Artificial Intelligence Lecture 4 Uninformed Search Dr Muhammad

Artificial Intelligence Lecture 4 – Uninformed Search Dr. Muhammad Adnan Hashmi 1/16/2022 1

Uninformed Search Strategies q Uninformed search strategies use only the information available in the problem definition q Breadth-first search q Uniform-cost search q Depth-first search q Depth-limited search q Iterative deepening search 1/16/2022 2

Breadth-first search q q Expand shallowest unexpanded node Implementation: Ø fringe is a FIFO queue, i. e. , new successors go at end 1/16/2022 3

Breadth-first search q q 1/16/2022 Expand shallowest unexpanded node Implementation: Ø fringe is a FIFO queue, i. e. , new successors go at end 4

Breadth-first search q q Expand shallowest unexpanded node Implementation: Ø fringe is a FIFO queue, i. e. , new successors go at end 1/16/2022 5

Breadth-first search q q Expand shallowest unexpanded node Implementation: Ø fringe is a FIFO queue, i. e. , new successors go at end 1/16/2022 6

Breadth-first search 1/16/2022 7

Properties of Breadth-first search q Complete? Yes (if b is finite) q Time? 1+b+b 2+b 3+… +bd + b(bd-1) = O(bd+1) q Space? O(bd+1) (keeps every node in memory) q Optimal? Yes (if cost = 1 per step) q Space is the bigger problem (more than time). 1/16/2022 8

Preventing Loopy Paths q q We can have search graphs (instead of trees) Ø Hence paths can go backwards, A B C B Ø Can get paths with loops A B C D B We can also have multiple paths to a node Ø From them, we are interested in the min-cost path q The Loop problem is that we “rediscover” nodes that the search has already discovered q Need to consider methods to suppress nodes that have already been visited. 1/16/2022 9

Uniform-Cost Search 1/16/2022 11

Consider the following problem… A 10 1 5 S B 5 G 5 15 C We wish to find the shortest route from node S to node G; that is, node S is the initial state and node G is the goal state. In terms of path cost, we can clearly see that the route SBG is the cheapest route. However, if we let breadth-first search loose on the problem it will find the non-optimal path SAG, assuming that A is the first node to be expanded at level 1.

Once Node node Astart is Sexpand removed is. B removed hasour been from expanded the queue it and is and removed the revealed fromnode the nodes queue (node are and G) added the is added revealed to to We We now with the initial node state at the and front expand ofthe queue, A. Press space tothe node queue. (node The G)queue isqueue added. isisthen again The sorted queue sorted on ison path again path cost. sorted cost. Nodes Note, on path with wecost. cheaper have. Note, now path found node cost G a have continue. it… goal now priority. In appears state but this in dothe case notqueue recognise the queue twice, itwill once as be it isas Node not G 10 at. Aand the (1), once front nodeof as. Bthe G (5), 11 queue. . followed As G 10 Node isbyatnode Bthe is C the(15). front cheaper of Press the queue, node. space. Press we now space. proceed to goal state. Press space. A 1 5 S 15 10 5 B C G The goal state is achieved and the path S-B-G is returned. In relation to path cost, UCS has found the optimal route. Size of Queue: 0 1 3 Queue: Empty S 10 G A, B, G B, , 11 GC, 11 C, C 15 Nodes expanded: 3 0 1 2 Current. FINISHED action: Expanding Waiting…. Backtracking SEARCH Current level: 2 n/a 0 1 UNIFORM COST SEARCH PATTERN

Uniform-Cost Search 1/16/2022 14

Uniform-Cost Search q q Expand least-cost unexpanded node Implementation: Ø q q q fringe = queue ordered by path cost Equivalent to breadth-first if step costs all equal Complete? Yes, if step cost ≥ ε Time? O(bceiling(C*/ ε)) where C* is the cost of the optimal solution Space? O(bceiling(C*/ ε)) Optimal? Yes – given the condition of completeness – you always expand the node with lowest cost Ø O(bceiling(C*/ ε)) can be greater than Ob/d 1/16/2022 15

Depth-first search q q Expand deepest unexpanded node Implementation: Ø fringe is a LIFO queue, i. e. , put successors in the front 1/16/2022 16

Depth-first search q q Expand deepest unexpanded node Implementation: Ø fringe is a LIFO queue, i. e. , put successors in the front 1/16/2022 17

Depth-first search q q Expand deepest unexpanded node Implementation: Ø fringe is a LIFO queue, i. e. , put successors in the front 1/16/2022 18

Depth-first search q q Expand deepest unexpanded node Implementation: Ø fringe is a LIFO queue, i. e. , put successors in the front 1/16/2022 19

Depth-first search q q Expand deepest unexpanded node Implementation: Ø fringe is a LIFO queue, i. e. , put successors in the front 1/16/2022 20

Depth-first search q q Expand deepest unexpanded node Implementation: Ø fringe is a LIFO queue, i. e. , put successors in the front 1/16/2022 21

Depth-first search q q Expand deepest unexpanded node Implementation: Ø fringe is a LIFO queue, i. e. , put successors in the front 1/16/2022 22

Properties of Depth-first search q Complete? No: fails in infinite-depth spaces, spaces with loops Ø q Time? O(bm): terrible if m is much larger than d Ø q q Complete in finite spaces But if solutions are dense, may be much faster than breadth-first Space? O(bm), i. e. , linear space! Optimal? No 1/16/2022 23

BFS or DFS

Depth-limited search q q Depth-first search with depth limit l, i. e. , nodes at depth l have no successors Recursive implementation: 1/16/2022 25

Depth-Limited Search q Complete? NO. Why? (l < d OR l > d) q Time? O(bl) q Space? O(bl) q Depth-first is a special case of depth-limited with l being infinite. 1/16/2022 26

Iterative deepening search 1/16/2022 27

Iterative deepening search l =0 1/16/2022 28

Iterative deepening search l =1 1/16/2022 29

Iterative deepening search l =2 1/16/2022 30

Iterative deepening search l =3 1/16/2022 31

Iterative Deepening search q q q Number of nodes generated in a depth-limited search to depth d with branching factor b: NDLS = b 0 + b 1 + b 2 + … + bd-2 + bd-1 + bd Number of nodes generated in an iterative deepening search to depth d with branching factor b: NIDS = (d+1)b 0 + d b 1 + (d-1)b 2 + … + 3 bd-2 +2 bd-1 + 1 bd For b = 10, d = 5, Ø NDLS = 1 + 100 + 1, 000 + 100, 000 = 111, 111 Ø NIDS = 6 + 50 + 400 + 3, 000 + 20, 000 + 100, 000 = 123, 456 Ø Overhead = (123, 456 - 111, 111)/111, 111 = 11% 1/16/2022 32

Properties of iterative deepening search q q Complete? Yes Time? (d+1)b 0 + d b 1 + (d-1)b 2 + … + bd = O(bd) q Space? O(bd) q Optimal? Yes, if step cost = 1 1/16/2022 33

Summary of Algorithms 1/16/2022 34

Questions 1/16/2022 35