Artificial Intelligence
|
|
- Juliet Ramsey
- 5 years ago
- Views:
Transcription
1 Artificial Intelligence Exercises & Solutions Chapters -4: Search methods. Search Tree. Draw the complete search tree (starting from S and ending at G) of the graph below. The numbers beside the nodes represent the estimated distances from the goal state. Show how the search procedure proceeds in the tree by using: 8 5 depth-first breadth-first A D hill-climbing 0 beam-search (w=) S best-first G 9 0 methods. B C. Search traces. Consider the graph shown in the figure to the right. We can search it with a variety of different algorithms, resulting in different search trees. Each of the trees (labelled G though G7, next page) was generated by searching this graph, but with a different algorithm. Assume that children of a node are visited in alphabetical order when no other order is specified by the search. Each tree shows all the nodes that have been seen during search. Numbers next to nodes indicate the relevant score used by the algorithm for those nodes. For each tree, indicate whether it was generated with Depth first search Breadth first search niform cost search A* search Best-first (greedy) search In all cases a strict expanded list was used. Furthermore, if you choose an algorithm that uses a heuristic function, say whether we used H: heuristic = {h(a) =, h(b) = 6, h(c) = 4, h(d) = } H: heuristic = {h(a) =, h(b) =, h(c) = 0, h(d) = } Also, for all algorithms, say whether the result was an optimal path (measured by sum of link costs), and if not, why not.
2 . Search problem. Consider the -puzzle problem, which is a simpler version of the 8-puzzle where the board is x and there are three tiles, numbered,, and, and one blank. There are four operators, which move the blank up, down, left, and right. The start and goal states are given below. Show how the path to the goal can be found using: a) breath first searh b) depth first search c) A* search with the heuristic being the sum of number of moves and the number of misplaced tiles. Start Goal Assume that there is no possibility to remember states that have been visited earlier. Also, use the given operators in the given order unless the search method defines otherwise. Label each visited node with a number indicating the order in which they are visited. If a search method doesn t find a solution, explain why this happened.
3 . Search Tree solution. The complete search tree can be generated by finding all possible routes that start from the node S and lead to a node that has not yet been visited on the route. The tree below has been constructed by always choosing the rightmost (from the nodes point of view) unvisited route. Note that the branches could be in different order if routes were selected in different order. The nodes are numbered (-8) to ease the analysis of the search methods. In depth first search method the tree is searched in the depth direction. The search always branches to the leftmost unvisited node. In case a leaf node is found or there are no more unvisited nodes, the search returns to the preceding level. In this case, the tree is searched in the order indicated by the node numbers and is illustrated with the dotted line. If one solution for reaching G was enough, the search would end at the node five. If the whole tree is searched, the best route to G can be selected at the end.
4 Breadth-first search method searches the tree in the breadth direction. In this case the nodes are searched in the following order:,, 0,, 4, 7,, 5, 5, 6, 8,,, 6, 8, 9, 4 and 7. Again, if one solution was enough, the search would end at node 5. Hill-climbing is a search algorithm that proceeds like depth-first search but so that the search order of the nodes is determined by the estimated distance from a node to the goal node (depth first would choose the leftmost). When starting from the node S, the search sees the estimated distances from the nodes (9) and 0 (8) and chooses the node 0 that is estimated to be closer to the goal. From node 0 the nodes (9) and 5 (5) become visible and the search proceeds to node 5. From node 5 the goal node becomes visible and the search has found a solution. One solution is usually enough for Hill-climbing since it usually finds good solutions. However, the image illustrates the search of the whole tree to better describe the search.
5 Beam-search proceeds much like breath first, however, at each level only w number of nodes are checked. First, nodes and 0 are opened. At this point five nodes can be seen ( (0), 4 (5), 7 (8), (9) and 5 (5)). Since only two nodes can be opened, nodes 4 and 5 are selected. After those nodes are opened four more nodes become visible and as the goal node becomes visible (actually twice) the search is completed. The nodes were visited in the following order:,, 0, 4, 5 and 5. Best-first search always chooses the best node, independent of where in the tree it is located. At first, the nodes (9) and 0 (8) can be seen and the node 0 is opened. Now, the nodes (9), (9) and 5 (5) can be seen and the node 5 is opened. At this point the nodes nodes (9), (9), 6 (9) and 8 (0) can be seen and as 8 is the goal node, the search is finished. If one would want to find an alternative route to the goal node, the search would be continued from where the nodes (9), (9), 6 (9) were seen. Now all the nodes have the same distance. If the leftmost node of same valued nodes was opened first the search would continue through nodes, 4 and 5. If on the other hand the node that was seen last of the same valued nodes was to be opened first, the search would continue through nodes 6,, and 4.
6 . Search traces solution. G:. Algorithm: Breadth First Search. Heuristic (if any): None. Did it find least-cost path? If not, why? No. Breadth first search is only guaranteed to find a path with the shortest number of links; it does not consider link cost at all. G:. Algorithm: Best First Search. Heuristic (if any): H. Did it find least-cost path? If not, why? No. Best first search is not guaranteed to find an optimal path. It takes the first path to goal it finds. G:. Algorithm: A*. Heuristic (if any): H. Did it find least-cost path? If not, why? No. A* is only guaranteed to find an optimal path when the heuristic is admissible (or consistent with a strict expanded list). H is neither: the heuristic value for C is not an underestimate of the optimal cost to goal. G4:. Algorithm: Best First Search. Heuristic (if any): H. Did it find least-cost path? If not, why? Yes. Though best first search is not guaranteed to find an optimal path, in this case it did G5:. Algorithm: Depth First Search. Heuristic (if any): None. Did it find least-cost path? If not, why? No. Depth first search is an any-path search; it does not consider link cost at all. G6:. Algorithm: A*. Heuristic (if any): H. Did it find least-cost path? If not, why? Yes. A* is guaranteed to find an optimal path when the heuristic is admissible (or consistent with a strict expanded list). H is admissible but not consistent, since the link from D to C decreases the heuristic cost by, which is greater than the link cost of. Still, the optimal path was found. G7:. Algorithm: niform Cost Search. Heuristic (if any): None. Did it find least-cost path? If not, why? Yes. niform Cost is guaranteed to find a shortest path.
7 . Search problem. a) Breadth first search will start from the root node, then expands all the successors of the root node, and then all their successors and so on. Breadth first search stops when first solution is found. L D L L D R b) Depth-first search expands the deepest node in the search tree. Notice that there was no mechanism to remember states that have been visited earlier. Depth first will not find a solution as it will start oscillating between movements and D D 4 etc..
8 c) A* is a search method that opens the node with smallest cost function value. The search begins from the start state.. When the start state is opened we see two states f=+= f=0+= f=0+= L f=+=4. The leftmost state has a lower cost so that one is choosen and opened. We now see states with costs 5, and 4 f=+= f=0+= L f=+=4 D L f=+=5 f=+=. The state with lowest cost is opened and we see two more nodes including the goal node. We notice that the goal node has the lowest cost so we choose that and can finish the search. If some other node with a lower cost function value was still visible, A* search would choose that instead of the higher cost goal node. This is because A* tries to find the path with lowest cost. D f=+=5 f=+0= D f=0+= L f=+= L f=+= R f=+=5 f=+=4
Midterm Examination CS540-2: Introduction to Artificial Intelligence
Midterm Examination CS540-2: Introduction to Artificial Intelligence March 15, 2018 LAST NAME: FIRST NAME: Problem Score Max Score 1 12 2 13 3 9 4 11 5 8 6 13 7 9 8 16 9 9 Total 100 Question 1. [12] Search
More informationProblem Solving & Heuristic Search
190.08 Artificial 2016-Spring Problem Solving & Heuristic Search Byoung-Tak Zhang School of Computer Science and Engineering Seoul National University 190.08 Artificial (2016-Spring) http://www.cs.duke.edu/courses/fall08/cps270/
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 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 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 informationCPS 170: Artificial Intelligence Search
CPS 170: Artificial Intelligence http://www.cs.duke.edu/courses/spring09/cps170/ Search Instructor: Vincent Conitzer Search We have some actions that can change the state of the world Change resulting
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 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 information4 Search Problem formulation (23 points)
4 Search Problem formulation (23 points) Consider a Mars rover that has to drive around the surface, collect rock samples, and return to the lander. We want to construct a plan for its exploration. It
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 informationSearching with Partial Information
Searching with Partial Information Above we (unrealistically) assumed that the environment is fully observable and deterministic Moreover, we assumed that the agent knows what the effects of each action
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 informationCS-171, Intro to A.I. Mid-term Exam Fall Quarter, 2017
CS-171, Intro to A.I. Mid-term Exam Fall Quarter, 2017 YOUR NAME: YOUR ID: ID TO RIGHT: ROW: SEAT: Please turn off all cell phones now. The exam will begin on the next page. Please, do not turn the page
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 informationUninformed Search Methods
Uninformed Search Methods Search Algorithms Uninformed Blind search Breadth-first uniform first depth-first Iterative deepening depth-first Bidirectional Branch and Bound Informed Heuristic search Greedy
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 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 information6.034 Quiz 1, Spring 2004 Solutions
6.034 Quiz 1, Spring 2004 Solutions Open Book, Open Notes 1 Tree Search (12 points) Consider the tree shown below. The numbers on the arcs are the arc lengths. Assume that the nodes are expanded in alphabetical
More informationArtificial Intelligence (Heuristic Search)
Artificial Intelligence (Heuristic Search) KR Chowdhary, Professor & Head Email: kr.chowdhary@acm.org Department of Computer Science and Engineering MBM Engineering College, Jodhpur kr chowdhary heuristic
More informationLast time: Problem-Solving
Last time: Problem-Solving Problem solving: Goal formulation Problem formulation (states, operators) Search for solution Problem formulation: Initial state??? 1 Last time: Problem-Solving Problem types:
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 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 information3 SOLVING PROBLEMS BY SEARCHING
48 3 SOLVING PROBLEMS BY SEARCHING A goal-based agent aims at solving problems by performing actions that lead to desirable states Let us first consider the uninformed situation in which the agent is not
More informationDIT411/TIN175, Artificial Intelligence. Peter Ljunglöf. 23 January, 2018
DIT411/TIN175, Artificial Intelligence Chapters 3 4: More search algorithms CHAPTERS 3 4: MORE SEARCH ALGORITHMS DIT411/TIN175, Artificial Intelligence Peter Ljunglöf 23 January, 2018 1 TABLE OF CONTENTS
More informationINTRODUCTION TO HEURISTIC SEARCH
INTRODUCTION TO HEURISTIC SEARCH What is heuristic search? Given a problem in which we must make a series of decisions, determine the sequence of decisions which provably optimizes some criterion. What
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 informationDownloaded from ioenotes.edu.np
Chapter- 3: Searching - Searching the process finding the required states or nodes. - Searching is to be performed through the state space. - Search process is carried out by constructing a search tree.
More informationLecture 4: Search 3. Victor R. Lesser. CMPSCI 683 Fall 2010
Lecture 4: Search 3 Victor R. Lesser CMPSCI 683 Fall 2010 First Homework 1 st Programming Assignment 2 separate parts (homeworks) First part due on (9/27) at 5pm Second part due on 10/13 at 5pm Send homework
More informationInformed Search and Exploration
Informed Search and Exploration Chapter 4 (4.1-4.3) CS 2710 1 Introduction Ch.3 searches good building blocks for learning about search But vastly inefficient eg: Can we do better? Breadth Depth Uniform
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 informationHeuristic Search. Robert Platt Northeastern University. Some images and slides are used from: 1. CS188 UC Berkeley 2. RN, AIMA
Heuristic Search Robert Platt Northeastern University Some images and slides are used from: 1. CS188 UC Berkeley 2. RN, AIMA Recap: What is graph search? Start state Goal state Graph search: find a path
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 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 informationMidterm Examination CS 540-2: Introduction to Artificial Intelligence
Midterm Examination CS 54-2: Introduction to Artificial Intelligence March 9, 217 LAST NAME: FIRST NAME: Problem Score Max Score 1 15 2 17 3 12 4 6 5 12 6 14 7 15 8 9 Total 1 1 of 1 Question 1. [15] State
More informationSolving Problems by Searching
INF5390 Kunstig intelligens Solving Problems by Searching Roar Fjellheim Outline Problem-solving agents Example problems Search programs Uninformed search Informed search Summary AIMA Chapter 3: Solving
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 informationDFS. Depth-limited Search
DFS Completeness? No, fails in infinite depth spaces or spaces with loops Yes, assuming state space finite. Time complexity? O(b m ), terrible if m is much bigger than d. can do well if lots of goals Space
More informationCS 188: Artificial Intelligence. Recap Search I
CS 188: Artificial Intelligence Review of Search, CSPs, Games DISCLAIMER: It is insufficient to simply study these slides, they are merely meant as a quick refresher of the high-level ideas covered. You
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 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 informationSolving Problems by Searching
INF5390 Kunstig intelligens Sony Vaio VPC-Z12 Solving Problems by Searching Roar Fjellheim Outline Problem-solving agents Example problems Search programs Uninformed search Informed search Summary AIMA
More informationArtificial Intelligence Search: summary&exercises. Peter Antal
Artificial Intelligence Search: summary&exercises Peter Antal antal@mit.bme.hu 1 A problem is defined by: An initial state, e.g. Arad Successor function S(X)= set of action-state pairs e.g. S(Arad)={
More informationGraphs vs trees up front; use grid too; discuss for BFS, DFS, IDS, UCS Cut back on A* optimality detail; a bit more on importance of heuristics,
Graphs vs trees up front; use grid too; discuss for BFS, DFS, IDS, UCS Cut back on A* optimality detail; a bit more on importance of heuristics, performance data Pattern DBs? General Tree Search function
More informationSet 2: State-spaces and Uninformed Search. ICS 271 Fall 2015 Kalev Kask
Set 2: State-spaces and Uninformed Search ICS 271 Fall 2015 Kalev Kask You need to know State-space based problem formulation State space (graph) Search space Nodes vs. states Tree search vs graph search
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 informationHeuristic Search: A* CPSC 322 Search 4 January 19, Textbook 3.6 Taught by: Vasanth
Heuristic Search: A* CPSC 322 Search 4 January 19, 2011 Textbook 3.6 Taught by: Vasanth 1 Lecture Overview Recap Search heuristics: admissibility and examples Recap of BestFS Heuristic search: A* 2 Example
More informationCS188: Artificial Intelligence, Fall 2008
CS188: Artificial Intelligence, Fall 008 CS188 Spring 010Written SectionAssignment 1: Search 1 Due: September 11th at the beginning of lecture 1 Search algorithms in action ( ) 1 Graph Search Strategies
More informationArtificial Intelligence
COMP224 Artificial Intelligence The Meaning of earch in AI The terms search, search space, search problem, search algorithm are widely used in computer science and especially in AI. In this context 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 informationHEURISTIC SEARCH. Heuristics: Rules for choosing the branches in a state space that are most likely to lead to an acceptable problem solution.
HEURISTIC SEARCH Heuristics: Used when: Rules for choosing the branches in a state space that are most likely to lead to an acceptable problem solution. Information has inherent ambiguity computational
More informationUniversity of Waterloo Department of Electrical and Computer Engineering ECE 457A: Cooperative and Adaptive Algorithms Midterm Examination
University of Waterloo Department of Electrical and Computer Engineering ECE 457A: Cooperative and Adaptive Algorithms Midterm Examination Exam Date/Time: Tuesday, June 13, 2017, 8:30-9:50 pm Exam Hall:
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 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 LECTURE 3. Ph. D. Lect. Horia Popa Andreescu rd year, semester 5
ARTIFICIAL INTELLIGENCE LECTURE 3 Ph. D. Lect. Horia Popa Andreescu 2012-2013 3 rd year, semester 5 The slides for this lecture are based (partially) on chapter 4 of the Stuart Russel Lecture Notes [R,
More informationGraph and Heuristic Search. Lecture 3. Ning Xiong. Mälardalen University. Agenda
Graph and Heuristic earch Lecture 3 Ning iong Mälardalen University Agenda Uninformed graph search - breadth-first search on graphs - depth-first search on graphs - uniform-cost search on graphs General
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 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 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 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 informationAI: Week 2. Tom Henderson. Fall 2014 CS 5300
AI: Week 2 Tom Henderson Fall 2014 What s a Problem? Initial state Actions Transition model Goal Test Path Cost Does this apply to: Problem: Get A in CS5300 Solution: action sequence from initial to goal
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 informationArtificial Intelligence. Chapters Reviews. Readings: Chapters 3-8 of Russell & Norvig.
Artificial Intelligence Chapters Reviews Readings: Chapters 3-8 of Russell & Norvig. Topics covered in the midterm Solving problems by searching (Chap. 3) How to formulate a search problem? How to measure
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 informationChapters 3-5 Problem Solving using Search
CSEP 573 Chapters 3-5 Problem Solving using Search First, they do an on-line search CSE AI Faculty Example: The 8-puzzle Example: The 8-puzzle 1 2 3 8 4 7 6 5 1 2 3 4 5 6 7 8 2 Example: Route Planning
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 informationLearning Objectives. c D. Poole and A. Mackworth 2010 Artificial Intelligence, Lecture 3.3, Page 1
Learning Objectives At the end of the class you should be able to: devise an useful heuristic function for a problem demonstrate how best-first and A search will work on a graph predict the space and time
More informationToday s s lecture. Lecture 3: Search - 2. Problem Solving by Search. Agent vs. Conventional AI View. Victor R. Lesser. CMPSCI 683 Fall 2004
Today s s lecture Search and Agents Material at the end of last lecture Lecture 3: Search - 2 Victor R. Lesser CMPSCI 683 Fall 2004 Continuation of Simple Search The use of background knowledge to accelerate
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 informationAnnouncements. Solution to Assignment 1 is posted Assignment 2 is available Video automatically uploaded (see web page)
Announcements Solution to Assignment 1 is posted Assignment 2 is available Video automatically uploaded (see web page) c D. Poole and A. Mackworth 2017 CPSC 322 Lecture 4 1 / 27 Review: Searching A frontier
More informationC P E / C S C A RTIFICIAL I N T E L L I G E N C E M I D T E R M S E C T I O N 1 FA L L
C P E / C S C 4 8 0 A RTIFICIAL I N T E L L I G E N C E M I D T E R M S E C T I O N 1 FA L L 2 0 0 5 PRO F. FRANZ J. KURFESS CAL POL Y, COMPUTER SCIENCE DE PARTMENT This is the Fall 2005 midterm exam for
More informationAdvanced A* Improvements
Advanced A* Improvements 1 Iterative Deepening A* (IDA*) Idea: Reduce memory requirement of A* by applying cutoff on values of f Consistent heuristic function h Algorithm IDA*: 1. Initialize cutoff to
More informationDIT411/TIN175, Artificial Intelligence. Peter Ljunglöf. 19 January, 2018
DIT411/TIN175, Artificial Intelligence Chapter 3: Classical search algorithms CHAPTER 3: CLASSICAL SEARCH ALGORITHMS DIT411/TIN175, Artificial Intelligence Peter Ljunglöf 19 January, 2018 1 DEADLINE FOR
More informationHW#1 due today. HW#2 due Monday, 9/09/13, in class Continue reading Chapter 3
9-04-2013 Uninformed (blind) search algorithms Breadth-First Search (BFS) Uniform-Cost Search Depth-First Search (DFS) Depth-Limited Search Iterative Deepening Best-First Search HW#1 due today HW#2 due
More informationSearch and Optimization
Search and Optimization Search, Optimization and Game-Playing The goal is to find one or more optimal or sub-optimal solutions in a given search space. We can either be interested in finding any one solution
More informationState Space Search. Many problems can be represented as a set of states and a set of rules of how one state is transformed to another.
State Space Search Many problems can be represented as a set of states and a set of rules of how one state is transformed to another. The problem is how to reach a particular goal state, starting from
More informationPrinciples of Artificial Intelligence Fall 2005 Handout #3 Heuristic Problem Solvers
Principles of Artificial Intelligence Fall 2005 Handout #3 Heuristic Problem Solvers Vasant Honavar Artificial Intelligence Research Laboratory Department of Computer Science 226 Atanasoff Hall Iowa State
More information3.6.2 Generating admissible heuristics from relaxed problems
3.6.2 Generating admissible heuristics from relaxed problems To come up with heuristic functions one can study relaxed problems from which some restrictions of the original problem have been removed The
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 informationCS 771 Artificial Intelligence. Problem Solving by Searching Uninformed search
CS 771 Artificial Intelligence Problem Solving by Searching Uninformed search Complete architectures for intelligence? Search? Solve the problem of what to do. Learning? Learn what to do. Logic and inference?
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 informationCS 5522: Artificial Intelligence II
CS 5522: Artificial Intelligence II Search Algorithms Instructor: Wei Xu Ohio State University [These slides were adapted from CS188 Intro to AI at UC Berkeley.] Today Agents that Plan Ahead Search Problems
More informationSearching. Assume goal- or utilitybased. Next task to achieve is to determine the best path to the goal
Searching Assume goal- or utilitybased agents: state information ability to perform actions goals to achieve Next task to achieve is to determine the best path to the goal CSC384 Lecture Slides Steve Engels,
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 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 informationArtificial Intelligence
Artificial Intelligence Dr. Malek Mouhoub Department of Computer Science University of Regina Fall 2005 Malek Mouhoub, CS820 Fall 2005 1 3. State-Space Search 3. State-Space Search Graph Theory Uninformed
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 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 informationCMU-Q Lecture 2: Search problems Uninformed search. Teacher: Gianni A. Di Caro
CMU-Q 15-381 Lecture 2: Search problems Uninformed search Teacher: Gianni A. Di Caro RECAP: ACT RATIONALLY Think like people Think rationally Agent Sensors? Actuators Percepts Actions Environment Act like
More informationHeuristic Search. CPSC 470/570 Artificial Intelligence Brian Scassellati
Heuristic Search CPSC 470/570 Artificial Intelligence Brian Scassellati Goal Formulation 200 Denver 300 200 200 Chicago 150 200 Boston 50 1200 210 75 320 255 Key West New York Well-defined function that
More informationPrincess Nora University Faculty of Computer & Information Systems ARTIFICIAL INTELLIGENCE (CS 370D) Computer Science Department
Princess Nora University Faculty of Computer & Information Systems 1 ARTIFICIAL INTELLIGENCE (CS 370D) Computer Science Department (CHAPTER-3-PART1) PROBLEM SOLVING AND SEARCH (Course coordinator) WHY
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 informationCS-171, Intro to A.I. Mid-term Exam Winter Quarter, 2016
CS-171, Intro to A.I. Mid-term Exam Winter Quarter, 016 YOUR NAME: YOUR ID: ID TO RIGHT: ROW: SEAT: The exam will begin on the next page. Please, do not turn the page until told. When you are told to begin
More informationCS 4700: Artificial Intelligence
CS 4700: Foundations of Artificial Intelligence Fall 2017 Instructor: Prof. Haym Hirsh Lecture 7 Extra Credit Opportunity: Lecture Today 4:15pm Gates G01 Learning to See Without a Teacher Phillip Isola
More informationInformed search algorithms. (Based on slides by Oren Etzioni, Stuart Russell)
Informed search algorithms (Based on slides by Oren Etzioni, Stuart Russell) The problem # Unique board configurations in search space 8-puzzle 9! = 362880 15-puzzle 16! = 20922789888000 10 13 24-puzzle
More information1 Tree Search (12 points)
1 Tree Search (12 points) Consider the tree shown below. The numbers on the arcs are the arc lengths. Assume that the nodes are expanded in alphabetical order when no other order is specified by the search,
More informationPAC-MAN is one of the most popular game
SCHOOL OF DATA SCIENCE 1 Assignment1. Search in Pacman Project Report Shihan Ran - 15307130424 Abstract This project is aimed at designing a intelligent Pacman agent that is able to find optimal paths
More informationAlgorithm Design Techniques (III)
Algorithm Design Techniques (III) Minimax. Alpha-Beta Pruning. Search Tree Strategies (backtracking revisited, branch and bound). Local Search. DSA - lecture 10 - T.U.Cluj-Napoca - M. Joldos 1 Tic-Tac-Toe
More informationCS 540: Introduction to Artificial Intelligence
CS 540: Introduction to Artificial Intelligence Midterm Exam: 7:15-9:15 pm, October, 014 Room 140 CS Building CLOSED BOOK (one sheet of notes and a calculator allowed) Write your answers on these pages
More informationCS 188 Introduction to Artificial Intelligence Fall 2018 Note 1
CS 188 Introduction to Artificial Intelligence Fall 2018 Note 1 These lecture notes are heavily based on notes originally written by Nikhil Sharma. Agents In artificial intelligence, the central problem
More information