Constarint Programming, Lecture Notes - Computer Science 3, Study notes of Computer Numerical Control

Download Constarint Programming, Lecture Notes - Computer Science 3 and more Study notes Computer Numerical Control in PDF only on Docsity! Constraint Programming Overview of Solution Methods Alan M. Frisch Artificial Intelligence Group Department of Computer Science University of York Types of Solution Methods • Constraint Synthesis • Problem Reduction or Simplfication • Total assignment search (consider 4 queens as example) • Also called local search or repair methods. • Examples: hill-climbing, simulated annealing, genetic algorithms, tabu search, stochastic local search • Partial Assignment Search • Also called constraint satisfaction search, partial-intantiate-and- prune, constraint programming. Other search distinctions: • stochastic vs. non-stochastic search • non-systematic vs. systematic search 1 Partial Assignments Both A1 = {X1 7→ r, X2 7→ b, X3 7→ g, X4 7→ r}, and A2 = {X1 7→ r, X2 7→ g, X3 7→ b, X4 7→ r} are total assignments. A3 = {X1 7→ r, X4 7→ r} is a (partial) assignment but not a total assign- ment. So is ∅. Total assignments are assignments. Both A1 and A2 extend A3. 4 Partial Assignement Search Space © X1 r b g © ⊗ ⊗ a a X2 r b g ⊗ © © b X3 r b g r b g ⊗ ⊗ © ⊗ © ⊗ e i e j X4 r b g r b g © ⊗ ⊗ © ⊗ ⊗ o m l p 5 Issues in Partial-Assignment Search How to recognize failure (prune) How to order the variables How to move through the search space How to order the values How to model/transform the problem 6