Introduction to AI Unit 4

7/27/2019 Introduction to AI Unit 4

1/8

3/5/2

Introduction to Artificial

Intelligence

Unit # 4

Artif icial Intelligence Lab, IBA 1Spring2011

Acknowledgement

The slides of this lecture have been taken from

the lecture slides of CS307 Introduction to

Artificial Intelligence by Dr. Sajjad Haider.

Artificial Intelligence Lab, IBA 2Spring2011

A* search

Idea: avoid expanding paths that are already

expensive

Evaluation function f(n) = g(n) + h(n)

g(n) = cost so fa r to reach n

h(n) = es tima ted cost from n to goal

f(n) = e sti mated total cost of path through n to

goal


A* Search

(Using Heuristic # 1)

We add a depth factor

to f: f(n) = g(n) + h(n).

g(n) is an estimate of the

depth of n in the graph.

h(n) is a heuristic

evaluation of node n.



2/8

3/5/2

A* Search(Using Heuristic # 2)

Expand the tree

Goal State

2 8 3

1 6 4

7 5


N-Queen

The N-queens problem is a

search problem where the

desired result is an N by N board

with N queens such that no

queen threatens another

The problem can be simplified

by assigning a queen to each

row on the board.

Enumerating the search space is

then defined as looking at the

possible moves of queens

horizontally.


Romania with step costs in km

(Russell & Norvig)


Best-first search example



3/8

3/5/2







A* search example



4/8

3/5/2

A* search example


A* search example


A* search example


A* search example



5/8

3/5/2

A* search example


The Modified Traveling Salesman Problem

Each node represents a town,and the vertices betweennodes represent roads that jointowns together.

A is the starting node, and F isthe goal node.

Each vertex is labeled with adistance, which shows howlong that road is.

The aim of this problem is tofind the shortest possible pathfrom city A to city F.


Search Tree for the Modified TSP


Search Demo

http://www.cs.rochester.edu/u/kautz

/Mazes/search_algorithm_demo.htm



6/8

3/5/2

Result


Karachi Path Finding by Google


Karachi Path Finding by Google

(Contd)


Karachi Path Finder Developed at IBA



7/8

3/5/2

Informed vs. Uniformed Search

A se arch method or heuristic i s informed if it usesaddi tional information about nodes that have not yetbee n e xplored to decide which no des to examinenext.

If a me thod is not informed, it is uninformed orblind.

Bes t-first search is an e xample of i nformed search,wherea s breadth-first and depth-first s earch areuni nformed or blin d.

The more in formed a s earch method is, the moreeffi ciently it will se arch.


Summary: Search

Depth-first s earch and breadth-first search are extremelycommonly used and well understood exhaustive searchmethods.

A search method is complete if it will always find a solutionif one exists. A se arch method is optimal (or admiss ible) if italways finds the bes t solution that exists.

Heuris tics can be use d to make search methods moreinformed about the proble m they are solving. A heuristic is amethod that provides a bett er guess about the correctchoice to make at any junction that would be achieved byrandom guess ing.

One heuris tic i s more informed than another heuristic if asearch method that use s it needs to examine fewer nodes toreach a goal.


More Search

Greedy Algorithm(Source: Wikipedia)

Greedy algorithms can be characterized as being 'short sighted',and as 'non-recoverable'. They are ideal only for problems whichhave 'optimal substructure'. Despite this, greedy algorithms arebest suited for simple problems (e.g. giving change).

Greedy choice property

We can make whatever choice seems best at the moment andthen solve the subproblems that arise later. The choice made bya greedy algorithm may depend on choices made so far but noton future choices or all the solutions to the subproblem. I t

iteratively makes one greedy choice after another, reducing eachgiven problem into a smaller one. In other words, a greedyalgorithm never reconsiders its choices.

Artif icial Intelligence Lab, IBA Spring 2011 27

Hill Climbing(Source: Wikipedia)

In computer science, hill climbing is amathematical optimizationtechnique which belongs to the family oflocal search. It is an ite rativealgorithm that starts with an arbitrary solution to a problem, thenattempts to find a better solution byincrementally changing a singleelemen t of the solution. If the change produces a better solution, anincremental change is made to the new solution, repeating until nofurther improve ments can be found.

For example, hill climbing can be applied to the traveling salesmanproblem. It is easy to find an initial so lution that visits all the cities but willbe very poor compared to the optimal solution. The algorithm starts withsuch a solution and makes small improvements to it, such as switching theorder in which two citie s are visited. Eventually, a much s horter route is

likely to be obtained. Hill climbing is good for finding a local optimum (a good solution that lies

relatively near the initial solution) but it is not guaranteed to find the bestpossible solution (the global o ptimum) out of all possible solutions (thesearch space).

Artificial Intelligence Lab, IBA Spring2011 28
http://en.wikipedia.org/wiki/Computer_sciencehttp://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/wiki/Local_search_(optimization)http://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/wiki/Local_search_(optimization)http://en.wikipedia.org/wiki/Incremental_heuristic_searchhttp://en.wikipedia.org/wiki/Incremental_heuristic_searchhttp://en.wikipedia.org/wiki/Incremental_heuristic_searchhttp://en.wikipedia.org/wiki/Traveling_salesman_problemhttp://en.wikipedia.org/wiki/Traveling_salesman_problemhttp://en.wikipedia.org/wiki/Traveling_salesman_problemhttp://en.wikipedia.org/wiki/Local_optimumhttp://en.wikipedia.org/wiki/Global_optimumhttp://en.wikipedia.org/wiki/Search_spacehttp://en.wikipedia.org/wiki/Global_optimumhttp://en.wikipedia.org/wiki/Search_spacehttp://en.wikipedia.org/wiki/Search_spacehttp://en.wikipedia.org/wiki/Global_optimumhttp://en.wikipedia.org/wiki/Local_optimumhttp://en.wikipedia.org/wiki/Traveling_salesman_problemhttp://en.wikipedia.org/wiki/Traveling_salesman_problemhttp://en.wikipedia.org/wiki/Incremental_heuristic_searchhttp://en.wikipedia.org/wiki/Local_search_(optimization)http://en.wikipedia.org/wiki/Optimization_(mathematics)http://en.wikipedia.org/wiki/Computer_science


8/8

3/5/2

Local vs Global Optimum?

Artif icial Intelligence Lab, IBA Spring 2011 29

What is the optimum point?

Local vs Global Optimum?

Artificial Intelligence Lab, IBA Spring2011 30

What do you think about the optimum point now?

Documents

Introduction to AI Unit 4