Dr. Alexandra I. Cristea acristea/ CS 319: Theory of Databases: C6.
Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.
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Transcript of Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.
![Page 1: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/1.jpg)
Intelligent Systems (2II40)C3
Alexandra I. CristeaSeptember 2005
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Outline
II. Intelligent agents
III. Search1. Uninformed
2. InformedA. Heuristic
B. Local
C. Online
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Iterative deepening search
• Depth first search with growing depth
ll = allowed maximal depth in tree
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Iterative deepening search example
Aradl = 0
![Page 5: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/5.jpg)
Iterative deepening search example
Aradl = 1
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Iterative deepening search example
l = 1Arad
Zerind Sibiu Timisoara
![Page 7: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/7.jpg)
Iterative deepening search example
Aradl = 2
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Iterative deepening search example
l = 2Arad
Zerind Sibiu Timisoara
![Page 9: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/9.jpg)
Iterative deepening search example
l = 2
Arad Oradea
Arad
Zerind Sibiu Timisoara
![Page 10: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/10.jpg)
Iterative deepening search example
l = 2
Arad
Arad
Sibiu Timisoara
Oradea Fagarash RamnicuValcea
![Page 11: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/11.jpg)
Iterative deepening search example
l = 2Arad
Timisoara
Arad Lugoj
![Page 12: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/12.jpg)
Proprieties of iterative deepening search
• Complete?Complete? Yes (b,d finite)
• Time?Time? (d+1) + db + (d-1)b2 + …+ bd = O(bd)
• Space?Space? O(bd)
• Optimal?Optimal? Yes (b,d finite & cost/step=1)
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Outline
II. Intelligent agents
III. Search1. Uninformed
2. InformedA. Heuristic
B. Local
C. Online
![Page 14: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/14.jpg)
Uniform cost search
• Expand least cost node first
• Implementation: increasing cost order queue
• = min(cost/step): the smallest step cost
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Ex: Romania w. step costs (km)
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Uniform cost example
Arad
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Uniform cost example
Arad
Zerind Sibiu Timisoara
75140
118
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Uniform cost example
Arad
Sibiu
75140
118
Arad Oradea
Zerind75+75=
150 75+71=146
Timisoara
Arad Lugoj236
111+118=229
![Page 19: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/19.jpg)
Uniform cost example
Arad
Sibiu
75140
118
Arad Oradea
Zerind
150 146
Timisoara
Arad Lugoj
220 229
Arad Oradea RamnicuValceaFagarash
280 239 291 236
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Uniform cost example
Arad
Sibiu
75140
118
Arad Oradea
Zerind
150 146
Timisoara
Arad Lugoj
220 229
Arad Oradea RamnicuValceaFagarash
280 239 291 236
Zerind Sibiu
297217
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Uniform cost example
Arad
Sibiu
75140
118
Arad Oradea
Zerind
150 146
Timisoara
Arad Lugoj
220 229
Arad Oradea RamnicuValceaFagarash
280 239 291 236
Zerind Sibiu
297217
225 290268
![Page 22: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/22.jpg)
Uniform cost example
Arad
Sibiu
75140
118
Arad Oradea
Zerind
150 146
Timisoara
Arad Lugoj
220 229
Arad Oradea RamnicuValceaFagarash
280 239 291 236
Zerind Sibiu
297217
225 290268
Sibiu Pitesti Craiova
300 317 382
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Uniform cost example
Arad
Sibiu
75140
118
Arad Oradea
Zerind
150 146
Timisoara
Arad Lugoj
220 229
Arad Oradea RamnicuValceaFagarash
280 239 291 236
Zerind Sibiu
297217
225 290268
Sibiu Pitesti Craiova
300 317 382
![Page 24: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/24.jpg)
Properties of uniform cost search
• Complete?Complete? Yes (b,d finite & cost/step )
• Optimal?Optimal? Yes (b,d finite & cost/step )• Time?Time? O(bC*/) (C* : cost optimal solution)
• Space?Space? O(bC*/)
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III.2. Informed search algorithms
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III.2. Informed Search Strategies
• A. Heuristic– Best-first search
• Greedy search
• A* search
• B. Local– Hill climbing– Simulated annealing– Genetic algorithms
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Best first search
• f(n)f(n): evaluation function: – desirability of n
• Implementation: – queue of decreasing desirability
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Greedy search
• f(n) = h(n)f(n) = h(n),
• h(n): heuristic : distance from n to goal
• expands n closest to goal
• Important: heuristic should be admissibleadmissible:– h(n) h*(n), with: – h*(n)= real cost from n to goal
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Example Greedy search
• Map of Romania
• possible heuristic :hsld(n) = straight_line_distance (n, Bucharest)
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Greedy search example
Arad 366
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Greedy search example
366Arad
Zerind Timisoara374 253 329
Sibiu
![Page 32: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/32.jpg)
Greedy search example
366Arad
Zerind Timisoara
366
253 329
Arad
Sibiu
Oradea RamnicuValcea
380 178 193Fagarash
374
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Greedy search example
366Arad
Zerind Timisoara
366
253 329
Arad
Sibiu
Oradea RamnicuValcea
380 178 193Fagarash
Sibiu Bucharest253 0
374
![Page 34: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/34.jpg)
Properties of Greedy search
• Complete?Complete? No (could get stuck in loops)
• Optimal?Optimal? No
• Time?Time? O(bm)
• Space?Space? O(bm)
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Homework 3 – part 1
1. Check Dijkstra’s Greedy algorithm and shortly compare!
2. Give 3 recent applications of a (modified) Greedy algorithm. Explain in what consists the application, evtl. the modification, and give your source.
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A* search
• f(n) = g(n) + h(n)f(n) = g(n) + h(n): – g(n)g(n): real (!!) cost from start to n– h(n)h(n): heuristic: distance from n to goal
• NOTE:– considers the whole cost incurred from start to
goal at all times !!
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A* search example
Arad 366
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A* search example
366Arad
Zerind Timisoara374+75
=449393 447
Sibiu
75140
118
![Page 39: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/39.jpg)
A* search example
366Arad
Zerind Timisoara
646
393 447
Arad
Sibiu
Oradea RamnicuValcea
671 417 413Fagarash
75140
118
140 151 99 80
449
![Page 40: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/40.jpg)
A* search example
366Arad
Zerind Timisoara
646
393 447
Arad
Sibiu
Oradea RamnicuValcea
671 417 413Fagarash
75140
118
140 80
449
Sibiu Craiova Pitesti
80 146 97
553 526 415
151 99
![Page 41: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/41.jpg)
A* search example
366Arad
Zerind Timisoara
646
393 447
Arad
Sibiu
Oradea RamnicuValcea
671 417 413Fagarash
75140
118
140 80
449
Sibiu Craiova Pitesti
80 146 97
553 526 415
Rm.Vilcea Craiova Bucharest607 615 418
97 138 101
151 99
![Page 42: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/42.jpg)
A* search example
366Arad
Zerind Timisoara
646
393 447
Arad
Sibiu
Oradea RamnicuValcea
671 417 413Fagarash
75140
118
140 80
449
Sibiu Bucharest591 450
21199
Sibiu Craiova Pitesti
80 146 97
553 526 415
Rm.Vilcea Craiova Bucharest138 101
97
607 615 418
151 99
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Properties of A* search
• Complete?Complete? Yes (if # nodes w. f C* finite)
• Optimal?Optimal? Yes; optimally efficient!! • Time?Time? O (b(rel. err. in h) x (length of solution))
• Space?Space? All nodes in memory
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Optimality A*
• Be G optimal goal state (path cost f*)
• Be G2 suboptimal goal state (local minimum)f(G2) = g(G2) (heuristic zero in goal state)
f(G2) > f* (G2 suboptimal)
• n fringe node on optimal path to G
• h is admissible : f(n) = g(n) + h(n) g(n) + h*(n) = f*.
f(n) f*< f(G2)
• n will be chosen instead of G2, q.e.d.
![Page 45: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/45.jpg)
Improved A* alg.
• IDA* = A* + iterative deepening depending on f• RBFS = recursive depth first search +
remembering value of best ancestor; space=O(bd)
• MA* = memory bound A* (use of available memo only)
• SMA* = simple MA* (A*; if memo full, discard worst node, but store f value of children w. parents)
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Summary (un-)informed search
• Uninformed – ‘blind’
– computationally cheaper (heuristic?)
• Research continues on finding better search – i.e., problem solving algorithms
• Informed + uninformed: – global search algorithms
– exponential time+space (10120 molecules in universe)
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Homework 3 - part 2
3. Read the LAO* paper find the different notations used by the author for the properties of the search algorithm and make a table of equivalences; Describe LAO* in terms of these properties; comment upon dimensions of AI (as in C1) that you find in the LAO* algorithm.
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II.2.B. Local Search
• Greedy local search (hill-climbing)
• Simulated annealing
• Genetic algorithms
![Page 49: Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005.](https://reader035.fdocuments.in/reader035/viewer/2022062221/56649ee65503460f94bf6ae9/html5/thumbnails/49.jpg)
Homework 3 – part 2
7. Perform steps FAQ 5-6 of the project.