Intelligent Systems (2II40) C3 Alexandra I. Cristea September 2005

Outline II.Intelligent agents III.Search 1.Uninformed 2.Informed A.Heuristic B.Local C.Online

Iterative deepening search Depth first search with growing depth l l = allowed maximal depth in tree

Iterative deepening search example Arad l = 0

Iterative deepening search example Arad l = 1

Iterative deepening search example l = 1 Arad ZerindSibiuTimisoara

Iterative deepening search example Arad l = 2

Iterative deepening search example l = 2 Arad ZerindSibiuTimisoara

Iterative deepening search example l = 2 AradOradea Arad ZerindSibiuTimisoara

Iterative deepening search example l = 2 Arad SibiuTimisoara OradeaFagarash Ramnicu Valcea

Iterative deepening search example l = 2 Arad Timisoara AradLugoj

Proprieties of iterative deepening search Complete?Complete? Yes (b,d finite) Time?Time? (d+1) + db + (d-1)b 2 + …+ b d = O(b d ) Space?Space? O(bd) Optimal?Optimal? Yes (b,d finite & cost/step=1)

Outline II.Intelligent agents III.Search 1.Uninformed 2.Informed A.Heuristic B.Local C.Online

Uniform cost search Expand least cost node first Implementation: increasing cost order queue   = min(cost/step): the smallest step cost

Ex: Romania w. step costs (km)

Uniform cost example Arad

Uniform cost example Arad ZerindSibiuTimisoara

Uniform cost example Arad Sibiu AradOradea Zerind 75+75= = 146 Timisoara AradLugoj = 229

Uniform cost example Arad Sibiu AradOradea Zerind Timisoara AradLugoj AradOradea Ramnicu Valcea Fagarash

Uniform cost example Arad Sibiu AradOradea Zerind Timisoara AradLugoj AradOradea Ramnicu Valcea Fagarash Zerind Sibiu

Uniform cost example Arad Sibiu AradOradea Zerind Timisoara AradLugoj AradOradea Ramnicu Valcea Fagarash Zerind Sibiu

Uniform cost example Arad Sibiu AradOradea Zerind Timisoara AradLugoj AradOradea Ramnicu Valcea Fagarash Zerind Sibiu SibiuPitestiCraiova

Uniform cost example Arad Sibiu AradOradea Zerind Timisoara AradLugoj AradOradea Ramnicu Valcea Fagarash Zerind Sibiu SibiuPitestiCraiova

Properties of uniform cost search Complete?Complete? Yes (b,d finite & cost/step   ) Optimal?Optimal? Yes (b,d finite & cost/step   ) Time?Time? O(b C*/  ) ( C* : cost optimal solution) Space?Space? O(b C*/  )

III.2. Informed search algorithms

III.2. Informed Search Strategies A. Heuristic –Best-first search Greedy search A* search B. Local –Hill climbing –Simulated annealing –Genetic algorithms

Best first search f(n)f(n) : evaluation function: –desirability of n Implementation: –queue of decreasing desirability

Greedy search f(n) = h(n)f(n) = h(n), h(n): heuristic : distance from n to goal expands n closest to goal admissibleImportant: heuristic should be admissible: –h(n)  h*(n), with: –h*(n)= real cost from n to goal

Example Greedy search Map of Romania possible heuristic : h sld (n) = straight_line_distance (n, Bucharest)

Greedy search example Arad 366

Greedy search example 366 Arad ZerindTimisoara Sibiu

Greedy search example 366 Arad ZerindTimisoara Arad Sibiu Oradea Ramnicu Valcea Fagarash 374

Greedy search example 366 Arad ZerindTimisoara Arad Sibiu Oradea Ramnicu Valcea Fagarash SibiuBucharest

Properties of Greedy search Complete?Complete? No (could get stuck in loops) Optimal?Optimal? No Time?Time? O(b m ) Space?Space? O(b m )

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.

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 !!

A* search example Arad 366

A* search example 366 Arad ZerindTimisoara = Sibiu

A* search example 366 Arad ZerindTimisoara Arad Sibiu Oradea Ramnicu Valcea Fagarash

A* search example 366 Arad ZerindTimisoara Arad Sibiu Oradea Ramnicu Valcea Fagarash SibiuCraiovaPitesti

A* search example 366 Arad ZerindTimisoara Arad Sibiu Oradea Ramnicu Valcea Fagarash SibiuCraiovaPitesti Rm.VilceaCraiova Bucharest

A* search example 366 Arad ZerindTimisoara Arad Sibiu Oradea Ramnicu Valcea Fagarash Sibiu Bucharest SibiuCraiovaPitesti Rm.VilceaCraiova Bucharest

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

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.

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)

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 ( molecules in universe)

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.LAO* paper

II.2.B. Local Search Greedy local search (hill-climbing) Simulated annealing Genetic algorithms

Homework 3 – part 2 7.Perform steps FAQ 5-6 of the project.