Lecture 3 - Artificial Intelligence - Solving Problems by Searching

Simplest kind of task environment for which the solution to a problem is always ____________

a fixed sequence of actions

Uninformed search definition

algorithms that are given no information about the problem except the problem definition

Search algorithms treat states and actions as

atomic

Problem solving agents

atomic goal based agent

Graph search

avoids redundant paths. Augment tree search with a data structure called the explored set

Tree Search

considers all possible paths

To characterize quality of heuristic

effective branching factor b*

h(n)

estimated cost of the cheapest path from state node n to a goal state

Greedy Best First Search heuristics

f(n) = h (n)

Planning agents

factored or structured goal based agents

For each node n, the structure will have the four components

n state, n action, n parent, n path cost

Problem formulation

process of deciding what actions and states to consider, given a goal.

A ______ takes a problem as input and returns a solution in the form of an action sequence.

search algorithm

Primary difference among search algorithm

search strategy - how they choose which node to expand next

A path through a state space from the initial state to the goal state is a

solution

Environment of the problem is represented by

state space

h2

sum of distances of the tiles from their goal positions because tiles cannot move diagonals the distance is the sum of horizontal and vertical distances

heuristic function

the degree to which a theory guides or influences future research efforts

A* search

Evaluates node by combining cost to reach node n and cost to reach goal from n f(n) = g(n) + h(n) F(n) is the estimated cost of the cheapest solution through n

Depth First Search

Expands deepest node in the current frontier of the search tree Explored nodes with no descendants in the frontier are removed from memory.

Uniform Cost Search - Definition

Expands node n with lowest path cost g(n)

Greedy Best First Search

Expands the node that is closest to the goal that is likely to lead to a solution quickly

Data structure for Breadth first search

FIFO queue

Comparing uninformed search strategies

Slide 68

Is h2 always better than h1

Yes

The process of removing details from a representation

abstraction

For any node n where h2(n) = h1(n)

h2 dominates h1 domination translates directly to efficiency

h1

number of misplaced tiles

Difference between BFS and UCS

- Goal test is applied to node when it is selected for expansion rather than when it is generated - A test is added in case a better path is found to a node currently on the frontier.

Before an agent starts searching for solutions

1. A goal must be identified 2. A well-defined problem must be formulated

Parts of problem

1. Initial State 2. A set of actions 3. Transition model describing the results of actions 4. Goal test function 5. Path cost function

Depth Limited Search

A depth first search with a predetermined depth limit. Incomplete if limit is less than depth. Not optimal if limit is greater than depth. Depth first search is depth limited search is with l = infinity

Iterative Deepening Search

A depth limited search that gradually increases the limit. Generates states multiple times. Finds the best depth limit

Search - Definition

An agent can select actions in the environment that are 1. Observable 2. Completely Known 3. Deterministic 4. Static An agent can construct sequence of actions that achieves its goal - this process is called search. The process of looking for a sequence of actions that reaches the goal

Completeness of Breadth firsts search

As soon as a goal node is generated we know it is the shallowest goal node because all other shallower nodes must have been generated and failed the goal test

Informed Search - Types

Best first search Greedy best first search A* search Space bounded A* - Iterative deepening A* Recursive Best First Search Memory Bounded A* Simplified Memory Bounded A*

Environment Scope - Parameters for search

Branching factor b - how many maximum adjacent nodes or maximum number of successors of any node Depth d - maximum depth of goal Cost g(n) to reach the node n - Keep a history of g(n) on the frontier

Uninformed search strategies

Breadth first search, Uniform cost search Depth first search Depth limited search Iterative deepening search Bidirectional search

A* Completeness and Optimality

Complete - Yes Optimal - Yes but space expensive

RBFS Completeness and Optimality

Complete - Yes Optimal - Yes provided heuristics is admissible

Greedy Best First Search Completeness and Optimality

Completeness - Yes Optimal - No

Search algorithms are judged based on

Completeness, optimality, time complexity, space complexity

Goal formulation

First step in problem solving Based on the current situation and agent's performance measure

h2 is also called

Manhattan distance

Informed Search

May have access to a heuristic function h(n) that estimates the cost of a solution from n

Breadth First Search Analysis

Memory requirement - high Time requirement - high

If the total number of nodes generated by A* for a particular problem is N, The solution depth is d, then b* is the branching factor that a uniform tree of depth d would have to have in order to contain N + 1 nodes. Thus,

N + 1 = 1 + b* + (b*)^2 + ... + (b*)^d

Optimality of breadth first search

Not necessarily the optimal one. Path is a non decreasing function of the depth of the node

Uniform Cost Search - Data Structure

Priority Queue ordered by g

Iterative Deepening Search A*

Reduces memory requirement for A* cutoff used is f-cost(g+h) rather than the depth

Infrastructure for search

Search algorithms require a data structure to keep track of the search tree being constructed.

Breadth First Search

Shallowest unexpanded node chosen for expansion

Informed search or heuristic search

Strategies that know whether one non goal state is better than the other

Tree Search - Definition

The process of choosing and expanding the node in the frontier continues until the goal node is found or there are no more states to be expanded

Bidirectional Search

Two searches: one forward form the root and one backward form the goal. Goal test replaced with frontier intersect test. Requires a method of computing predecessors.