AI Lecture 3

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Lecture 3 Problem-Solving(Search) Agents

Dr. Muhammad Adnan Hashmi

11 June 2013


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Problem-solving agents

Problem types

Problem formulation

Example problems Basic search algorithms


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Suppose an agent can execute several actionsimmediately in a given state

It doesnt know the utility of these actions

Then, for each action, it can execute a sequenceof actions until it reaches the goal

The immediate action which has the bestsequence (according to the performancemeasure) is then the solution

Finding this sequence of actions is called search,

and the agent which does this is called theproblem-solver.

NB: Its possible that some sequence might fail,e.g., getting stuck in an infinite loop, or unableto find the goal at all.

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You can begin to visualize the concept of a

graph Searching along different paths of the graph

until you reach the solution

The nodes can be considered congruous to the

states The whole graph can be the state space

The links can be congruous to the actions

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On holiday in Romania; currently in Arad.

Flight leaves tomorrow from Bucharest

Formulate goal: Be in Bucharest

Formulate problem:

States: various cities

Actions: drive between cities

Find solution:

Sequence of cities, e.g., Arad, Sibiu, Fagaras,Bucharest.


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Static: The configuration of the graph (the city map)is unlikely to change during search

Observable: The agent knows the state (node)

completely, e.g., which city I am in currently

Discrete: Discrete number of cities and routesbetween them

Deterministic: Transiting from one city (node) onone route, can lead to only one possible city

Single-Agent: We assume only one agent searchesat one time, but multiple agents can also be used.


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A problem is defined by five items:

1. An Initial state, e.g., In Arad

2. Possible actions available, ACTIONS(s) returns the set ofactions that can be executed in s.

3. A successor functionS(x) = the set of all possible{ActionState} pairs from some state, e.g., Succ(Arad) ={, }

4. Goal test, can be explicit, e.g.,x= "In Bucharest implicit, e.g., Checkmate(x)

5. Path cost (additive) e.g., sum of distances, number of actions executed, etc. c(x,a,y) is the step cost, assumed to be 0

A solution is a sequence of actions leading from the initialstate to a goal state.


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States? Actions? Goal test? Path cost?


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States?dirt and robot location

Actions?Left, Right, Pick

Goal test?no dirt at all locations

Path cost?1 per action


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States?

Actions?

Goal test?

Path cost?


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States? locations of tiles Actions?move blank left, right, up, down Goal test?= goal state (given) Path cost? 1 per move

[Note: optimal solution ofn-Puzzle family is NP-hard]


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States?: real-valued coordinates of robotjoint angles, parts of the object to beassembled, current assembly

Actions?: continuous motions of robotjoints

Goal test?: complete assembly

Path cost?: time to execute


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Basic idea:

Offline (not dynamic), simulated exploration ofstate space by generating successors of already-explored states (a.k.a. expanding the states)

The expansion strategy defines the differentsearch algorithms.


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Fringe: The collection of nodes that have beengenerated but not yet expanded

Each element of the fringe is a leaf node, with(currently) no successors in the tree

The search strategy defines which element to

choose from the fringe

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The fringe is implemented as a queue

MAKE_QUEUE(element,): makes a queue withthe given elements

EMPTY?(queue): checks whether queue is empty FIRST(queue): returns 1st element of queue

REMOVE_FIRST(queue): returns FIRST(queue)and removes it from queue

INSERT(element, queue): add elementto queue INSERT_ALL(elements,queue): adds the set

elements to queue and return the resulting queue

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A state is a representation of a physical

configuration A node is a data structure constituting part of a

search tree includes state, parent node, action,path costg(x), depth

The Expand function creates new nodes, filling in

the various fields and using the SuccessorFn ofthe problem to create the corresponding states.


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A search strategy is defined by picking the orderof node expansion

Strategies are evaluated along the followingdimensions: Completeness: Does it always find a solution if one

exists? Time complexity: Number of nodes generated

Space complexity: Maximum number of nodes inmemory

Optimality: Does it always find a least-cost solution?

Time and space complexity are measured interms of b: maximum no. of successors of any node

d: depth of the shallowest goal node

m: maximum length of any path in the state space.


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