- NuPBO: Pseudo-Boolean Optimization local search solver