Solving problems by searching
|
|
- Arabella Barnett
- 6 years ago
- Views:
Transcription
1 Solving problems by searching CE417: Introduction to Artificial Intelligence Sharif University of Technology Spring 2014 Soleymani Artificial Intelligence: A Modern Approach, Chapter 3
2 Outline Problem-solving agents Problem formulation and some examples of problems Search algorithms Uninformed Using only the problem definition Informed Using also problem specific knowledge 2
3 Problem-Solving Agents Problem Formulation: process of deciding what actions and states to consider States of the world Actions as transitions between states Goal Formulation: process of deciding what the next goal to be sought will be Agent must find out how to act now and in the future to reach a goal state Search: process of looking for solution (a sequence of actions that reaches the goal starting from initial state) 3
4 Problem-Solving Agents A goal-based agent adopts a goal and aim at satisfying it (as a simple version of intelligent agent maximizing a performance measure) How does an intelligent system formulate its problem as a search problem Goal formulation: specifying a goal (or a set of goals) that agent must reach Problem formulation: abstraction (removing detail) Retaining validity and ensuring that the abstract actions are easy to perform 4
5 Example: Romania On holiday in Romania; currently in Arad. Flight leaves tomorrow from Bucharest Initial state currently in Arad Map of Romania Formulate goal be in Bucharest Formulate problem states: various cities actions: drive between cities Solution sequence of cities, e.g., Arad, Sibiu, Fagaras, Bucharest 5
6 Example: Romania (Cont.) Assumptions about environment Known Observable The initial state can be specified exactly. Deterministic Each applied action to a state results in a specified state. Discrete Given the above first three assumptions, by starting in an initial state and running a sequence of actions, it is absolute where the agent will be Perceptions after each action provide no new information Can search with closed eyes (open-loop) 6
7 Problem-solving agents Formulate, Search, Execute 7
8 Problem types Deterministic and fully observable (single-state problem) Agent knows exactly its state even after a sequence of actions Solution is a sequence Non-observable or sensor-less (conformant problem) Agent s percepts provide no information at all Solution is a sequence Nondeterministic and/or partially observable (contingency problem) Percepts provide new information about current state Solution can be a contingency plan (tree or strategy) and not a sequence Often interleave search and execution Unknown state space (exploration problem) 8
9 Belief State In partially observable & nondeterministic environments, a state is not necessarily mapped to a world configuration State shows the agent s conception of the world state Agent's current belief (given the sequence of actions and percepts up to that point) about the possible physical states it might be in. 9 World states A sample belief state
10 Example: vacuum world Single-state, start in {5} Solution? [Right, Suck] Sensorless, start in {1,2,3,4,5,6,7,8} e.g., Right goes to {2,4,6,8} Solution? [Right,Suck,Left,Suck] Contingency Nondeterministic: Suck may dirty a clean carpet Partially observable: location, dirt only at the current location Percept: [L, Clean], i.e., start in {5} or {7} Solution? [Right, if dirt then Suck] 10 [Right, while dirt do Suck]
11 Single-state problem In this lecture, we focus on single-state problem Search for this type of problems is simpler And also provide strategies that can be base for search in more complex problems 11
12 Single-state problem formulation A problem is defined by five items: Initial state e.g., In( Arad) Actions: ACTIONS(s) shows set of actions that can be executed in s e.g., ACTIONS(In(Arad)) = {Go(Sibiu), Go(Timisoara), Go(Zerind)} 12
13 Single-state problem formulation A problem is defined by five items: Initial state e.g., In( Arad) Actions: ACTIONS(s) shows set of actions that can be executed in s Transition model: RESULTS(s, a) shows the state that results from doing action a in state s e.g., RESULTS(In(Arad), Go(Zerind)) = In(Zerind) 13
14 Single-state problem formulation A problem is defined by five items: Initial state e.g., In( Arad) Actions: ACTIONS(s) shows set of actions that can be executed in s Transition model: RESULTS(s, a) shows the state that results from doing action a in state s Goal test: GOAL_TEST(s) shows whether a given state is a goal state explicit, e.g., x = "at Bucharest" abstract e.g., Checkmate(x) 14
15 Single-state problem formulation A problem is defined by five items: Initial state e.g., In( Arad) Actions: ACTIONS(s) shows set of actions that can be executed in s Transition model: RESULTS(s, a) shows the state that results from doing action a in state s Goal test: GOAL_TEST(s) shows whether a given state is a goal state Path cost (additive): assigns a numeric cost to each path that reflects agent s performance measure e.g., sum of distances, number of actions executed, etc. c(x, a, y) 0 is the step cost 15
16 Single-state problem formulation A problem is defined by five items: Initial state e.g., In( Arad) Actions: ACTIONS(s) shows set of actions that can be executed in s Transition model: RESULTS(s, a) shows the state that results from doing action a in state s Goal test: GOAL_TEST(s) shows whether a given state is a goal state Path cost (additive): assigns a numeric cost to each path that reflects agent s performance measure Solution: a sequence of actions leading from the initial state to a goal state Optimal Solution has the lowest path cost among all solutions. 16
17 State Space State space: set of all reachable states from initial state Initial state, actions, and transition model together define it It forms a directed graph Nodes: states Links: actions Constructing this graph on demand 17
18 Vacuum world state space graph = 8 States States? Actions? Goal test? Path cost? dirt locations & robot location Left, Right, Suck no dirt at all locations one per action 18
19 Example: 8-puzzle 9!/2 = 181,440 States States? Actions? Goal test? Path cost? locations of eight tiles and blank in 9 squares move blank left, right, up, down (within the board) e.g., the above goal state one per move 19 Note: optimal solution of n-puzzle family is NP-complete
20 Example: 8-queens problem States Initial State? no queens on the board States? any arrangement of 0-8 queens on the board is a state Actions? Goal test? Path cost? add a queen to the state (any empty square) 8 queens are on the board, none attacked of no interest search cost vs. solution path cost 20
21 Example: 8-queens problem (other formulation) 2,057 States Initial state? States? Actions? Goal test? Path cost? 21 no queens on the board any arrangement of k queens one per column in the leftmost k columns with no queen attacking another add a queen to any square in the leftmost empty column such that it is not attacked by any other queen 8 queens are on the board of no interest
22 Example: Knuth problem Knuth Conjecture: Starting with 4, a sequence of factorial, square root, and floor operations will reach any desired positive integer. Example: 4!! = 5 States? Positive numbers Initial State? 4 Actions? Factorial (for integers only), square root, floor Goal test? State is the objective positive number Path cost? Of no interest 23
23 Read-world problems Route finding Travelling salesman problem VLSI layout Robot navigation Automatic assembly sequencing 24
24 Example: Robot navigation (real-world) Infinite set of possible actions and states Techniques are required to make the search space finite. For the robot with arms and legs or wheels, the search space becomes many-dimensional. Dealing with errors in sensor readings and motor controls 25
25 Tree search algorithm Basic idea offline, simulated exploration of state space by generating successors of already-explored states function TREE-SEARCH( problem) returns a solution, or failure initialize the frontier using the initial state of problem loop do if the frontier is empty then return failure choose a leaf node and remove it from the frontier if the node contains a goal state then return the corresponding solution expand the chosen node, adding the resulting nodes to the frontier Frontier: all leaf nodes available for expansion at any given point Different data structures (e.g, FIFO, LIFO) for frontier can cause different orders of node expansion and thus produce different search algorithms. 27
26 Tree search example 28
27 Tree search example 29
28 Tree search example 30
29 Graph Search Redundant paths in tree search: more than one way to get from one state to another may be due to a bad problem definition or the essence of the problem can cause a tractable problem to become intractable function GRAPH-SEARCH( problem) returns a solution, or failure initialize the frontier using the initial state of problem loop do if the frontier is empty then return failure choose a leaf node and remove it from the frontier if the node contains a goal state then return the corresponding solution add the node to the explored set expand the chosen node, adding the resulting nodes to the frontier only if not in the frontier or explored set explored set: remembered every explored node 31
30 Graph Search Example: rectangular grid explored frontier 32
31 Search for 8-puzzle Problem Start Goal 33 Taken from:
32 Implementation: states vs. nodes 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 cost g(x), depth 34
33 Search strategies Search strategy: order of node expansion Strategies performance evaluation: Completeness: Does it always find a solution when there is one? Time complexity: How many nodes are generated to find solution? Space complexity: Maximum number of nodes in memory during search Optimality: Does it always find a solution with minimum path cost? Time and space complexity are expressed by b (branching factor): maximum number of successors of any node d (depth): depth of the shallowest goal node m: maximum depth of any node in the search space (may be ) Time & space are described for tree search For graph search, analysis depends on redundant paths 35
34 36 Uninformed Search Algorithms
35 Uninformed (blind) search strategies No additional information beyond the problem definition Breadth-First Search (BFS) Uniform-Cost Search (UCS) Depth-First Search (DFS) Depth-Limited Search (DLS) Iterative Deepening Search (IDS) Bidirectional search 37
36 Breadth-first search Expand the shallowest unexpanded node Implementation: FIFO queue for the frontier 38
37 Breadth-first search 39
38 Breadth-first search 40
39 Breadth-first search 41
40 Properties of breadth-first search Complete? Time Yes (for finite b and d) b + b 2 + b b d = O(b d ) total number of generated nodes Space goal test has been applied to each node when it is generated O(b d 1 ) + O(b d ) = O(b d ) (graph search) Optimal? Tree search does not save much space while may cause a great time excess Yes, if path cost is a non-decreasing function of d explored frontier e.g. all actions having the same cost 43
41 Properties of breadth-first search Space complexity is a bigger problem than time complexity Time is also prohibitive Exponential-complexity search problems cannot be solved by uninformed methods (only the smallest instances) 1 million node/sec, 1kb/node d Time Memory 10 3 hours 10 terabytes days 1 pentabyte years 99 pentabytes years 10 exabytes 44
42 Uniform-Cost Search (UCS) Expand node n (in the frontier) with the lowest path cost g(n) Extension of BFS that is proper for any step cost function Implementation: Priority queue (ordered by path cost) for frontier Equivalent to breadth-first if all step costs are equal Two differences Goal test is applied when a node is selected for expansion A test is added when a better path is found to a node currently on the frontier <
43 Properties of uniform-cost search Complete? Time Yes, if step cost ε > 0 (to avoid infinite sequence of zero-cost actions) Number of nodes with g cost of optimal solution, O(b 1+ C ε ) where C is the optimal solution cost Space O(b d+1 ) when all step costs are equal Number of nodes with g cost of optimal solution, O(b 1+ C ε ) Optimal? Yes nodes expanded in increasing order of g(n) Difficulty: many long paths may exist with cost C 46
44 Uniform-cost search (proof of optimality) Lemma: If UCS selects a node n for expansion, the optimal solution to that node has been found. Proof by contradiction: Another frontier node n must exist on the optimal path from initial node to n (using graph separation property). Moreover, based on definition of path cost (due to non-negative step costs, paths never get shorter as nodes are added), we have g n g n and thus n would have been selected first. Nodes are expanded in order of their optimal path cost. 47
45 Depth First Search (DFS) Expand the deepest node in frontier Implementation: LIFO queue (i.e., put successors at front) for frontier 48
46 DFS Expand the deepest unexpanded node in frontier 49
47 DFS Expand the deepest unexpanded node in frontier 50
48 DFS Expand the deepest unexpanded node in frontier 51
49 DFS Expand the deepest unexpanded node in frontier 52
50 DFS Expand the deepest unexpanded node in frontier 53
51 DFS Expand the deepest unexpanded node in frontier 54
52 DFS Expand the deepest unexpanded node in frontier 55
53 DFS Expand the deepest unexpanded node in frontier 56
54 DFS Expand the deepest unexpanded node in frontier 57
55 DFS Expand the deepest unexpanded node in frontier 58
56 DFS Expand the deepest unexpanded node in frontier 59
57 Properties of DFS Complete? Tree-search version: not complete (repeated states & redundant paths) Graph-search version: fails in infinite state spaces (with infinite non-goal path) but complete in finite ones Time O(b m ): terrible if m is much larger than d Space In tree-version, m can be much larger than the size of the state space O(bm), i.e., linear space complexity for tree search So depth first tree search as the base of many AI areas Recursive version called backtracking search can be implemented in O(m) space Optimal? No DFS: tree-search version 61
58 Depth Limited Search Depth-first search with depth limit l (nodes at depth l have no successors) Solves the infinite-path problem In some problems (e.g., route finding), using knowledge of problem to specify l Complete? Time If l > d, it is complete O(b l ) Space O(bl) Optimal? No 62
59 Iterative Deepening Search (IDS) Combines benefits of DFS & BFS DFS: low memory requirement BFS: completeness & also optimality for special path cost functions Not such wasteful (most of the nodes are in the bottom level) 63
60 IDS: Example l =0 64
61 IDS: Example l =1 65
62 IDS: Example l =2 66
63 IDS: Example d =3 67
64 Properties of iterative deepening search Complete? Time Yes (for finite b and d) d b 1 + (d 1) b b d b d = O(b d ) Space O(bd) Optimal? Yes, if path cost is a non-decreasing function of the node depth IDS is the preferred method when search space is large and the depth of solution is unknown 68
65 Iterative deepening search Number of nodes generated to depth d: N IDS = d b 1 + (d 1) b b d b d = O(b d ) For b = 10, d = 5, we compute number of generated nodes: N BFS = , , ,000 = 111,110 N IDS = , , ,000 = 123,450 Overhead of IDS = (123, ,110)/111,110 = 11% 69
66 Bidirectional search Simultaneous forward and backward search (hoping that they meet in the middle) Idea: b d/2 + b d/2 is much less than b d Do the frontiers of two searches intersect? instead of goal test First solution may not be optimal Implementation Hash table for frontiers in one of these two searches Space requirement: most significant weakness Computing predecessors? May be difficult List of goals? a new dummy goal Abstract goal (checkmate)?! 70
67 Summary of algorithms (tree search) a Complete if b is finite b Complete if step cost ε>0 c Optimal if step costs are equal d If both directions use BFS Iterative deepening search uses only linear space and not much more time than other uninformed algorithms 71
68 Informed Search When exhaustive search is impractical, heuristic methods are used to speed up the process of finding a satisfactory solution. 72
69 Outline Best-first search Greedy best-first search A * search Finding heuristics 73
70 Best-first search Idea: use an evaluation function f(n) for each node and expand the most desirable unexpanded node More general than g n = cost so far to reach n Evaluation function provides an upper bound on the desirability (lower bound on the cost) that can be obtained through expanding a node Implementation: priority queue with decreasing order of desirability (search strategy is determined based on evaluation function) Special cases: Greedy best-first search A * search Uniform-cost search 74
71 Heuristic Function Incorporating problem-specific knowledge in search Information more than problem definition In order to come to an optimal solution as rapidly as possible Heuristic function can be used as a component of f(n) h n : estimated cost of cheapest path from n to a goal Depends only on n (not path from root to n) If n is a goal state then h(n)=0 h(n) 0 Examples of heuristic functions include using a rule-of-thumb, an educated guess, or an intuitive judgment 75
72 Greedy best-first search Evaluation function f n = h(n) e.g., h SLD n = straight-line distance from n to Bucharest Greedy best-first search expands the node that appears to be closest to goal Greedy 76
73 Romania with step costs in km 77
74 Greedy best-first search example 78
75 Greedy best-first search example 79
76 Greedy best-first search example 80
77 Greedy best-first search example 81
78 Properties of greedy best-first search Complete? No Time Space Similar to DFS, only graph search version is complete in finite spaces Infinite loops, e.g., (Iasi to Fagaras) Iasi Neamt Iasi Neamt O(b m ), but a good heuristic can give dramatic improvement O(b m ): keeps all nodes in memory Optimal? No 82
79 A * search Idea: minimizing the total estimated solution cost Evaluation function f n = g n + h(n) g n = cost so far to reach n h n = estimated cost of the cheapest path from n to goal So, f n = estimated total cost of path through n to goal Actual cost g n Estimated cost h n start n goal 83 f n = g n + h(n)
80 A * search Combines advantages of uniform-cost and greedy searches A * can be complete and optimal when h(n) has some properties 84
81 A * search: example 85
82 A * search: example 86
83 A * search: example 87
84 A * search: example 88
85 A * search: example 89
86 A * search: example 90
87 Conditions for optimality of A * Admissibility: h(n) be a lower bound on the cost to reach goal Condition for optimality of TREE-SEARCH version of A * Consistency (monotonicity): h n c n, a, n + h n Condition for optimality of GRAPH-SEARCH version of A * 91
88 Admissible heuristics Admissible heuristic h(n) never overestimates the cost to reach the goal (optimistic) h(n) is a lower bound on path cost from n to goal n, h(n) h (n) where h (n) is the real cost to reach the goal state from n Example: h SLD (n) the actual road distance 92
89 Consistent heuristics Triangle inequality n c(n, a, n ) n h(n) h(n ) G for every node n and every successor n generated by any action a h n c n, a, n + h n c n, a, n : cost of generating n by applying action to n 93
90 Consistency vs. admissibility Consistency Admissblity All consistent heuristic functions are admissible Nonetheless, most admissible heuristics are also consistent c(n 1, a 1, n 2 ) c(n 2, a 2, n 3 ) c(n k, a k, G) n 1 n 2 n 3 n k G h n 1 c n 1, a 1, n 2 + h(n 2 ) c n 1, a 1, n 2 + c n 2, a 2, n 3 + h(n 3 ) k i=1 c n i, a i, n i+1 + h(g) 0 h n 1 cost of (every) path from n 1 to goal cost of optimal path from n 1 to goal 94
91 Admissible but not consistent: Example G n n g n = 5 h n = 9 f(n) = 14 g n = 6 h n = 6 f(n ) = 12 c(n, a, n ) = 1 h(n) = 9 h(n ) = 6 h n h n + c(n, a, n ) f (for admissible heuristic) may decrease along a path Is there any way to make h consistent? h n = max (h n, h n c(n, a, n )) 95
92 Optimality of A * (admissible heuristics) Theorem: If h(n) is admissible, A * using TREE-SEARCH is optimal Assumptions: G 2 is a suboptimal goal in the frontier, n is an unexpanded node in the frontier and it is on a shortest path to an optimal goal G. I. h G 2 = 0 f G 2 = g G 2 II. h(g) = 0 f(g) = g(g) III. G 2 is suboptimal g G 2 > g G IV. I, II, III f G 2 > f G V. h is admissible h n h n g(n) + h(n) g(n) + h (n) A * will never select G 2 for expansion 96 f n f G IV f n < f(g 2 )
93 Optimality of A * (consistent heuristics) Theorem: If h(n) is consistent, A* using GRAPH-SEARCH is optimal Lemma1: if h(n) is consistent then f(n) values are nondecreasing along any path Proof: Let n be a successor of n I. f(n ) = g(n ) + h(n ) II. g(n ) = g(n) + c(n, a, n ) III. I, II f n = g n + c n, a, n + h n IV. h n is consistent h n c n, a, n + h n V. III, IV f(n ) g(n) + h(n) = f(n) 97
94 Optimality of A * (consistent heuristics) Lemma 2: If A* selects a node n for expansion, the optimal solution to that node has been found. Proof by contradiction: Another frontier node n must exist on the optimal path from initial node to n (using graph separation property). Moreover, based on Lemma 1, f n f n and thus n would have been selected first. The sequence of nodes expanded by A* (using GRAPH-SEARCH) is in nondecreasing order of f(n) Since h = 0 for goal nodes, the first selected goal node for expansion is an optimal solution (f is the true cost for goal nodes) 98
95 Admissible vs. consistent (tree vs. graph search) Consistent heuristic: When selecting a node for expansion, the path with the lowest cost to that node has been found When an admissible heuristic is not consistent, a node will need repeated expansion, every time a new best (so-far) cost is achieved for it. 99
96 Contours in the state space A * (using GRAPH-SEARCH) expands nodes in order of increasing f value Gradually adds "f-contours" of nodes Contour i has all nodes with f = f i wheref i < f i+1 A* expands all nodes with f(n) < C* A* expands some nodes with f(n) = C* (nodes on the goal contour) A* expands no nodes with f(n) > C* pruning 100
97 A * search vs. uniform cost search Uniform-cost search (A * using h(n) = 0) causes circular bands around initial state A * causes irregular bands More accurate heuristics stretched toward the goal (more narrowly focused around the optimal path) States are points in 2-D Euclidean space. g(n)=distance from start h(n)=estimate of distance from goal goal Start 101
98 Properties of A* Complete? Yes if nodes with f f G = C are finite Time? Step cost ε > 0 and b is finite Exponential But, with a smaller branching factor b h h or when equal step costs b d h h h Polynomial when h(x) h (x) = O(log h (x)) However, A* is optimally efficient for any given consistent heuristic Space? No optimal algorithm of this type is guaranteed to expand fewer nodes than A* (except to node with f = C ) Keeps all leaf and/or explored nodes in memory Optimal? Yes (expanding node in non-decreasing order of f) 102
99 Robot navigation example Initial state? Red cell States? Cells on rectangular grid (except to obstacle) Actions? Move to one of 8 neighbors (if it is not obstacle) Goal test? Green cell Path cost? Action cost is the Euclidean length of movement 103
100 A* vs. UCS: Robot navigation example Heuristic: Euclidean distance to goal Expanded nodes: filled circles in red & green Color indicating g value (red: lower, green: higher) Frontier: empty nodes with blue boundary Nodes falling inside the obstacle are discarded 104 Adopted from:
101 Robot navigation: Admissible heuristic Is Manhattan d M x, y = x 1 y 1 + x 2 y 2 distance an admissible heuristic for previous example? 105
102 A*: inadmissible heuristic h = 5 h_sld h = h_sld Adopted from: 106
103 A*, Greedy, UCS: Pacman UCS Heuristic: Manhattan distance Greedy Color: expanded in which iteration (red: lower) A* 107 Adapted from Dan Klein s slides
104 8-puzzle problem: state space b 3, average solution cost for random 8-puzzle 22 Tree search: b 3, d states Graph search: 9!/2 181,440 states for 8-puzzle for 15-puzzle 108
105 Admissible heuristics: 8-puzzle h 1 (n) = number of misplaced tiles h 2 (n) = sum of Manhattan distance of tiles from their target position i.e., no. of squares from desired location of each tile h 1 (S) = h 2 (S) = =
106 Effect of heuristic on accuracy N: number of generated nodes by A* d: solution depth Effective branching factor b : branching factor of a uniform tree of depth d containing N + 1 nodes. N + 1 = 1 + b + (b ) (b ) d Well-defined heuristic: b is close to one 110
107 Comparison on 8-puzzle Search Cost (N) d IDS A*(h 1 ) A*(h 2 ) Effective branching factor (b ) d IDS A*(h 1 ) A*(h 2 )
108 Heuristic quality If n, h 2 (n) h 1 (n) (both admissible) then h 2 dominates h 1 and it is better for search Surely expanded nodes: f n < C h n < C g n If h 2 (n) h 1 (n) then every node expanded for h 2 will also be surely expanded with h 1 (h 1 may also causes some more node expansion) 112
109 More accurate heuristic Max of admissible heuristics is admissible (while it is a more accurate estimate) h n = max (h 1 n, h 2 n ) How about using the actual cost as a heuristic? h(n) = h (n) for all n Will go straight to the goal?! Trade of between accuracy and computation time 113
110 Generating heuristics Relaxed problems Inventing admissible heuristics automatically Sub-problems (pattern databases) Learning heuristics from experience 114
111 Relaxed problem Relaxed problem: Problem with fewer restrictions on the actions Optimal solution to the relaxed problem may be computed easily (without search) The cost of an optimal solution to a relaxed problem is an admissible heuristic for the original problem The optimal solution is the shortest path in the super-graph of the statespace. 115
112 Relaxed problem: 8-puzzle 8-Puzzle: move a tile from square A to B if A is adjacent (left, right, above, below) to B and B is blank Relaxed problems 1) can move from A to B if A is adjacent to B (ignore whether or not position is blank) 2) can move from A to B if B is blank (ignore adjacency) 3) can move from A to B (ignore both conditions) Admissible heuristics for original problem (h 1 (n) and h 2 (n)) are optimal path costs for relaxed problems First case: a tile can move to any adjacent square h 2 (n) Third case: a tile can move anywhere h 1 (n) 116
113 Sub-problem heuristic The cost to solve a sub-problem Store exact solution costs for every possible sub-problem Admissible? The cost of the optimal solution to this problem is a lower bound on the cost of the complete problem 117
114 Pattern databases heuristics Storing the exact solution cost for every possible subproblem instance Combination (taking maximum) of heuristics resulted by different sub-problems 15-Puzzle: 10 3 times reduction in no. of generated nodes vs. h 2 118
115 Disjoint pattern databases Adding these pattern-database heuristics yields an admissible heuristic?! Dividing up the problem such that each move affects only one sub-problem (disjoint sub-problems) and then adding heuristics 15-puzzle: 10 4 times reduction in no. of generated nodes vs. h 2 24-Puzzle: 10 6 times reduction in no. of generated nodes vs. h 2 Can Rubik s cube be divided up to disjoint sub-problems? 119
116 Learning heuristics from experience Machine Learning Techniques Learn h(n) from samples of optimally solved problems (predicting solution cost for other states) Features of state (instead of raw state description) 8-puzzle number of misplaced tiles number of adjacent pairs of tiles that are not adjacent in the goal state Linear Combination of features 120
117 A* difficulties Space is the main problem of A* Overcoming space problem while retaining completeness and optimality IDA*, RBFS, MA*, SMA* A* time complexity Variants of A* trying to find suboptimal solutions quickly More accurate but not strictly admissible heuristics 121
Solving 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 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 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 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 informationSolving Problem by Searching. Chapter 3
Solving Problem by Searching Chapter 3 Outline Problem-solving agents Problem formulation Example problems Basic search algorithms blind search Heuristic search strategies Heuristic functions Problem-solving
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 informationSolving problems by searching
Solving problems by searching Chapter 3 Systems 1 Outline Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms Systems 2 Problem-solving agents Systems 3 Example:
More informationCS 380: Artificial Intelligence Lecture #3
CS 380: Artificial Intelligence Lecture #3 William Regli Outline Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms 1 Problem-solving agents Example: Romania
More informationOutline. Solving problems by searching. Problem-solving agents. Example: Romania
Outline Solving problems by searching Chapter 3 Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms Systems 1 Systems 2 Problem-solving agents Example: Romania
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 informationChapter 2. Blind Search 8/19/2017
Chapter 2 1 8/19/2017 Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms 8/19/2017 2 8/19/2017 3 On holiday in Romania; currently in Arad. Flight leaves tomorrow
More informationEE562 ARTIFICIAL INTELLIGENCE FOR ENGINEERS
EE562 ARTIFICIAL INTELLIGENCE FOR ENGINEERS Lecture 3, 4/6/2005 University of Washington, Department of Electrical Engineering Spring 2005 Instructor: Professor Jeff A. Bilmes 4/6/2005 EE562 1 Today: Basic
More informationSolving problems by searching
Solving problems by searching 1 C H A P T E R 3 Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms Outline 2 Problem-solving agents 3 Note: this is offline
More informationArtificial Intelligence
Artificial Intelligence CSC348 Unit 3: Problem Solving and Search Syedur Rahman Lecturer, CSE Department North South University syedur.rahman@wolfson.oxon.org Artificial Intelligence: Lecture Notes The
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 informationUninformed Search. Problem-solving agents. Tree search algorithms. Single-State Problems
Uninformed Search Problem-solving agents Tree search algorithms Single-State Problems Breadth-First Search Depth-First Search Limited-Depth Search Iterative Deepening Extensions Graph search algorithms
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 informationSolving Problems by Searching
Solving Problems by Searching Berlin Chen 2004 Reference: 1. S. Russell and P. Norvig. Artificial Intelligence: A Modern Approach. Chapter 3 1 Introduction Problem-Solving Agents vs. Reflex Agents Problem-solving
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 informationChapter 3 Solving problems by searching
1 Chapter 3 Solving problems by searching CS 461 Artificial Intelligence Pinar Duygulu Bilkent University, Slides are mostly adapted from AIMA and MIT Open Courseware 2 Introduction Simple-reflex agents
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 informationChapter3. Problem-Solving Agents. Problem Solving Agents (cont.) Well-defined Problems and Solutions. Example Problems.
Problem-Solving Agents Chapter3 Solving Problems by Searching Reflex agents cannot work well in those environments - state/action mapping too large - take too long to learn Problem-solving agent - is one
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 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 informationCAP 4630 Artificial Intelligence
CAP 4630 Artificial Intelligence Instructor: Sam Ganzfried sganzfri@cis.fiu.edu 1 http://www.ultimateaiclass.com/ https://moodle.cis.fiu.edu/ 2 Solving problems by search 3 8-puzzle 4 8-queens 5 Search
More informationAI: problem solving and search
: problem solving and search Stefano De Luca Slides mainly by Tom Lenaerts Outline Problem-solving agents A kind of goal-based agent Problem types Single state (fully observable) Search with partial information
More informationSolving problems by searching. Chapter 3
Solving problems by searching Chapter 3 Outline Problem-solving agents Problem types Problem formulation Example problems Basic search algorithms 2 Example: Romania On holiday in Romania; currently in
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 informationS A E RC R H C I H NG N G IN N S T S A T T A E E G R G A R PH P S
LECTURE 2 SEARCHING IN STATE GRAPHS Introduction Idea: Problem Solving as Search Basic formalism as State-Space Graph Graph explored by Tree Search Different algorithms to explore the graph Slides mainly
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 informationCS 8520: Artificial Intelligence
CS 8520: Artificial Intelligence Solving Problems by Searching Paula Matuszek Spring, 2013 Slides based on Hwee Tou Ng, aima.eecs.berkeley.edu/slides-ppt, which are in turn based on Russell, aima.eecs.berkeley.edu/slides-pdf.
More informationRobot Programming with Lisp
6. Search Algorithms Gayane Kazhoyan (Stuart Russell, Peter Norvig) Institute for University of Bremen Contents Problem Definition Uninformed search strategies BFS Uniform-Cost DFS Depth-Limited Iterative
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 informationAr#ficial)Intelligence!!
Introduc*on! Ar#ficial)Intelligence!! Roman Barták Department of Theoretical Computer Science and Mathematical Logic Problem Solving: Uninformed Search Simple reflex agent only transfers the current percept
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 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 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 informationProblem solving and search
Problem solving and search Chapter 3 Chapter 3 1 Problem formulation & examples Basic search algorithms Outline Chapter 3 2 On holiday in Romania; currently in Arad. Flight leaves tomorrow from Bucharest
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 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 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 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 informationChapter 3: Solving Problems by Searching
Chapter 3: Solving Problems by Searching Prepared by: Dr. Ziad Kobti 1 Problem-Solving Agent Reflex agent -> base its actions on a direct mapping from states to actions. Cannot operate well in large environments
More informationSolving problems by searching
Solving problems by searching Chapter 3 CS 2710 1 Outline Problem-solving agents Problem formulation Example problems Basic search algorithms CS 2710 - Blind Search 2 1 Goal-based Agents Agents that take
More informationBasic Search. Fall Xin Yao. Artificial Intelligence: Basic Search
Basic Search Xin Yao Fall 2017 Fall 2017 Artificial Intelligence: Basic Search Xin Yao Outline Motivating Examples Problem Formulation From Searching to Search Tree Uninformed Search Methods Breadth-first
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 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 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 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 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 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 informationArtificial Intelligence Problem Solving and Uninformed Search
Artificial Intelligence Problem Solving and Uninformed Search Maurizio Martelli, Viviana Mascardi {martelli, mascardi}@disi.unige.it University of Genoa Department of Computer and Information Science AI,
More informationArtificial Intelligence Uninformed search
Artificial Intelligence Uninformed search A.I. Uninformed search 1 The symbols&search hypothesis for AI Problem-solving agents A kind of goal-based agent Problem types Single state (fully observable) Search
More informationMultiagent Systems Problem Solving and Uninformed Search
Multiagent Systems Problem Solving and Uninformed Search Viviana Mascardi viviana.mascardi@unige.it MAS, University of Genoa, DIBRIS Classical AI 1 / 36 Disclaimer This presentation may contain material
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 informationGoal-Based Agents Problem solving as search. Outline
Goal-Based Agents Problem solving as search Vasant Honavar Bioinformatics and Computational Biology Program Center for Computational Intelligence, Learning, & Discovery honavar@cs.iastate.edu www.cs.iastate.edu/~honavar/
More informationSolving Problems: Blind Search
Solving Problems: Blind 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 are
More informationProblem solving and search
Problem solving and search Chapter 3 Chapter 3 1 How to Solve a (Simple) Problem 7 2 4 1 2 5 6 3 4 5 8 3 1 6 7 8 Start State Goal State Chapter 3 2 Introduction Simple goal-based agents can solve problems
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 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 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 informationChapter 3. A problem-solving agent is a kind of goal-based agent. It decide what to do by finding sequences of actions that lead to desirable states.
Chapter 3 A problem-solving agent is a kind of goal-based agent. It decide what to do by finding sequences of actions that lead to desirable states. A problem can be defined by four components : 1. The
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 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 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 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 informationPengju XJTU 2016
Introduction to AI Chapter03 Solving Problems by Uninformed Searching(3.1~3.4) Pengju Ren@IAIR Outline Problem-solving agents Problem types Problem formulation Search on Trees and Graphs Uninformed algorithms
More informationARTIFICIAL INTELLIGENCE (CSC9YE ) LECTURES 2 AND 3: PROBLEM SOLVING
ARTIFICIAL INTELLIGENCE (CSC9YE ) LECTURES 2 AND 3: PROBLEM SOLVING BY SEARCH Gabriela Ochoa http://www.cs.stir.ac.uk/~goc/ OUTLINE Problem solving by searching Problem formulation Example problems Search
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 informationOutline for today s lecture. Informed Search I. One issue: How to search backwards? Very briefly: Bidirectional search. Outline for today s lecture
Outline for today s lecture Informed Search I Uninformed Search Briefly: Bidirectional Search (AIMA 3.4.6) Uniform Cost Search (UCS) Informed Search Introduction to Informed search Heuristics 1 st attempt:
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 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 informationReview Search. This material: Chapter 1 4 (3 rd ed.) Read Chapter 18 (Learning from Examples) for next week
Review Search This material: Chapter 1 4 (3 rd ed.) Read Chapter 13 (Quantifying Uncertainty) for Thursday Read Chapter 18 (Learning from Examples) for next week Search: complete architecture for intelligence?
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 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 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 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
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 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 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 informationClass Overview. Introduction to Artificial Intelligence COMP 3501 / COMP Lecture 2. Problem Solving Agents. Problem Solving Agents: Assumptions
Class Overview COMP 3501 / COMP 4704-4 Lecture 2 Prof. JGH 318 Problem Solving Agents Problem Solving Agents: Assumptions Requires a goal Assume world is: Requires actions Observable What actions? Discrete
More informationCS 4700: Foundations of Artificial Intelligence. Bart Selman. Search Techniques R&N: Chapter 3
CS 4700: Foundations of Artificial Intelligence Bart Selman Search Techniques R&N: Chapter 3 Outline Search: tree search and graph search Uninformed search: very briefly (covered before in other prerequisite
More informationWeek 3: Path Search. COMP9414/ 9814/ 3411: Artificial Intelligence. Motivation. Example: Romania. Romania Street Map. Russell & Norvig, Chapter 3.
COMP9414/9814/3411 17s1 Search 1 COMP9414/ 9814/ 3411: Artificial Intelligence Week 3: Path Search Russell & Norvig, Chapter 3. Motivation Reactive and Model-Based Agents choose their actions based only
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 informationITCS 6150 Intelligent Systems. Lecture 3 Uninformed Searches
ITCS 6150 Intelligent Systems Lecture 3 Uninformed Searches Outline Problem Solving Agents Restricted form of general agent Problem Types Fully vs. partially observable, deterministic vs. stochastic Problem
More information4. Solving Problems by Searching
COMP9414/9814/3411 15s1 Search 1 COMP9414/ 9814/ 3411: Artificial Intelligence 4. Solving Problems by Searching Russell & Norvig, Chapter 3. Motivation Reactive and Model-Based Agents choose their actions
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 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 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 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 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 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 informationSearch I. slides from: Padhraic Smyth, Bryan Low, S. Russell and P. Norvig
Search I slides from: Padhraic Smyth, Bryan Low, S. Russell and P. Norvig Problem-Solving Agents Intelligent agents can solve problems by searching a state-space State-space Model the agent s model of
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 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 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 informationPengju
Introduction to AI Chapter03 Solving Problems by Uninformed Searching(3.1~3.4) Pengju Ren@IAIR Outline Problem-solving agents Problem types Problem formulation Search on Trees and Graphs Uninformed algorithms
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 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 informationInformed Search CS457 David Kauchak Fall 2011
Admin Informed Search CS57 David Kauchak Fall 011 Some material used from : Sara Owsley Sood and others Q3 mean: 6. median: 7 Final projects proposals looked pretty good start working plan out exactly
More information