Computer Science CPSC 322 Lecture 4 Search: Intro (textbook Ch: 3.0-3.4) 1

Computer Science CPSC 322

Lecture 4

Search: Intro

(textbook Ch: 3.0-3.4)

1

Announcements

(1) Reminder on Slide Posting

• I post a version of the lecture slides by 2:30pm

• after class (by the end of the day usually) I’ll post the version

with material filled-in in class.

So you’ll always have to double check the posted slides after class

if you want to have the most up-to-date copy

(2) Office hours are posted on the class syllabus

2

Course OverviewEnvironment

Problem Type

Query

Planning

Deterministic Stochastic

Constraint Satisfaction Search

Arc Consistency

Search

Search

Logics

STRIPS

Vars + Constraints

Value Iteration

Variable

Elimination

Belief Nets

Decision Nets

Markov Processes

Static

Sequential

Representation

ReasoningTechnique

Variable

Elimination

First Part of the Course 3

Course OverviewEnvironment

Problem Type

Query

Planning

Deterministic Stochastic

Constraint Satisfaction Search

Arc Consistency

Search

Search

Logics

STRIPS

Vars + Constraints

Value Iteration

Variable

Elimination

Belief Nets

Decision Nets

Markov Processes

Static

Sequential

Representation

ReasoningTechnique

Variable

Elimination

We’ll focus on Search 4

(Adversarial) Search: Checkers

Source: IBM Research

• Early learning work in 1950s by

Arthur Samuel at IBM

• Chinook program by Jonathan Schaeffer

(UofA)

• Search explores the space of

possible moves and their

consequence

1994: world champion

2007: declared unbeatable

5

Slide 6

(Adversarial) Search: Chess In 1997, Gary Kasparov, the chess grandmaster and

reigning world champion played against Deep Blue, a program written by researchers at IBM

Source: IBM Research

Slide 7

(Adversarial) Search: Chess• Deep Blue’s won 3 games, lost 2, tied 1

• 30 CPUs + 480 chess processors• Searched 126.000.000 nodes per sec• Generated 30 billion positions per move

reaching depth 14 routinely

Today’s Lecture

• Simple Search Agent

• Examples

• General Search Procedure (time permitting)

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• Often we are not given an algorithm to solve a problem, but only a specification of what a solution is

we have to search for a solution.

– Enumerate a set of potential partial solutions

– Check to see if they are solutions or could lead to one

Search

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Simple Search Agent

Deterministic, goal-driven agent • Agent is in a start state• Agent is given a goal (subset of possible states)• Environment changes only when the agent acts• Agent perfectly knows:

• actions that can be applied in any given state• the state it is going to end up in when an action is applied in

a given state• The sequence of actions (and appropriate ordering) taking the

agent from the start state to a goal state is the solution

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Definition of a search problem• Initial state(s)

• Set of actions (operators) available to the agent• An action function that, given a state and an action,

returns a new state • Goal state(s)

• Search space: set of states that will be searched for a path from initial state to goal, given the available actions• states are nodes and actions are links between them.• Not necessarily given explicitly (state space might be infinite)

• Path Cost (we ignore this for now)

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Today’s Lecture


• Examples


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Slide 13

Three examples1. The delivery robot planning the route it will take in a

bldg. to get from one room to another (Ch 1.6)

2. Vacuum cleaner world

3. Solving an 8-puzzle

Environment for Delivery Robot (ch.1.6)

Simplified• Consider only bold

locations here

• Limits in direction of movement (e.g., can only move in the direction a door opens, can’t go back to previous location, etc.)

• Start: o103

• Goal: r123

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Search Space for the Delivery Robot

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Slide 16

Example: vacuum world

Possible start state Possible goal state

• States• Two rooms: r1, r2

• Each room can be either dirty or not

• Vacuuming agent can be in either in r1 or r2

Slide 17

Example: vacuum world

• States• Two rooms: r1, r2

• Each room can be either dirty or not

• Vacuuming agent can be in either in r1 or r2

Feature-based representation: - Features?- how many states?

Possible start state Possible goal state

Suppose we have the same problem with k rooms.

The number of states is….

D. 2 * kk

A. k3

C. k * 2k

B. k * 2k

…..

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Cleaning Robot

• States – one of the eight states in the picture

• Actions –left, right, suck• Possible Goal – no dirt

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Search Space

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• Actions – left, right, suck - Successor states in the graph describe the effect of each action

applied to a given state

• Possible Goal – no dirt

Search Space

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Search Space

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• Actions– left, right, suck - Successor states in the graph describe the effect of each action



Search Space

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Search Space

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Eight Puzzle

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Eight Puzzle

States:

Actions:

Goal:26

Eight Puzzle

States: each state specifies which number/blank occupies each of the 9 tiles HOW MANY STATES ?

Actions: blank moves left, right, up down

Goal: configuration with numbers in right sequence

9!

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Slide 28

Search space for 8puzzle

Slide 29

Search space for 8puzzle

Slide 30

How can we find a solution?

• How can we find a sequence of actions and their appropriate ordering that lead to the goal?

• Need smart ways to search the space graph

Today’s Lecture


• Examples


31

Slide 32

Search: Abstract Definition

How to search• Start at the start state• Evaluate the effect of taking different actions starting from

states that have been encountered in the search so far• Stop when a goal state is encountered

To make this more formal, we'll use the formal definition of a graph that you reviewed for today

• A directed graph consists of a set N of nodes (vertices) and a set A of ordered pairs of nodes, called edges (arcs).

• Node n2 is a neighbor of n1 if there is an arc from n1 to n2. That is, if n1, n2 A.

• A path is a sequence of nodes n0, n1,..,nk such that ni-1, ni A.

• A cycle is a non-empty path such that the start node is the same as the end node.

• A directed acyclic graph (DAG) is a graph with no cycles

• Given a set of start nodes and goal nodes, a solution is a path from a start node to a goal node

Graphs

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Graph specification for the Delivery Robot

N={mail, ts, o103, b3, o109,...}

A={ ⟨ts,mail , ⟩ ⟨o103,ts , o103,b3 , o103,o109 , ⟩ ⟨ ⟩ ⟨ ⟩ ...}

One of several solution paths:

⟨o103, o109, o119, o123, r123⟩

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• Generic search algorithm: given a graph, start nodes, and goal nodes,

incrementally explore paths from the start nodes.

Maintain a frontier of paths from the start node that have been explored.

As search proceeds, the frontier expands into the unexplored nodes until a goal node is encountered.

• The way in which the frontier is expanded defines the search strategy.

Graph Searching

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Problem Solving by Graph Searching

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Input: - a graph - a set of start nodes - Boolean procedure goal(n) testing if

n is a goal node

frontier:= [<s>: s is a start node]; While frontier is not empty: select and remove path <no,….,nk>

from frontier; If goal(nk)

return <no,….,nk>;

For every neighbor n of nk,

add <no,….,nk, n> to frontier;

end

Generic Search Algorithm

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• The forward branching factor of a node is the number of arcs going out of the node

• The backward branching factor of a node is the number of arcs going into the node

• If the forward branching factor of a node is b and the graph is a tree, how many nodes are n steps away from that node?

Branching Factor (you reviewed this for today)

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C. nb

A. nb

B. bn

D. n/b

• The forward branching factor of a node is the number of arcs going out of the node

• The backward branching factor of a node is the number of arcs going into the node

• If the forward branching factor of a node is b and the graph is a tree, how many nodes are n steps away from that node?

Branching Factor (you reviewed this for today)

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B. bn

Slide 40

Comparing Searching Algorithms: Will it find a solution? the best one?

Def. : A search algorithm is complete if

whenever there is at least one solution, the algorithm is guaranteed to find it within a finite amount of time.

Def.: A search algorithm is optimal if

when it finds a solution, it is the best one

Slide 41

Comparing Searching Algorithms: Complexity

Def.: The time complexity of a search algorithm is

the worst- case amount of time it will take to run, expressed in terms of

• maximum path length m • maximum branching factor b.

Def.: The space complexity of a search algorithm is

the worst-case amount of memory that the algorithm will use (i.e., the maximum number of nodes on the frontier),

also expressed in terms of m and b.

Branching factor b of a node is the number of arcs going out

of the node

Slide 42

• Search is a key computational mechanism in many AI agents • We will study the basic principles of search on the simple

deterministic search agent model• Generic search approach:

• define a search space graph• start from initial state state, • incrementally explore paths from current state until goal state is reached.

The way in which the frontier is expanded defines the search strategy.

To Summarize

Learning Goals for today’s class

• Identify real world examples that make use of deterministic, goal-driven search agents

• Assess the size of the search space of a given search problem.

• Implement the generic solution to a search problem.

• Define completeness, optimality, time complexity and space complexity for search algorithms

TODO for Wednesday

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• Uninformed search strategies (read textbook Sec. 3.5)

• First Practice Exercise 3.A• http://www.aispace.org/

exercises.shtml

Documents

Computer Science CPSC 322 Lecture 4 Search: Intro (textbook Ch: 3.0-3.4) 1