Transforming Constraint Programs to Input for Local Search

University of Leuven, Belgium

Jo Devriendt, Patrick De Causmaecker, Marc Denecker
jo.devriendt@cs.kuleuven.be

Context: NP optimization problems

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

Examples: TSP, knapsack, chromatic number, etc.

Search & Explanation

• Choice based search tree
• Explanations (nogoods)
  construct infeasibility proof
• CP, SAT, SMT

Approach 1:

Relaxation & Cutting

• Relax problemon by dropping discreteness
  • Poly-time algorithm finds optimal solution
• Add valid constraints that cut away approximate solutions
• MIP, Convex Programming

Approach 2:

Local Search

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

Approach 3:

Local Search:
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
• ...

All information available in problem specification.

This talk:

Automated derivation of local search input (using symmetry)