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Chapter 2 Heuristic Search Techniques

Chapter 2 Heuristic Search Techniques. Defining the problem. A water jug problem: 4-gallon and 3-gallon no marker on the bottle pump to fill the water into the jug How can you get exactly 2 gallons of water into the 4-gallons jug?. 4. 3. A state space search. (x,y) : order pair

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Chapter 2 Heuristic Search Techniques

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  1. Chapter 2Heuristic Search Techniques

  2. Defining the problem • A water jug problem: 4-gallon and 3-gallon • no marker on the bottle • pump to fill the water into the jug • How can you get exactly 2 gallons of water into the 4-gallons jug? 4 3 Chapter 2

  3. A state space search (x,y) : order pair x : water in 4-gallons  x = 0,1,2,3,4 y : water in 3-gallons  y = 0,1,2,3 start state : (0,0) goal state : (2,n) where n = any value Rules : 1. Fill the 4 gallon-jug (4,-) 2. Fill the 3 gallon-jug (-,3) 3. Empty the 4 gallon-jug (0,-) 4. Empty the 3 gallon-jug (-,0) Chapter 2

  4. Water jug rules 1 (x,y) (4,y) Fill the 4-gallon jug if x < 4 2 (x,y) (x,3) Fill the 3-gallon jun if y < 3 3 (x,y) (x – d,y) Pour some water out of if x > 0 the 4-gallon jun 4 (x,y) (x,y – d) Pour some water out of if y > 0 the 3-gallon jun 5 (x,y) (0,y) Empty the 4-gallon jun if x > 0 on the ground 6 (x,y) (x,0) Empty the 3-gallon jun if y > 0 on the ground Chapter 2

  5. Water jug rules 7 (x,y) (4,y – (4 - x)) Pour water from the if x+y >= 4 and y > 0 3-gallon jug into the 4-gallon jug until the 4-gallon jug is full 8 (x,y) (x – (3 - y),3) Pour water from the if x+y >= 3 and y > 0 4-gallon jug into the 3-gallon jug until the 3-gallon jug is full 9 (x,y) (x+y,0) Pour all water from the if x+y <= 4 and y > 0 from the 3-gallon jug into the 4-gallon jug 10 (x,y) (0,x + y ) Pour all water from the if x + y <= 3 and X > 0 from the 4-gallon jug into the 3-gallon jug 11 (0,2) (2,0) Pour the 2 gallons from the 3- gallon jug into the 4-gallon jug 12 (2,y) (0,y) Empty the 2 gallons in the 4-gallon jug on the ground Chapter 2

  6. A water jug solution 4-Gallon Jug 3-Gallon Jug Rule Applied 0 0 0 3 2 3 0 9 3 3 2 4 2 7 0 2 5 or 12 2 0 9 or 11 Solution : path / plan Chapter 2

  7. Formal description of a problem The End • Define a state space that contains all the possible configurations of the relevant objects. • Specify state/states that describes the situation of start state. • Specify state/states that describes the situation of goal state. • Specify the set of rules. • assumption, generalization Chapter 2

  8. (0,0) (4,0) (0,3) (4,3) (0,0) (1,3) (4,3) (0,0) (3,0) Search Tree The End Water jug problem. Chapter 2

  9. (0,0) • (4,0) • (0,3) • (4,3) • (1,3) • (4,3) • (3,0) Search Graph The End Water jug problem. • Cycle • When will the search terminate? Chapter 2

  10. Homework 2 (1%) The End • Is there any other solution for a water jug problem? • If there is some other solution, describe in an order pair of how to solve it. • due date ................................ Chapter 2

  11. Question answering question The End Marcus was a man. Marcus was a Pompeian. Marcus was born in 40 A.D. All men are mortal. All Pompeians died when the volcano erupted in 79 A.D. No mortal lives longer than 150 years. It is now 1991 A.D. Is Marcus alive? Chapter 2

  12. Solution 1 The End 1. Marcus was man. axiom 1 4. All men are mortal. axiom 4 8. Marcus is mortal. 1,4 3. Marcus was born in 40 A.D. axiom 3 7. It is now 1991 A.D. axiom 7 9. Marcus’ age is 1951 years. 3,7 6. No mortal lives longer than 150 years axiom 6 10.Marcus is dead. 8,6,9 Chapter 2

  13. Solution 2 The End 7. It is now 1991 A.D. axiom 7 5. All Pompeians died in 79 A.D. axiom 5 11. All Pompeians are dead now. 7,5 2. Marcus was a Pompeian. axiom 2 12. Marcus is dead. 11,2 Chapter 2

  14. Understanding a sentence The End The bank president ate a dish of pasta salad with the fork. bank = financial institution / a side of a river dish = eat dish / eat pasta pasta salad : dog food  food with dog meat? with a fork : with ....her friend. / with vegetable. solution : state of the world Chapter 2

  15. A blocks world on(c,a). on(b,d). ontable(a). ontable(d). clear(b). clear(c). hand_empty. c b a d Chapter 2

  16. Seven problem characteristics The End • Decomposable Problem • Block world problem • Can solution steps be ignored or undone? • Ignorable : theorem proving solution steps can be ignored • Recoverable : 8 puzzle solution steps can be undone (backtracking) • Irrecoverable : chess solution steps can not be undone Chapter 2

  17. Seven problem characteristics The End 3. Is the universe predictable? 8-puzzel (yes) bridge (no)  but we can use probabilities of each possible outcomes controlling robot arm  gear of the arm might stuck helping the lawyer to decide how to defend his client against a murder charge. 4. Is a good solution absolute or relative? - formal inference methods - More than one solution? - traveling salesman problem Chapter 2

  18. Seven problem characteristics The End 5. Is the solution a state or a path? - consistent interpretation for the sentence - water jug problem  path / plan 6. What is the role of knowledge? knowledge for perfect program of chess (need knowledge to constrain the search) newspaper story understanding (need knowledge to recognize a solution) 7. Does the task require interaction with a person? solitary/ conversational Chapter 2

  19. Production system The End • A set of rules. • Knowledge contains information for a particular task. • A control strategy. • resolve conflict rule. • Breadth-first search • Depth-first search Chapter 2

  20. Breadth-first search The End • Algorithm BFS: • Create a variable called NODE-LIST and set it to the initial state. • Until a goal state is found or NODE-LIST is empty do: • Remove the first element from NODE-LISTand call it E. If NODE-LIST was empty, quit. • For each way that each rule can match the state described in E do: • Apply the rule to generate a new state. • If the new state is a goal state, quit and return this state. • Otherwise, add the new state to the end of NODE-LIST. Chapter 2

  21. Advantage BFS The End • will not trapped exploring a blind alley (ไม่ลงลึกไปทางใดทางหนึ่งเฉพาะ ที่อาจจะไม่ใช่คำตอบ) • if there is a solution, DFS is guaranteed to find it. • if there are multiple solutions, a minimum solution will be found. Chapter 2

  22. Depth-first search The End • Algorithm DFS: • If the initial state is a goal state, quit and return success. • Otherwise, do the following until success or failure is signaled: • Generate a successor, E, of the initial state. If there are no more successors, signal failure. • Call Depth-First Search with E as the initial state. • If success is returned, signal success. Otherwise continue in this loop. Chapter 2

  23. Advantage DFS The End • require less memory • may find a solution without examining much of the search space. Chapter 2

  24. Production System The End • Working memory • Production set = Rules Figure 5.3 • Trace Figure 5.4 • Data driven Figure 5.9 • Goal driven Figure 5.10 • Iteration # • Working memory • Conflict sets • Rule fired Chapter 2

  25. Production System Chapter 2

  26. Production System Chapter 2

  27. Production System Chapter 2

  28. Production System Chapter 2

  29. And-Or Graph start Data driven Goal driven The End b c d e f goal Chapter 2

  30. Heuristic Search The End Heuriskein  to discover (Greek word) Heuristic is a technique that improves the efficiency of the search process. - It is often useful to introduce heuristics based on relatively unstructured knowledge. - can not use Mathematical analysis. Heuristic function : is the function that maps from problem state descriptions to measures of desirability, usually represent as number  guide the most profitable direction Chapter 2

  31. Generate-and-test The End • Generate all possible solutions • DFS + backtracking • Generate randomly • Test function ANSWER yes/no • Algorithm page 64.... Chapter 2

  32. Hill Climbing The End • Similar to generate-and-test • Test function + heuristic function  Tell how close to the goal state • EX : In unfamiliar city without a map... downtown = tall building... heuristic function = distance between downtown and tall building • Stop • Goal state meet • No alternative state to move Chapter 2

  33. Simple Hill Climbing The End • Taskspecific knowledge into the control process • Is one state better than another • If the new state is ...better... than the current state then make it the current state • Algorithm page 66..... Chapter 2

  34. Steepest-Ascent Hill Climbing The End • Consider all moves from the current state • Select the best one as the next state • Algorithm page 67.... Chapter 2

  35. Hill Climbing Characteristic The End • Local method • It decides what to do next by looking only at the immediate consequences of its choice (rather than by exhaustively exploring all of the consequence) • Look only one more ahead Chapter 2

  36. Local heuristic function The End Heuristic function : max value • Block world figure 3.1 p. 69.... • Local heuristic function 1. Add one point for every block that is resting on the thing it is supposed to be resting on. 2. Subtract one point for every block that is sitting on the wrong thing. • Initial state score = 4 (6-2) • C,D,E,F,G,H correct = 6 • A,B wrong = -2 • Goal state score = 8 • A,B,C,D,E,F,F,H all correct Chapter 2

  37. Local heuristic function Heuristic function : max value Current state: figure 3.1 หยิบ A วางบนโต๊ะ B C D E F G H วางเรียงเหมือนเดิม  Score = 6(B C D E F G Hcorrect) Block world figure 3.2 p. 69 case a : Next state score = 4 (6-2) case b : Next state score = 4 (6-2) case c : Next state score = 4 (6-2) All 3 cases a,b,c ...have no better score than the current state = 6  so we... Stop Local minimum problem ติดอยู่ในกลุ่มระดับ local มองไปไม่พ้นอ่าง Chapter 2

  38. Global heuristic function The End • Block world figure 3.1 p. 69.... • Global heuristic function For each block that has the correct support structure (บริเวณฐานของมันต้องถูกหมด)add one point for every block in the support structure. For each block that has an incorrect support structure, subtract one pointfor every block in the existing support structure. Chapter 2

  39. Global heuristic function The End Heuristic function : max value • initial state score = -28 • C = -1, D = -2, E = -3, F = -4, G = -5, H = -6, A = -7 C บริเวณฐานของมันต้องผิด 1 ตัว D บริเวณฐานของมันต้องผิด 2 ตัว... • Goal state score = 28 • B = 1, C = 2, D = 3, E = 4, F = 5, G = 6, H = 7 B บริเวณฐานของมันต้องถูกหมด 1 ตัว C บริเวณฐานของมันต้องถูกหมด 2 ตัว.... Chapter 2

  40. Global heuristic function Heuristic function : max value Current state: figure 3.1 หยิบ A วางบนโต๊ะ B C D E F G H วางเรียงเหมือนเดิม Score = -21 (C = -1, D = -2, E= -3, F = -4, G= -5, H = -6) Block world figure 3.2 p. 69 Next state : move to case(c) case a = -28 same as initial state case b =-16 (C = -1, D = -2, E= -3, F = -4, G= -5, H = -1) case c = -15 (C = -1, D = -2, E= -3, F = -4, G= -5) No Local minimum problem  It’s work Chapter 2

  41. New heuristic function The End 1. Incorrect structure are bad and should be taken apart. More subtract score 2. Correct structure are good and should built up. Add more score for the correct structure. • สิ่งที่เราต้องพิจารณา How to find a perfect heuristic function? เข้าไปในเมองที่ไม่เคยไปจะหลีกเลี่ยงทางตัน dead end ได้อย่างไร Chapter 2

  42. Best first search Heuristic function : min value The End page 74 Chapter 2

  43. Best first search • OR GRAPH : each of its branches represents an alternative problem-solving pattern • we assumed that we could evaluate multiple paths to the same node independently of each other • we want to find a single path to the goal • use DFS : select most promising path • use BSF : when no promising path/ switch part to receive the better value • old branch is not forgotten • solution can be find without all completing branches having to expanded Chapter 2

  44. Best first search f’ = g + h’g: cost from initial state to current stateh’: estimate cost current state to goal state f’: estimate cost initial state to goal state Open node: most promising node Close node : keep in memory, already discover node. Chapter 2

  45. Best First Search Algorithm page 75-76 Chapter 2

  46. Heuristic function : min value f’ = g + h’ A* algorithm • h’ : count the nodes that we step down the path, 1 level down = 1 point, except the root node. • Underestimate : we generate up until f ’(F)= 6 > f ’(C) =5 then we have to go back to C. The End 1 level 2 level f’(E) = f’(C) = 5 3 level Chapter 2

  47. Heuristic function : min value f’ = g + h’ A* algorithm The End ปัญหาOverestimate : Suppose the solution is under D but we will not generate D because f’(D) = 6 > f’(G) = 4. 1 level 2 level 3 level page 76 Chapter 2

  48. And-Or Graph / Tree The End • can be solved by decomposing them into a set of smaller problems • And arcs are indicated with a line connecting all the components Chapter 2

  49. Heuristic function : min value And-Or Graph / Tree • each arc with the successor has a cost of 1 The End 9+27+1+1 3+4+1+1 15+10+1+1 choose lowest value = f’(B) = 5+1 ABEF = 17 + 1 Chapter 2

  50. And-Or Graph / Tree The End Chapter 2

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