General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

Example 613 If the rules of the 8-puzzle are relaxed so that a tile can move anywhere,
then we get heuristic h1.
Example 614 If the rules are relaxed so that a tile can move to any adjacent square, then
we get heuristic h2.
Key point: The optimal solution cost of a relaxed problem is not greater than the optimal
solution cost of the real problem
c○: Michael Kohlhase 491
Relaxation means to remove some of the constraints or requirements of the original problem, so
that a solution becomes easy to find. Then the cost of this easy solution can be used as an
optimistic approximation of the problem.
4.1.5 Local Search
Local Search Problems
Idea: Sometimes the path to the solution is irrelevant
Example 615 (8 Queens Problem)
Place 8 queens on a chess board, so that
no two queens threaten each other.
This problem has various solutions, e.g.
the one on the right
Definition 616 A local search algorithm
is a search algorithm that operates
on a single state, the current
state (rather than multiple paths).
(advantage: constant space)
Typically local search algorithms only move to successors of the current state, and do not
retain search paths.
Applications include: integrated circuit design, factory-floor layout, job-shop scheduling, portfolio
management, fleet deployment,. . .
c○: Michael Kohlhase 492
Local Search: Iterative improvement algorithms
Definition 617 (Traveling Salesman Problem) Find shortest trip through set of cities
such that each city is visited exactly once.
Idea: Start with any complete tour, perform pairwise exchanges
259