University of Leuven, Belgium

Jo Devriendt, Patrick De Causmaecker, Marc Denecker

jo.devriendt@cs.kuleuven.be

- Find optimal feasible solution
- Deciding existence feasible solution: in NP
- Computing objective value: poly-time

Examples: TSP, knapsack, chromatic number, etc.

Different technologies

- Choice based search tree
- Explanations (nogoods)

construct infeasibility proof - CP, SAT, SMT

- Relax problemon by dropping discreteness
- Poly-time algorithm finds optimal solution

- Add valid constraints that cut away approximate solutions
- MIP, Convex Programming

- Initial feasible solution
- Move between neighboring feasible solutions
- Metaheuristics, Evolutionary computing

Neigborhood examples

- Permuting cities in Traveling Salesman Problem
- Swapping shifts in Nurse Scheduling Problem
- Flipping boolean values in SAT
- Changing location of facility in Facility Location Problem
- Permuting rounds in Sport Scheduling problems
- Adding or removing node from vertex cover
- ...