CS 380: ARTIFICIAL INTELLIGENCE PROBLEM SOLVING: INFORMED SEARCH, A* Santiago Ontañón
|
|
- Ruth Thomas
- 6 years ago
- Views:
Transcription
1 S 380: RTIFIIL INTELLIGENE PROLEM SOLVING: INFORMED SERH, * Santiago Ontañón so367@drexel.edu
2 Note on Graph Search Repeated-state checking: When the search state is a graph strategies like DFS can get stuck in loops. lgorithms need to keep a list (LOSED) of already visited nodes. In DFS: If we want to avoid repeating states completely, we need to keep LL the visited states in memory (in the LOSED list) If we just want to avoid loops, we only need to remember the current branch (linear memory as a function of m )
3 Evaluation Functions Idea: represent the information we have about the domain as an evaluation function h Evaluation function (heuristic): Given a state s h(s) it estimates how close or how far it is from the goal Example: In a maze solving problem: Euclidean distance to the goal
4 * t each cycle, * expands the node with the lowest f(n): f(n) = g(n) + h(n) * implementations assume repeated state checking (i.e. assume search space is a graph): OPEN: list of nodes that need to be expanded LOSED: list of nodes that have already been expanded
5 Example: * OPEN = [] LOSED = [] Heuristic used: Manhattan Distance
6 Example: * 3 OPEN = [] LOSED = [] ssigns an estimated cost, f, to each node: f(n) = g(n) + h(n) Heuristic Real cost from to n Heuristic used: Manhattan Distance
7 Example: * 3 OPEN = [,,] LOSED = [] 3 h = 2 Expands the node with the lowest Estimated cost first
8 Example: * 3 OPEN = [,, D] LOSED = [, ] 3 D D h = 2
9 Example: * 3 OPEN = [, D, E] LOSED = [,, ] 3 D E 7 D E h = h = 2
10 Example: * 3 OPEN = [D, E, F, G] LOSED = [,,, ] 3 D E 7 F G 7 D E h = h = 2 F G h =
11 Example: * 3 OPEN = [E, F, G] LOSED = [,,,, D] 3 D E 7 F G 7 D E h = h = 2 F G h =
12 Example: * 3 OPEN = [E, G, I, J] LOSED = [,,,, D, F] 3 D E 7 F I 7 G 7 J D E h = h = 2 G h = F I g = 3 J g = 3 h = 2
13 Example: * 3 OPEN = [E, G, I, K, L] LOSED = [,,,, D, F, J] 3 D E 7 F I 7 K 7 G 7 J L D E h = h = 2 G h = F I g = 3 L g = 4 h = 1 J g = 3 h = 2 K g = 4
14 Example: * 3 OPEN = [E, G, I, K, ] LOSED = [,,,, D, F, J, L] 3 D E 7 F I 7 K 7 G 7 J L D E h = h = 2 G h = F I g = 3 g = h = 0 L g = 4 h = 1 J g = 3 h = 2 K g = 4
15 Example: * 3 OPEN = [E, G, I, K] LOSED = [,,,, D, F, J, L, ] 3 D E 7 F I 7 K 7 G 7 J L D E h = h = 2 G h = F I g = 3 g = h = 0 L g = 4 h = 1 J g = 3 h = 2 K g = 4
16 Example: * 3 OPEN = [E, G, I, K] LOSED = [,,,, D, F, J, L, ] 3 D E 7 F I 7 K 7 G 7 J L D E h = h = 2 G h = F I g = 3 g = h = 0 L g = 4 h = 1 J g = 3 h = 2 K g = 4
17 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE
18 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE Differences wrt readth First Search
19 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE Nodes in red are in LOSED Nodes in grey are in OPEN
20 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE Nodes in red are in LOSED Nodes in grey are in OPEN
21 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE Nodes in red are in LOSED Nodes in grey are in OPEN
22 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE Nodes in red are in LOSED Nodes in grey are in OPEN
23 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE Nodes in red are in LOSED Nodes in grey are in OPEN
24 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE Nodes in red are in LOSED Nodes in grey are in OPEN
25 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE N Nodes in red are in LOSED Nodes in grey are in OPEN
26 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE N Nodes in red are in LOSED Nodes in grey are in OPEN
27 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE N Nodes in red are in LOSED Nodes in grey are in OPEN
28 * children(n) N.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE Nodes in red are in LOSED Nodes in grey are in OPEN
29 * children(n) N M.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE Nodes in red are in LOSED Nodes in grey are in OPEN
30 * children(n) N M.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE Nodes in red are in LOSED Nodes in grey are in OPEN
31 * children(n) N M.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE h = 2 Nodes in red are in LOSED Nodes in grey are in OPEN
32 * children(n) N M.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE h = 2 Nodes in red are in LOSED Nodes in grey are in OPEN
33 * children(n) N.;.h = heuristic() OPEN = []; LOSED = [] M WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE h = 2 Nodes in red are in LOSED Nodes in grey are in OPEN
34 * children(n) N.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N M LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE h = 2 Nodes in red are in LOSED Nodes in grey are in OPEN
35 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE N h = 2 Nodes in red are in LOSED Nodes in grey are in OPEN
36 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE N h = 2 Nodes in red are in LOSED Nodes in grey are in OPEN
37 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE h = 2 Nodes in red are in LOSED Nodes in grey are in OPEN
38 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE N h = 2 Nodes in red are in LOSED Nodes in grey are in OPEN
39 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE N h = 2 Nodes in red are in LOSED Nodes in grey are in OPEN
40 *.;.h = heuristic() OPEN = []; LOSED = [] WHILE OPEN is not empty N = OPEN.removeLowestF() IF goal(n) RETURN path to N LOSED.add(N) FOR all children M of N not in LOSED: M.parent = N M.g = N.g + 1; M.h = heuristic(m) OPEN.add(M) ENDFOR ENDWHILE N h = 2 Nodes in red are in LOSED Nodes in grey are in OPEN
41 Implementation Notes Remember the distinction between state and node State: The configuration of the problem (e.g. coordinates of a robot, positions of the pieces in the 8-puzzle, etc.) Node: state plus: current cost (g), current heuristic (h), parent node, action that got us here form the parent node It is important to remember who was the parent, and which action, so that once the solution is found, we can reconstruct the path
42 * Intuition The heuristic biases the search of the algorithm towards the goal: readth First Search No bias
43 * Intuition The heuristic biases the search of the algorithm towards the goal: * readth First Search No bias iased towards the goal
44 dmissible Heuristics To ensure optimality, * requires the heuristic to be admissible: h(n) h * (n) ctual cost to the goal In other words: the heuristic underestimates the actual remaining cost to the goal.
45 * Optimality Proof Suppose some suboptimal goal G 2 has been generated and is in the queue. Let n be an unexpanded node on a shortest path to an optimal goal G 1. n G G 2 f(g 2 ) = g(g 2 ) since h(g 2 ) = 0 > g(g 1 ) since G 2 is suboptimal f(n) since h is admissible Since f(g 2 ) > f(n), will never select G 2 for expansion
46 Heuristic Dominance If h 2 (n) h 1 (n) for all n (both admissible) then h 2 dominates h 1 and is better for search Typical search costs: d = 14 IDS = 3,473,941 nodes (h 1 ) = 39 nodes (h 2 ) = 113 nodes d = 24 IDS 4,000,000,000 nodes (h 1 ) = 39,13 nodes (h 2 ) = 1,641 nodes Given any admissible heuristics h a, h b, h(n) = max(h a (n), h b (n)) is also admissible and dominates h a, h b
47 onsistent Heuristics heuristic is consistent if h(n) c(n, a, n ) + h(n ) If h is consistent, we have f(n ) = g(n ) + h(n ) = g(n) + c(n, a, n ) + h(n ) g(n) + h(n) = f(n) I.e., f(n) is nondecreasing along any path. n c(n,a,n ) n h(n ) h(n) G onsistent heuristics ensure * will not try to expand a node more than once (i.e., they make it more efficient). ut regardless of whether the heuristic is consistent or not, * is still guaranteed to find the optimal path if the heuristic is admissible.
48 onstructing Heuristics by Relaxation h 1 (n) = number of tiles out of place. h 2 (n) = Manhattan distance of tiles to proper locations. dmissible heuristics can be derived from the exact solution cost of a relaxed version of the problem If the rules of the 8-puzzle are relaxed so that a tile can move anywhere, then h 1 (n) gives the shortest solution If the rules are relaxed so that a tile can move to any adjacent square, then h 2 (n) gives the shortest solution Key point: the optimal solution cost of a relaxed problem is no greater than the optimal solution cost of the real problem
49 * everywhere Even for videogame playing:
50 Variations of * SM*: * with bounded memory usage T*: * for real-time domains where we have a bounded time before producing an action LRT*: another real-time version of * (very simple, and the basis of a whole family of algorithms) D*: * for dynamic domains (problem configuration can change) etc.
CS 380: ARTIFICIAL INTELLIGENCE
S 380: RTIFIIL INTELLIGENE PROLEM SOLVING: INFORMED SERH, * 10/9/2013 Santiago Ontañón santi@cs.drexel.edu https://www.cs.drexel.edu/~santi/teaching/2013/s380/intro.html larification Repeated-state checking:
More informationCS 387/680: GAME AI PATHFINDING
CS 8/680: GAME AI PATHFINDING 4/12/2016 Instructor: Santiago Ontañón santi@cs.drexel.edu Class website: https://www.cs.drexel.edu/~santi/teaching/2016/cs8/intro.html Reminders Check Vista site for the
More informationInformed Search and Exploration for Agents
Informed Search and Exploration for Agents R&N: 3.5, 3.6 Michael Rovatsos University of Edinburgh 29 th January 2015 Outline Best-first search Greedy best-first search A * search Heuristics Admissibility
More informationOutline. Informed search algorithms. Best-first search. Review: Tree search. A search Heuristics. Chapter 4, Sections 1 2 4
Outline Best-first search Informed search algorithms A search Heuristics Chapter 4, Sections 1 2 Chapter 4, Sections 1 2 1 Chapter 4, Sections 1 2 2 Review: Tree search function Tree-Search( problem, fringe)
More informationChapter 3: Informed Search and Exploration. Dr. Daisy Tang
Chapter 3: Informed Search and Exploration Dr. Daisy Tang Informed Search Definition: Use problem-specific knowledge beyond the definition of the problem itself Can find solutions more efficiently Best-first
More informationA.I.: Informed Search Algorithms. Chapter III: Part Deux
A.I.: Informed Search Algorithms Chapter III: Part Deux Best-first search Greedy best-first search A * search Heuristics Outline Overview Informed Search: uses problem-specific knowledge. General approach:
More informationInformed search algorithms
Informed search algorithms Chapter 4, Sections 1 2 Chapter 4, Sections 1 2 1 Outline Best-first search A search Heuristics Chapter 4, Sections 1 2 2 Review: Tree search function Tree-Search( problem, fringe)
More informationInformed search algorithms. Chapter 4
Informed search algorithms Chapter 4 Material Chapter 4 Section 1 - Exclude memory-bounded heuristic search 3 Outline Best-first search Greedy best-first search A * search Heuristics Local search algorithms
More informationInformed search algorithms. Chapter 4, Sections 1 2 1
Informed search algorithms Chapter 4, Sections 1 2 Chapter 4, Sections 1 2 1 Outline Best-first search A search Heuristics Chapter 4, Sections 1 2 2 Review: Tree search function Tree-Search( problem, fringe)
More informationInformed/Heuristic Search
Informed/Heuristic Search Outline Limitations of uninformed search methods Informed (or heuristic) search uses problem-specific heuristics to improve efficiency Best-first A* Techniques for generating
More informationCS 387/680: GAME AI PATHFINDING
CS 387/680: GAME AI PATHFINDING 4/14/2014 Instructor: Santiago Ontañón santi@cs.drexel.edu TA: Alberto Uriarte office hours: Tuesday 4-6pm, Cyber Learning Center Class website: https://www.cs.drexel.edu/~santi/teaching/2014/cs387-680/intro.html
More informationInformed search. Soleymani. CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2016
Informed search CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2016 Soleymani Artificial Intelligence: A Modern Approach, Chapter 3 Outline Best-first search Greedy
More informationInformed search strategies (Section ) Source: Fotolia
Informed search strategies (Section 3.5-3.6) Source: Fotolia Review: Tree search Initialize the frontier using the starting state While the frontier is not empty Choose a frontier node to expand according
More informationInformed Search. Best-first search. Greedy best-first search. Intelligent Systems and HCI D7023E. Romania with step costs in km
Informed Search Intelligent Systems and HCI D7023E Lecture 5: Informed Search (heuristics) Paweł Pietrzak [Sec 3.5-3.6,Ch.4] A search strategy which searches the most promising branches of the state-space
More informationLecture 4: Informed/Heuristic Search
Lecture 4: Informed/Heuristic Search Outline Limitations of uninformed search methods Informed (or heuristic) search uses problem-specific heuristics to improve efficiency Best-first A* RBFS SMA* Techniques
More informationCSE 473. Chapter 4 Informed Search. CSE AI Faculty. Last Time. Blind Search BFS UC-BFS DFS DLS Iterative Deepening Bidirectional Search
CSE 473 Chapter 4 Informed Search CSE AI Faculty Blind Search BFS UC-BFS DFS DLS Iterative Deepening Bidirectional Search Last Time 2 1 Repeated States Failure to detect repeated states can turn a linear
More informationCS 331: Artificial Intelligence Informed Search. Informed Search
CS 331: Artificial Intelligence Informed Search 1 Informed Search How can we make search smarter? Use problem-specific knowledge beyond the definition of the problem itself Specifically, incorporate knowledge
More informationEE562 ARTIFICIAL INTELLIGENCE FOR ENGINEERS
EE562 ARTIFICIAL INTELLIGENCE FOR ENGINEERS Lecture 4, 4/11/2005 University of Washington, Department of Electrical Engineering Spring 2005 Instructor: Professor Jeff A. Bilmes Today: Informed search algorithms
More informationInformed (Heuristic) Search. Idea: be smart about what paths to try.
Informed (Heuristic) Search Idea: be smart about what paths to try. 1 Blind Search vs. Informed Search What s the difference? How do we formally specify this? A node is selected for expansion based on
More informationArtificial Intelligence
Artificial Intelligence Search Marc Toussaint University of Stuttgart Winter 2015/16 (slides based on Stuart Russell s AI course) Outline Problem formulation & examples Basic search algorithms 2/100 Example:
More informationCS 331: Artificial Intelligence Informed Search. Informed Search
CS 331: Artificial Intelligence Informed Search 1 Informed Search How can we make search smarter? Use problem-specific knowledge beyond the definition of the problem itself Specifically, incorporate knowledge
More informationMustafa Jarrar: Lecture Notes on Artificial Intelligence Birzeit University, Chapter 3 Informed Searching. Mustafa Jarrar. University of Birzeit
Mustafa Jarrar: Lecture Notes on Artificial Intelligence Birzeit University, 2018 Chapter 3 Informed Searching Mustafa Jarrar University of Birzeit Jarrar 2018 1 Watch this lecture and download the slides
More informationArtificial Intelligence Informed search. Peter Antal
Artificial Intelligence Informed search Peter Antal antal@mit.bme.hu 1 Informed = use problem-specific knowledge Which search strategies? Best-first search and its variants Heuristic functions? How to
More informationLecture 5 Heuristics. Last Time: A* Search
CSE 473 Lecture 5 Heuristics CSE AI Faculty Last Time: A* Search Use an evaluation function f(n) for node n. f(n) = estimated total cost of path thru n to goal f(n) = g(n) + h(n) g(n) = cost so far to
More informationCS:4420 Artificial Intelligence
CS:4420 Artificial Intelligence Spring 2018 Informed Search Cesare Tinelli The University of Iowa Copyright 2004 18, Cesare Tinelli and Stuart Russell a a These notes were originally developed by Stuart
More informationInformed Search and Exploration
Ch. 03 p.1/47 Informed Search and Exploration Sections 3.5 and 3.6 Ch. 03 p.2/47 Outline Best-first search A search Heuristics, pattern databases IDA search (Recursive Best-First Search (RBFS), MA and
More informationInformed search algorithms. Chapter 4
Informed search algorithms Chapter 4 Outline Best-first search Greedy best-first search A * search Heuristics Memory Bounded A* Search Best-first search Idea: use an evaluation function f(n) for each node
More informationProblem solving and search
Problem solving and search Chapter 3 Chapter 3 1 Outline Problem-solving agents Problem types Problem formulation Example problems Uninformed search algorithms Informed search algorithms Chapter 3 2 Restricted
More informationmywbut.com Informed Search Strategies-I
Informed Search Strategies-I 1 3.1 Introduction We have outlined the different types of search strategies. In the earlier chapter we have looked at different blind search strategies. Uninformed search
More informationPlanning, Execution & Learning 1. Heuristic Search Planning
Planning, Execution & Learning 1. Heuristic Search Planning Reid Simmons Planning, Execution & Learning: Heuristic 1 Simmons, Veloso : Fall 2001 Basic Idea Heuristic Search Planning Automatically Analyze
More informationArtificial Intelligence: Search Part 2: Heuristic search
Artificial Intelligence: Search Part 2: Heuristic search Thomas Trappenberg January 16, 2009 Based on the slides provided by Russell and Norvig, Chapter 4, Section 1 2,(4) Outline Best-first search A search
More informationARTIFICIAL INTELLIGENCE. Informed search
INFOB2KI 2017-2018 Utrecht University The Netherlands ARTIFICIAL INTELLIGENCE Informed search Lecturer: Silja Renooij These slides are part of the INFOB2KI Course Notes available from www.cs.uu.nl/docs/vakken/b2ki/schema.html
More informationDr. Mustafa Jarrar. Chapter 4 Informed Searching. Sina Institute, University of Birzeit
Lecture Notes, Advanced Artificial Intelligence (SCOM7341) Sina Institute, University of Birzeit 2 nd Semester, 2012 Advanced Artificial Intelligence (SCOM7341) Chapter 4 Informed Searching Dr. Mustafa
More informationInformed Search and Exploration
Ch. 03b p.1/51 Informed Search and Exploration Sections 3.5 and 3.6 Nilufer Onder Department of Computer Science Michigan Technological University Ch. 03b p.2/51 Outline Best-first search A search Heuristics,
More informationInformed Search Algorithms
Informed Search Algorithms CITS3001 Algorithms, Agents and Artificial Intelligence Tim French School of Computer Science and Software Engineering The University of Western Australia 2017, Semester 2 Introduction
More informationArtificial Intelligence, CS, Nanjing University Spring, 2018, Yang Yu. Lecture 3: Search 2.
Artificial Intelligence, CS, Nanjing University Spring, 2018, Yang Yu Lecture 3: Search 2 http://cs.nju.edu.cn/yuy/course_ai18.ashx Previously... function Tree-Search( problem, fringe) returns a solution,
More information2006/2007 Intelligent Systems 1. Intelligent Systems. Prof. dr. Paul De Bra Technische Universiteit Eindhoven
test gamma 2006/2007 Intelligent Systems 1 Intelligent Systems Prof. dr. Paul De Bra Technische Universiteit Eindhoven debra@win.tue.nl 2006/2007 Intelligent Systems 2 Informed search and exploration Best-first
More informationCS 380: Artificial Intelligence Lecture #4
CS 380: Artificial Intelligence Lecture #4 William Regli Material Chapter 4 Section 1-3 1 Outline Best-first search Greedy best-first search A * search Heuristics Local search algorithms Hill-climbing
More informationA* optimality proof, cycle checking
A* optimality proof, cycle checking CPSC 322 Search 5 Textbook 3.6 and 3.7.1 January 21, 2011 Taught by Mike Chiang Lecture Overview Recap Admissibility of A* Cycle checking and multiple path pruning Slide
More informationInformed Search A* Algorithm
Informed Search A* Algorithm CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2018 Soleymani Artificial Intelligence: A Modern Approach, Chapter 3 Most slides have
More informationInformed search algorithms. (Based on slides by Oren Etzioni, Stuart Russell)
Informed search algorithms (Based on slides by Oren Etzioni, Stuart Russell) Outline Greedy best-first search A * search Heuristics Local search algorithms Hill-climbing search Simulated annealing search
More informationOutline. Best-first search
Outline Best-first search Greedy best-first search A* search Heuristics Admissible Heuristics Graph Search Consistent Heuristics Local search algorithms Hill-climbing search Beam search Simulated annealing
More informationArtificial Intelligence
Artificial Intelligence Information Systems and Machine Learning Lab (ISMLL) Tomáš Horváth 10 rd November, 2010 Informed Search and Exploration Example (again) Informed strategy we use a problem-specific
More informationThe wolf sheep cabbage problem. Search. Terminology. Solution. Finite state acceptor / state space
Search The wolf sheep cabbage problem What is search? Terminology: search space, strategy Modelling Uninformed search (not intelligent ) Breadth first Depth first, some variations omplexity space and time
More informationCOMP9414/ 9814/ 3411: Artificial Intelligence. 5. Informed Search. Russell & Norvig, Chapter 3. UNSW c Alan Blair,
COMP9414/ 9814/ 3411: Artificial Intelligence 5. Informed Search Russell & Norvig, Chapter 3. COMP9414/9814/3411 15s1 Informed Search 1 Search Strategies General Search algorithm: add initial state to
More informationTDT4136 Logic and Reasoning Systems
TDT4136 Logic and Reasoning Systems Chapter 3 & 4.1 - Informed Search and Exploration Lester Solbakken solbakke@idi.ntnu.no Norwegian University of Science and Technology 18.10.2011 1 Lester Solbakken
More informationPROBLEM SOLVING AND SEARCH IN ARTIFICIAL INTELLIGENCE
Artificial Intelligence, Computational Logic PROBLEM SOLVING AND SEARCH IN ARTIFICIAL INTELLIGENCE Lecture 3 Informed Search Sarah Gaggl Dresden, 22th April 2014 Agenda 1 Introduction 2 Uninformed Search
More informationDr. Mustafa Jarrar. Chapter 4 Informed Searching. Artificial Intelligence. Sina Institute, University of Birzeit
Lecture Notes on Informed Searching University of Birzeit, Palestine 1 st Semester, 2014 Artificial Intelligence Chapter 4 Informed Searching Dr. Mustafa Jarrar Sina Institute, University of Birzeit mjarrar@birzeit.edu
More informationArtificial Intelligence
Artificial Intelligence hapter 1 hapter 1 1 Iterative deepening search function Iterative-Deepening-Search( problem) returns a solution inputs: problem, a problem for depth 0 to do result Depth-Limited-Search(
More informationIntroduction to Artificial Intelligence. Informed Search
Introduction to Artificial Intelligence Informed Search Bernhard Beckert UNIVERSITÄT KOBLENZ-LANDAU Winter Term 2004/2005 B. Beckert: KI für IM p.1 Outline Best-first search A search Heuristics B. Beckert:
More informationInformed search algorithms. Chapter 3 (Based on Slides by Stuart Russell, Dan Klein, Richard Korf, Subbarao Kambhampati, and UW-AI faculty)
Informed search algorithms Chapter 3 (Based on Slides by Stuart Russell, Dan Klein, Richard Korf, Subbarao Kambhampati, and UW-AI faculty) Intuition, like the rays of the sun, acts only in an inflexibly
More informationCS 771 Artificial Intelligence. Informed Search
CS 771 Artificial Intelligence Informed Search Outline Review limitations of uninformed search methods Informed (or heuristic) search Uses problem-specific heuristics to improve efficiency Best-first,
More informationInformed Search. CMU Snake Robot. Administrative. Uninformed search strategies. Assignment 1 was due before class how d it go?
Informed Search S151 David Kauchak Fall 2010 MU Snake Robot http://www-cgi.cs.cmu.edu/afs/cs.cmu.edu/web/people/biorobotics/projects/ modsnake/index.html Some material borrowed from : Sara Owsley Sood
More informationCS 387/680: GAME AI PATHFINDING
CS 387/680: GAME AI PATHFINDING 4/16/2015 Instructor: Santiago Ontañón santi@cs.drexel.edu Class website: https://www.cs.drexel.edu/~santi/teaching/2015/cs387/intro.html Reminders Check BBVista site for
More informationProblem Solving and Search
Artificial Intelligence Problem Solving and Search Dae-Won Kim School of Computer Science & Engineering Chung-Ang University Outline Problem-solving agents Problem types Problem formulation Example problems
More informationInformed Search. CS 486/686 University of Waterloo May 10. cs486/686 Lecture Slides 2005 (c) K. Larson and P. Poupart
Informed Search CS 486/686 University of Waterloo May 0 Outline Using knowledge Heuristics Best-first search Greedy best-first search A* search Other variations of A* Back to heuristics 2 Recall from last
More informationArtificial Intelligence
Artificial Intelligence Dr Ahmed Rafat Abas Computer Science Dept, Faculty of Computers and Informatics, Zagazig University arabas@zu.edu.eg http://www.arsaliem.faculty.zu.edu.eg/ Informed search algorithms
More informationSolving problems by searching
Solving problems by searching Chapter 3 Some slide credits to Hwee Tou Ng (Singapore) Outline Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms Heuristics
More informationInformed search algorithms
Informed search algorithms This lecture topic Chapter 3.5-3.7 Next lecture topic Chapter 4.1-4.2 (Please read lecture topic material before and after each lecture on that topic) Outline Review limitations
More information4 INFORMED SEARCH AND EXPLORATION. 4.1 Heuristic Search Strategies
55 4 INFORMED SEARCH AND EXPLORATION We now consider informed search that uses problem-specific knowledge beyond the definition of the problem itself This information helps to find solutions more efficiently
More informationProblem solving and search
Problem solving and search Chapter 3 TB Artificial Intelligence Slides from AIMA http://aima.cs.berkeley.edu 1 /1 Outline Problem-solving agents Problem types Problem formulation Example problems Basic
More informationOutline for today s lecture. Informed Search. Informed Search II. Review: Properties of greedy best-first search. Review: Greedy best-first search:
Outline for today s lecture Informed Search II Informed Search Optimal informed search: A* (AIMA 3.5.2) Creating good heuristic functions Hill Climbing 2 Review: Greedy best-first search: f(n): estimated
More informationOutline. Best-first search
Outline Best-first search Greedy best-first search A* search Heuristics Local search algorithms Hill-climbing search Beam search Simulated annealing search Genetic algorithms Constraint Satisfaction Problems
More informationSolving Problems: Intelligent Search
Solving Problems: Intelligent Search Instructor: B. John Oommen Chancellor s Professor Fellow: IEEE; Fellow: IAPR School of Computer Science, Carleton University, Canada The primary source of these notes
More informationHeuristic (Informed) Search
Heuristic (Informed) Search (Where we try to choose smartly) R&N: Chap. 4, Sect. 4.1 3 1 Recall that the ordering of FRINGE defines the search strategy Search Algorithm #2 SEARCH#2 1. INSERT(initial-node,FRINGE)
More informationArtificial Intelligence
Artificial Intelligence Informed Search and Exploration Chapter 4 (4.1 4.2) A General Search algorithm: Chapter 3: Search Strategies Task : Find a sequence of actions leading from the initial state to
More informationLecture Plan. Best-first search Greedy search A* search Designing heuristics. Hill-climbing. 1 Informed search strategies. Informed strategies
Lecture Plan 1 Informed search strategies (KA AGH) 1 czerwca 2010 1 / 28 Blind vs. informed search strategies Blind search methods You already know them: BFS, DFS, UCS et al. They don t analyse the nodes
More informationArtificial Intelligence Informed search. Peter Antal Tadeusz Dobrowiecki
Artificial Intelligence Informed search Peter Antal antal@mit.bme.hu Tadeusz Dobrowiecki tade@mit.bme.hu A.I. 9/17/2018 1 Informed = use problem-specific knowledge Which search strategies? Best-first search
More informationInformed search methods
Informed search methods Tuomas Sandholm Computer Science Department Carnegie Mellon University Read Section 3.5-3.7 of Russell and Norvig Informed Search Methods Heuristic = to find, to discover Heuristic
More informationAdvanced Artificial Intelligence (DT4019, HT10)
Advanced Artificial Intelligence (DT4019, HT10) Problem Solving and Search: Informed Search Strategies (I) Federico Pecora School of Science and Technology Örebro University federico.pecora@oru.se Federico
More information1 Introduction and Examples
1 Introduction and Examples Sequencing Problems Definition A sequencing problem is one that involves finding a sequence of steps that transforms an initial system state to a pre-defined goal state for
More informationInformed Search. Xiaojin Zhu Computer Sciences Department University of Wisconsin, Madison
Informed Search Xiaojin Zhu jerryzhu@cs.wisc.edu Computer Sciences Department University of Wisconsin, Madison [Based on slides from Andrew Moore http://www.cs.cmu.edu/~awm/tutorials ] slide 1 Main messages
More informationArtificial Intelligence p.1/49. n-queens. Artificial Intelligence p.2/49. Initial state: the empty board or a board with n random
Example: n-queens Put n queens on an n n board with no two queens on the same row, column, or diagonal A search problem! State space: the board with 0 to n queens Initial state: the empty board or a board
More informationHeuristic (Informed) Search
Heuristic (Informed) Search (Where we try to choose smartly) R&N: Chap., Sect..1 3 1 Search Algorithm #2 SEARCH#2 1. INSERT(initial-node,Open-List) 2. Repeat: a. If empty(open-list) then return failure
More informationHeuris'c Search. Reading note: Chapter 4 covers heuristic search.
Heuris'c Search Reading note: Chapter 4 covers heuristic search. Credits: Slides in this deck are drawn from or inspired by a multitude of sources including: Shaul Markovitch Jurgen Strum Sheila McIlraith
More informationInformed Search. Notes about the assignment. Outline. Tree search: Reminder. Heuristics. Best-first search. Russell and Norvig chap.
Notes about the assignment Informed Search Russell and Norvig chap. 4 If it says return True or False, return True or False, not "True" or "False Comment out or remove print statements before submitting.
More informationProblem-solving agents. Solving Problems by Searching. Outline. Example: Romania. Chapter 3
Problem-solving agents olving Problems by earching hapter 3 function imple-problem-olving-gent( percept) returns an action static: seq, an action sequence, initially empty state, some description of the
More informationProblem Solving: Informed Search
Problem Solving: Informed Search References Russell and Norvig, Artificial Intelligence: A modern approach, 2nd ed. Prentice Hall, 2003 (Chapters 1,2, and 4) Nilsson, Artificial intelligence: A New synthesis.
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science Artificial Intelligence Fall, 2010
MSSHUSETTS INSTITUTE OF TEHNOLOY epartment of Electrical Engineering and omputer Science 6.0 rtificial Intelligence Fall, 00 Search Me! Recitation, Thursday September Prof. ob erwick. ifference between
More informationInformed Search Methods
Informed Search Methods How can we improve searching strategy by using intelligence? Map example: Heuristic: Expand those nodes closest in as the crow flies distance to goal 8-puzzle: Heuristic: Expand
More informationInformed search algorithms
Artificial Intelligence Topic 4 Informed search algorithms Best-first search Greedy search A search Admissible heuristics Memory-bounded search IDA SMA Reading: Russell and Norvig, Chapter 4, Sections
More informationInformed search algorithms
CS 580 1 Informed search algorithms Chapter 4, Sections 1 2, 4 CS 580 2 Outline Best-first search A search Heuristics Hill-climbing Simulated annealing CS 580 3 Review: General search function General-Search(
More informationDownloded from: CSITauthority.blogspot.com
[Unit : Searching] (CSC 355) Central Department of Computer Science & Information Technology Tribhuvan University 1 Searching search problem Figure below contains a representation of a map. The nodes represent
More informationCOMP9414: Artificial Intelligence Informed Search
COMP9, Wednesday March, 00 Informed Search COMP9: Artificial Intelligence Informed Search Wayne Wobcke Room J- wobcke@cse.unsw.edu.au Based on slides by Maurice Pagnucco Overview Heuristics Informed Search
More informationArtificial Intelligence
Artificial Intelligence Information Systems and Machine Learning Lab (ISMLL) Tomáš Horváth 16 rd November, 2011 Informed Search and Exploration Example (again) Informed strategy we use a problem-specific
More informationITCS 6150 Intelligent Systems. Lecture 5 Informed Searches
ITCS 6150 Intelligent Systems Lecture 5 Informed Searches Informed Searches We are informed (in some way) about future states and future paths We use this information to make better decisions about which
More informationCS 520: Introduction to Artificial Intelligence. Lectures on Search
CS 520: Introduction to Artificial Intelligence Prof. Louis Steinberg Lecture : uninformed search uninformed search Review Lectures on Search Formulation of search problems. State Spaces Uninformed (blind)
More informationHeuristic Search. Rob Platt Northeastern University. Some images and slides are used from: AIMA
Heuristic Search Rob Platt Northeastern University Some images and slides are used from: AIMA Recap: What is graph search? Start state Goal state Graph search: find a path from start to goal what are the
More informationCS 4700: Foundations of Artificial Intelligence
CS 4700: Foundations of Artificial Intelligence Bart Selman selman@cs.cornell.edu Module: Informed Search Readings R&N - Chapter 3: 3.5 and 3.6 Search Search strategies determined by choice of node (in
More informationAr#ficial)Intelligence!!
Introduc*on! Ar#ficial)Intelligence!! Roman Barták Department of Theoretical Computer Science and Mathematical Logic Uninformed (blind) search algorithms can find an (optimal) solution to the problem,
More informationInformed Search. CS 486/686: Introduction to Artificial Intelligence Fall 2013
Informed Search CS 486/686: Introduction to Artificial Intelligence Fall 2013 1 Outline Using knowledge Heuristics Bestfirst search Greedy bestfirst search A* search Variations of A* Back to heuristics
More informationInformed search algorithms
Informed search algorithms This lecture topic Chapter 3.5-3.7 Next lecture topic Chapter 4.1-4.2 (Please read lecture topic material before and after each lecture on that topic) Outline Review limitations
More informationInformed search algorithms
Informed search algorithms This lecture topic Chapter 3.5-3.7 Next lecture topic Chapter 4.1-4.2 (Please read lecture topic material before and after each lecture on that topic) Outline Review limitations
More informationIntroduction HEURISTIC SEARCH. Introduction. Heuristics. Two main concerns of AI researchers. Two problems with the search process
HEURISTIC SERCH George F Luger RTIFICIL INTELLIGENCE 6th edition Structures and Strategies for Complex Problem Solving Introduction Two main concerns of I researchers 1) Representation of the knowledge
More informationLecture 2: Fun with Search. Rachel Greenstadt CS 510, October 5, 2017
Lecture 2: Fun with Search Rachel Greenstadt CS 510, October 5, 2017 Reminder! Project pre-proposals due tonight Overview Uninformed search BFS, DFS, Uniform-Cost, Graph-Search Informed search Heuristics,
More informationHeuristic Search. Heuristic Search. Heuristic Search. CSE 3401: Intro to AI & LP Informed Search
CSE 3401: Intro to AI & LP Informed Search Heuristic Search. Required Readings: Chapter 3, Sections 5 and 6, and Chapter 4, Section 1. In uninformed search, we don t try to evaluate which of the nodes
More informationCS 4700: Foundations of Artificial Intelligence
CS 4700: Foundations of Artificial Intelligence Bart Selman selman@cs.cornell.edu Informed Search Readings R&N - Chapter 3: 3.5 and 3.6 Search Search strategies determined by choice of node (in queue)
More informationA* Optimality CS4804
A* Optimality CS4804 Plan A* in a tree A* in a graph How to handle multiple paths to a node Intuition about consistency Search space + heuristic design practice A* Search Expand node in frontier with best
More informationIntroduction to Computer Science and Programming for Astronomers
Introduction to Computer Science and Programming for Astronomers Lecture 9. István Szapudi Institute for Astronomy University of Hawaii March 21, 2018 Outline Reminder 1 Reminder 2 3 Reminder We have demonstrated
More informationSolving problems by searching
Solving problems by searching CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2017 Soleymani Artificial Intelligence: A Modern Approach, Chapter 3 Outline Problem-solving
More information