Jarrar.lecture notes.aai.2011s.ch3.uniformedsearch

Dr. Mustafa Jarrar [email_address] University of Birzeit Chapter 3 Uni-Informed Search Advanced Artificial Intelligence (SCOM7341) Lecture Notes, Advanced Artificial Intelligence (SCOM7341) University of Birzeit 2 nd Semester, 2011

Example: Romania You are in Arad and want to go to Bucharest  How to design an intelligent agent to find the way between 2 cities?

Example: The 8-puzzle  How can we design an intelligent agent to solve the 8-puzzel?

Search as Problem-Solving Strategy ,[object Object],[object Object],[object Object]

Search as Problem-Solving Strategy ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Motivation ,[object Object],[object Object],[object Object]

Problem Formulation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Problem Formulation (The Romania Example) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Problem Formulation (The 8- Puzzle Example) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Problem Formulation (Real-life Applications) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Car Navigation Routing in Computer networks Military operation planning Airline travel planning

Problem Formulation (Real-life Applications) ,[object Object], What is the state space for each of them? A set of places with links between them, which have been visited

Problem Formulation (Real-life Applications) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Problem Formulation (Real-life Applications) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Problem Formulation (Real-life Applications) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Problem Formulation (Real-life Applications) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Searching for Solutions ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Search Terminology ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Example: Graph Search ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],S3 A4 C2 D3 E1 B2 G0 1 1 1 3 1 3 3 4 5 1 2

Traversing a Graph as Tree S3 5 A4 D3 1 1 3 3 4 2 C2 D3 G0 G0 G0 E1 G0 1 1 3 3 4 2 C2 D3 G0 G0 E1 G0 1 3 B2 1 3 C2 D3 G0 G0 E1 G0 1 3 4 E1 G0 2 4 3 2 4 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],2 S3 A4 C2 D3 E1 B2 G0 1 1 1 3 1 3 3 4 5 1 2

Discussion Who can give examples of tree search strategies? Why a search strategy is better than another?

Example: Breadth First Search S3 5 A4 D3 1 1 3 3 4 2 C2 D3 G0 G0 G0 E1 G0 1 1 3 3 4 2 C2 D3 G0 G0 E1 G0 1 3 B2 1 3 C2 D3 G0 G0 E1 G0 1 3 4 E1 G0 2 4 3 2 4 S3 A4 C2 D3 E1 B2 G0 1 1 1 3 1 3 3 4 5 1 2

Example: Greedy Search S3 5 A4 D3 1 1 3 3 4 2 C2 D3 G0 G0 G0 E1 G0 1 1 3 3 4 2 C2 D3 G0 G0 E1 G0 1 3 B2 1 3 C2 D3 G0 G0 E1 G0 1 3 4 E1 G0 2 4 3 2 4 S3 A4 C2 D3 E1 B2 G0 1 1 1 3 1 3 3 4 5 1 2

Example: A* Search S3 5 A4 D3 1 1 3 3 4 2 C2 D3 G0 G0 G0 E1 G0 1 1 3 3 4 2 C2 D3 G0 G0 E1 G0 1 3 B2 1 3 C2 D3 G0 G0 E1 G0 1 3 4 E1 G0 2 4 3 2 4 S3 A4 C2 D3 E1 B2 G0 1 1 1 3 1 3 3 4 5 1 2

General Tree Search ,[object Object],[object Object],[object Object],[object Object],[object Object]

Search Strategies ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Evaluation of Search Strategies ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

[object Object],Breadth-First Search ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Breadth-First Snapshot 1 Initial Visited Fringe Current Visible Goal 1 2 3 Fringe: [] + [2,3]

Breadth-First Snapshot 2 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 Fringe: [3] + [4,5]

Breadth-First Snapshot 3 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 Fringe: [4,5] + [6,7]

Breadth-First Snapshot 4 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 Fringe: [5,6,7] + [8,9]

Breadth-First Snapshot 5 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 Fringe: [6,7,8,9] + [10,11]

Breadth-First Snapshot 6 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 Fringe: [7,8,9,10,11] + [12,13]

Breadth-First Snapshot 7 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Fringe: [8,9.10,11,12,13] + [14,15]

Breadth-First Snapshot 8 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Fringe: [9,10,11,12,13,14,15] + [16,17]

Breadth-First Snapshot 9 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 Fringe: [10,11,12,13,14,15,16,17] + [18,19]

Breadth-First Snapshot 10 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 Fringe: [11,12,13,14,15,16,17,18,19] + [20,21]

Breadth-First Snapshot 11 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 Fringe: [12, 13, 14, 15, 16, 17, 18, 19, 20, 21] + [22,23]

Breadth-First Snapshot 12 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 Fringe: [13,14,15,16,17,18,19,20,21] + [22,23] Note: The goal node is “visible” here, but we can not perform the goal test yet.

Breadth-First Snapshot 13 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 Fringe: [14,15,16,17,18,19,20,21,22,23,24,25] + [26,27]

Breadth-First Snapshot 14 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 Fringe: [15,16,17,18,19,20,21,22,23,24,25,26,27] + [28,29]

Breadth-First Snapshot 15 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Fringe: [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29] + [30,31]

Breadth-First Snapshot 16 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Fringe: [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31]

Breadth-First Snapshot 17 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Fringe: [18,19,20,21,22,23,24,25,26,27,28,29,30,31]

Breadth-First Snapshot 18 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Fringe: [19,20,21,22,23,24,25,26,27,28,29,30,31]

Breadth-First Snapshot 19 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Fringe: [20,21,22,23,24,25,26,27,28,29,30,31]

Breadth-First Snapshot 20 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Fringe: [21,22,23,24,25,26,27,28,29,30,31]

Breadth-First Snapshot 21 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Fringe: [22,23,24,25,26,27,28,29,30,31]

Breadth-First Snapshot 22 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Fringe: [23,24,25,26,27,28,29,30,31]

Breadth-First Snapshot 23 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Fringe: [24,25,26,27,28,29,30,31]

Breadth-First Snapshot 24 Initial Visited Fringe Current Visible Goal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Fringe: [25,26,27,28,29,30,31] Note: The goal test is positive for this node, and a solution is found in 24 steps.

Properties of Breadth-First Search (BFS) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],b Branching Factor d The depth of the goal

[object Object],[object Object],[object Object],Uniform-Cost -First

Properties of Uniform-cost Search (UCS) ,[object Object],[object Object],[object Object],[object Object],[object Object],b Branching Factor d Depth of the goal/tree

Breadth-First vs. Uniform-Cost ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Depth-First Search ,[object Object],[object Object],[object Object],L M N O P G Q H J I K F E D B C A

Depth-First Search ,[object Object],[object Object],[object Object],[object Object],[object Object]

Recursive Depth-First Search ,[object Object],[object Object],[object Object],[object Object],print node and print c and

Properties of Depth-First Search ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Depth-First vs. Breadth-First ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

4- Depth-Limited Search ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],b branching factor l depth limit

5- Iterative Deepening Depth-First Search

[object Object],[object Object],[object Object],Iterative Deepening Depth-First Search

Iterative deepening search l =0

[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Iterative Deepening Depth-First Search

Iterative Deepening Search ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Properties of Iterative Deepening Search ,[object Object],[object Object],[object Object],[object Object],b branching factor d Tree/goal depth

6- Bi-directional Search ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],b branching factor d tree depth Time Complexity b d/2 Space Complexity b d/2 Completeness yes (b finite, breadth-first for both directions) Optimality yes (all step costs identical, breadth-first for both directions)

Summary ,[object Object],[object Object],Iterative deepening search uses only linear space and not much more time than other uninformed algorithms

[object Object],[object Object],[object Object],[object Object],Summary

Summary (When to use what) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Improving Search Methods ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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