Artificial Intelligence Methods

Artificial Intelligence Methods Searching - 2 Rao Vemuri

Problem Definition - 1 • Initial State • The initial state of the problem, defined in some suitable manner • Operator • A set of actions that moves the problem from one state to another

Problem Definition - 1 • Neighbourhood (Successor Function) • The set of all possible states reachable from a given state • State Space • The set of all states reachable from the initial state

Problem Definition - 2 • Goal Test • A test applied to a state which returns if we have reached a state that solves the problem • Path Cost • How much it costs to take a particular path

5 4 1 2 3 6 1 8 8 4 7 3 2 7 6 5 1 1 2 4 3 7 4 2 5 5 6 8 7 3 8 6 Problem Definition - Example Initial State Goal State

Problem Definition - Example • States • A description of each of the eight tiles in each location that it can occupy. It is also useful to include the blank • Operators • The blank moves left, right, up or down

Problem Definition - Example • Goal Test • The current state matches a certain state (e.g. one of the ones shown on previous slide) • Path Cost • Each move of the blank costs 1

Problem Definition - Datatype • Datatype PROBLEM • Components • INITIAL-STATE, • OPERATORS, • GOAL-TEST, • PATH-COST-FUNCTION

How Good is a Solution? • Does our search method actually find a solution? • Is it a good solution? • Path Cost • Search Cost (Time and Memory) • Does it find the optimal solution? • But what is optimal?

Evaluating a Search • Completeness • Is the strategy guaranteed to find a solution? • Time Complexity • How long does it take to find a solution?

Evaluating a Search • Space Complexity • How much memory does it take to perform the search? • Optimality • Does the strategy find the optimal solution where there are several solutions?

x x x x x x x x x ……….. o o x x x x o Search Trees

Search Trees • ISSUES • Search trees grow very quickly • The size of the search tree is governed by the branching factor • Even this simple game has a complete search tree of 984,410 potential nodes • The search tree for chess has a branching factor of about 35

Implementing a Search - What we need to store • State • This represents the state in the state space to which this node corresponds • Parent-Node • This points to the node that generated this node. In a data structure representing a tree it is usual to call this the parent node

Implementing a Search - What we need to store • Operator • The operator that was applied to generate this node • Depth • The number of nodes from the root (i.e. the depth) • Path-Cost • The path cost from the initial state to this node

Implementing a Search - Datatype • Datatype node • Components: • STATE, • PARENT-NODE, • OPERATOR, • DEPTH, • PATH-COST

Using a Tree – The Obvious Solution? • Advantages • It’s intuitive • Parent’s are automatically catered for

Using a Tree – The Obvious Solution? • But • It can be wasteful on space • It can be difficult the implement, particularly if there are varying number of children (as in tic-tac-toe) • It is not always obvious which node to expand next. We may have to search the tree looking for the best leaf node (sometimes called the fringe or frontier nodes). This can obviously be computationally expensive

Using a Tree – Maybe not so obvious • Therefore • It would be nice to have a “simpler” data structure to represent our tree • And it would be nice if the next node to be expanded was an O(1) operation

Basic Queue Operations • Make-Queue(Elements) • Create a queue with the given elements • Empty?(Queue) • Returns true if the queue is empty • Remove-Front(Queue) • Removes the element at the head of the queue and returns it

Queue Operations - Adding Elements • Queuing-FN(Elements,Queue) • Inserts a set of elements into the queue. Different queuing functions produce different search algorithms.

General Search • Function GENERAL-SEARCH(problem, QUEUING-FN) returns a solution or failure • nodes = MAKE-QUEUE(MAKE-NODE(INITIAL-STATE[problem])) • Loop do • If nodes is empty then return failure • node = REMOVE-FRONT(nodes) • If GOAL-TEST[problem] applied to STATE(node) succeeds then return node • nodes = QUEUING-FN(nodes,EXPAND(node,OPERATORS[problem])) • End • End Function

Artificial Intelligence Methods End of Searching-2 Rao Vemuri

Artificial Intelligence Methods