SEARCH STRATEGIES KANOKWATT SHIANGJEN COMPUTER SCIENCE SCHOOL OF INFORMATION AND COMMUNICATION TECHNOLOGY UNIVERSITY OF PHAYAO

Transcription

1 SEARCH STRATEGIES KANKWATT SHIANGJEN CMPUTER SCIENCE SCHL F INFRMATIN AND CMMUNICATIN TECHNLGY UNIVERSITY F PHAYA

2 Search Strategies Uninformed Search Strategies (Blind Search): เป นกลย ทธ การ ค นหาเหม อนคนตาบอดคลาช าง ค อ ไม ม ข อม ลเก ยวก บสถานะ (State) ก อนหน า โดยทาการสร าง Successor แล วน ามาเปร ยบเท ยบเพ อหา Goal State Informed Search and Exploration: เป นกลย ทธ การค นหาท สามารถ เปร ยบเท ยบผลการค นหาก อนหน า ก บผลค นหาป จจ บ น เพ อให ได คาตอบท ด กว า 2

3 Uninformed Search Strategies Breadth-First Search Depth-First Search Bidirectional Search Etc. Source: Source: 3

4 Graph Representation A regular graph Adjacency matrix Adjacency list Source: 4

5 Informed Search and Exploration Greedy Best-First Search A* Search Heuristic Local Search Hill-climbing Search Simulated Annealing Genetic Algorithms Etc. 5

6 Greedy Best-First Search: GBFS Source: 6

7 GBFS: Arad To Bucharest f(n) = h(n) where f(n) is evaluation function h(n) is heuristic function Sibiu 253 Arad 366 Timisoara 329 Zerind 374 Fagaras Rimnicu Vilcea Arad radea Bucharest 0 Sibiu 253 Total Distance = = 450 km 7

8 A* Search 8

9 A* Search: Arad To Bucharest f(n) = g(n) + h(n) where f(n) is evaluation function g(n) is path cost h(n) is heuristic function 99 Fagaras 415= = Bucharest Sibiu Arad Sibiu Timisoara 393= = = = = = = = Bucharest 0 97 Pitesti Craiova 160 Craiova Rimnicu Vilcea Rimnicu Arad Vilcea = = = = = Sibiu 253 Zerind radea 380 Source: 9

10 Heuristic Heuristic is the problem solving approach that can find some of satisfy solution. However, the solution may not guaranteed to be optimal. Source: 10

11 Heuristic: 8-Puzzle problem Source: 11

12 Heuristic: 8-Puzzle problem If the solution to the puzzle has 20 steps. The branching factor is about 3 Therefore, an exhaustive search to depth will be 3 20 states Source: 12

13 4 Queen Problem Source: 13

14 4 Queen Problem Greedy algorithm: first fit cannot find the solution Backtracking depth-first search: found the solution14

15 Minimax (Tic-Tac-Toe) MA () MIN () 15

16 Minimax (Tic-Tac-Toe) MA () MIN () MA () 16

17 Minimax (Tic-Tac-Toe) MA () MIN () MA () 17

18 MA () MIN () MA () MIN () 18

19 MA () MIN () MA () MIN () = = 2-10 กำหนดค ำ Weight ในแต ละระด บม ค ำ เพ มข นท ละ 1 โดยกำรวำงท งหมด 9 ช องม ได ไม เก น 10 คร ง กำหนดให Weight = ค ำระด บ 10 กรณ ท ชนะกำหนดให Weight = = = = = 2-10

20 MA () MIN () MA () MIN () กำรกำหนดค ำ Weight คงท ในบำง กรณ อำจส งผลให ไม สำมำรถสร ำง ทำงเล อกได อย ำงเหมำะสม กรณ ท ชนะกำหนดให Weight = -1 กรณ ท ชนะกำหนดให Weight =

21 Alpha-Beta 2 MA 2 1 MIN

22 Alpha-Beta MA MIN MA MIN

23 Alpha-Beta MA 6 MIN 5 6 MA MIN

24 Alpha-Beta MA 6 MIN 5 6 MA MIN

25 Alpha-Beta Pruning MA 5 6 MIN MA MIN

26 Heuristic: Bin Packing 26

27 Heuristic: Bin Packing Image from 27

28 Heuristic: Bin Packing Next Fit: The algorithm will consider only the current level of spaces for packing the item. If the item can fit the space, then place it into that space. therwise, a new level of spaces will be created and place it into the new level. The computational time of NF is (n). First Fit: The FF algorithm is designed for reducing the wastage of space from NF. This algorithm will consider every level of spaces for packing the item, start from bottom to the top of the container and place the item at the first space that it can fit the space. The computational time of FF is Θ(n log n). 28

29 Heuristic: Bin Packing Best Fit: The BF algorithm is designed for reducing the wastage of space from FF. This algorithm will consider every level of spaces for packing the item, start from bottom to the top of the container and place the item at the space that it can fit and leave the least wastage of the space. The computational time of BF is (n 2 ). 29

30 30

31 Example Bin packing problem given Input = 12, 9, 17, 12, 10, 15, 10, 8, 1, 7, 2, 5, 2, 10 Bin capacity = 30 bjective function Minimize: #Bin Constraint: σ n i=1 input ij bin j 31

32 Example (Cont.) Input = 12, 9, 17, 12, 10, 15, 10, 8, 1, 7, 2, 5, 2, 10 Sort = 17, 15, 12, 12, 10, 10, 10, 9, 8, 7, 5, 2, 2, 1 Bin capacity = 30 #Bin = n input Τ i bin capacity σ i=1 = σ 14 i=1 input i Τ30 = 120/30 = 4 Meta-heuristic Bin #1: {17}, {10}, {2}, {1} Bin #2: {15}, {10}, {5} Bin #3: {12}, {10}, {8} Bin #4: {12}, {9}, {7}, {2} Best Fit Bin #1: {17}, {12}, {1} Bin #2: {15}, {12}, {2} Bin #3: {10}, {10}, {10} Bin #4: {9}, {8}, {7}, {5} Bin #5: {2} Next Fit Bin #1: {17} Bin #2: {15}, {12} Bin #3: {12}, {10} Bin #4: {10}, {10}, {9} Bin #5: {8}, {7}, {2}, {2}, {1} First Fit Bin #1: {17}, {12}, {1} Bin #2: {15}, {12}, {2} Bin #3: {10}, {10}, {10} Bin #4: {9}, {8}, {7}, {5} Bin #5: {2} 32

33 Local Search Source: 33

34 Hill-climbing Search Cost 10 Up hill Down hill 0 Global minimum Configuration 34

35 Hill-climbing Search Cost 10 Up hill 0 Global minimum Down hill Configuration 35

36 Simulated Annealing Cost 10 S 1 0 Global minimum Configuration 36

37 Simulated Annealing Cost 10 Acceptance Criteria S 1 0 Global minimum Configuration 37

38 Genetic Algorithms Source: Source: 38

39 Genetic Algorithms Source: Source: 39

40 Source: 40

41 Genetic with Neural Network Source:

42 Evolutionary Algorithms Source: Source: 42

43 Q & A 43