of Classification Search Problems
http://www.cis.temple.edu/~ingargio/cis587/readings/constraints.html
State Space Search
Constraint Satisfaction Problems
Optimization Problems
Search
Uninformed Search
Heuristic Search
Ch. Eick: Introduction to Search
Example: State Space Search
Figure
Goal: find an operator sequence that leads from the start state to the goa State Space: a 3x3 matrix containing the numbers 1,...,8 and *(empty) Operators: North, South, East, West Ch. Eick: Introduction to Search
Constraint Satisfaction Problems
Problem: Assign value to a set of variable V, such that a set of constraints is satisfied. Example: 8Queen Problem: Place queens on a 8x8 chessboard so that they cannot capture each other Find values for: (x1,y1),...,(x8,y8) such that: ( i,j (xi,yi) (xj,yj) Attack((xi,yi),(xj,yj)) ) i j (xi,yi) (xj,yj)
Ch. Eick: Introduction to Search
Optimization Problems
Maximize f(x,y,z)=|xy0.2|*|x*z0.8|*|0.3z*z*y| with x,y,z in [0,1]
Characteristics: No explicit operators the path that leads to the solution is not important Frequently involves real numbers number of solutions is not finite Problems might be complicated by additionally requiring that the solution satisfies a set of contraints. Life is easier if the function is continuous and differentiable e.g. classical numerical optimization techniques can directly be applied AI and evolutionary computing are more attractive for "nasty" optimization problems.
Ch. Eick: Introduction to Search
Heuristic Search
augment
General Search Algorithms Domain-specific Knowledge
Ch. Eick: Introduction to Search
Classification of Search Algorithms
To be discussed in depth Next Tueseday!!
State Space Search
Expansion Search Hill Climbing
Backtracking
Best First Search
Uniform Cost
Breadth First
Depth First
A* f(n)=g(n)+h(n)
Greedy Search f(n)=h(n) Expand the best state/node with respect To an evaluation function f:NR
Remark: Many other search algorithms exist that do not appear above
Ch. Eick: Introduction to Search
Characterization of State Space Search Algorithms
A search strategy consists of the following: A state space S, set of operators O: SS, an initial state, and a (set of) goal state(s). A control strategy that determines how the search space will be searched; it consists of an operator selection and state selection function: Operator selection function: selects which operator(s) is applied to a given state State selection function: selects the state to which an operator (selected by the operator selection function) is applied next. Remarks: Operator selection functions only return operators that have not been applied yet, and state selection functions return only states that have not been completely expanded yet (some applicable operators have not been applied to this state yet); moreover, we assume that ties are broken randomly.
Ch. Eick: Introduction to Search
Example: Strategies Search for the 8 Puzzle Strategy 1 (Breadth First):
Operator Selection Function: select all operators State Selection Function: Select a state s giving preference to states that are closer to the initial state i(closeness is evaluated by the number of operator applications it took to reach s from i) Strategy 2 (Backtracking with depth bound set to 3): Operator Selection Function : Select (applicable) operator by priorities: N>S>E>W State Selection Function : If the most recently created state is less than 3 operator applications away from the initial state, use this state; otherwise, use the predecessor of the most recent state. Strategy 3 (Greedy Search) Operator Selection Function: select all operators State Selection Function: Select the state s that is closest to the goal state g using a distance function d(s,g)="number of positions in which in which s and g disagree"
Ch. Eick: Introduction to Search
Un-graded Homework1 2004
Assume you have to search a labyrinth of interconnected rooms trying to find a particular room that contain a red flower. There will be many intersections of walkways that connect rooms all of which look completely the same; you will not know if you entered a particular crossing before; however, you will be given a piece of chalk that allow you to mark the to put signs of your own choosing on a wall. Devise a search strategy that will find a room with a red flower assuming that such a room exists. To be discussed on Sept. 30, 2004 in class!
Goal State
Ch. Eick: Introduction to Search
Use of search strategies that are not suitable for real-time search problem (e.g. breadth first search as explained in the textbook or best first search) --- you cannot jump between stat...