Artificial Intelligence Lecture 7-12Page 2 Production System 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
Artificial Intelligence Lecture 7-12Page 3 And-Or Graph a Data driven Goal driven b cd efg
Artificial Intelligence Lecture 7-12Page 4 Generate-and-test Generate all possible solutions DFS + backtracking Generate randomly Test function yes/no Algorithm page 64
Artificial Intelligence Lecture 7-12Page 5 Hill Climbing Similar to generate-and-test Test function + heuristic function Stop Goal state meet No alternative state to move
Artificial Intelligence Lecture 7-12Page 6 Simple Hill Climbing Task specific knowledge into the control process Is one state better than another The first state is better than the current state Algorithm page 66
Artificial Intelligence Lecture 7-12Page 7 Steepest-Ascent Hill Climbing Consider all moves from the current state Select the best one as the next state Algorithm page 67 Searching time?
Artificial Intelligence Lecture 7-12Page 8 Hill Climbing Problem No solution found : Problem Local maximum : a state that is better than all its neighbors but it is not better than some other states farther away. backtracking Plateau : a flat area of the search space in which a whole set of neighboring states have the same value. It is not possible to determine the best direction by using local comparison. Make big jump
Artificial Intelligence Lecture 7-12Page 9 Hill Climbing Problem Ridge : an area of the search space that is higher than surrounding areas and itself has a slope. We can not do with a single move. Fired more rules for several direction
Artificial Intelligence Lecture 7-12Page 10 Hill Climbing Characteristic 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
Artificial Intelligence Lecture 7-12Page 11 Local heuristic function 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
Artificial Intelligence Lecture 7-12Page 12 Local heuristic function Current state : จากรูป 3.1 หยิบ A วางบนโต๊ะ B C D E F G H วางเรียง เหมือนเดิม Score = 6 (B C D E F G H correct) Block world figure 3.2 p. 69 Next state score = 4 All 3 cases Stop : no better score than the current state = 6 Local minimum problem ติดอยู่ในกลุ่มระดับ local มองไปไม่พ้นอ่าง
Artificial Intelligence Lecture 7-12Page 13 Global heuristic function Block world figure 3.1 p. 69 Global heuristic function 1.For each block that has the correct support structure add one point for every block in the support structure. ( นับ หมด ) For each block that has an incorrect support structure, subtract one point for every block in the existing support structure.
Artificial Intelligence Lecture 7-12Page 14 Global heuristic function initial state score = -28 C = -1, D = -2, E = -3, F = -4, G = -5, H = -6, A = -7 Goal state score = 28 B = 1, C = 2, D = 3, E = 4, F = 5, G = 6, H = 7
Artificial Intelligence Lecture 7-12Page 15 Global heuristic function Current state : จากรูป 3. 1 หยิบ A วางบนโต๊ะ B C D E F G H วางเรียง เหมือนเดิม 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
Artificial Intelligence Lecture 7-12Page 16 New heuristic function 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
Artificial Intelligence Lecture 7-12Page 17 Simulated Annealing Hill climbing variation At the beginning of the process some down hill moves may be made. Do enough exploration of the whole space early on so that the final solution is relatively insensitive to the starting state. ป้องกันปัญหา local maximum, plateau,ridge Use objective function (not heuristic function) Use minimize value of objective function
Artificial Intelligence Lecture 7-12Page 18 Simulated Annealing Annealing schedule ถ้าเราทำให้เย็นเร็วมาก จะได้ผลลัพธ์ high energy อาจเกิด local minimum ได้ ถ้าเราทำให้เย็นช้ามาก จะได้ผลลัพธ์ดี แต่ เสียเวลามาก at low temperatures a lot of time may be wasted after the final structure has already been formed. ควรทำแบบพอดี empirical structure
Artificial Intelligence Lecture 7-12Page 19 Simulated Annealing Annealing : metals are melted Cool down to get the solid structure Objective function : energy level Try to use less energy P : probability T : temperature : annealing schedule K : Boltzmann’s constant : describe the correspondence between the units of temperature and the unit of energy E = ( value of current) – (value of new state) positive change in the energy - e/KT p = e
Artificial Intelligence Lecture 7-12Page 20 Simulated Annealing Probability of a large uphill move is lower than probability of a small uphill move Probability uphill move decrease when temperature decrease. In the beginning of the annealing large upward moves may occur early on Downhill moves are allowed anytime Only relative small upward moves are allowed until finally the process converges to a local minimum configuration
Artificial Intelligence Lecture 7-12Page 21 Simulated Annealing - e/KT p = e
Artificial Intelligence Lecture 7-12Page 22 เหมาะสำหรับปัญหาที่มีจำนวน move มากๆ หลักการ 1. What is initial Temperature 2. Criteria for decreasing T 3. Level to decrease T value 4. When to quit ข้อสังเกต 1. When T approach 0 simulated annealing identical with simple hill climbing Algorithm Simulated Annealing
Artificial Intelligence Lecture 7-12Page 23 ข้อแตกต่าง Algorithm Simulated Annealing p.71 และ Hill Climbing 1. The annealing schedule must be maintained. 2. Move to worse states may be accepted. 3. Maintain the best state found so far. If the final state is worse than that earlier state, then earlier state is still available. Algorithm Simulated Annealing
Artificial Intelligence Lecture 7-12Page 24 Best first search OR GRAPH : Search in the graph Heuristic function : min value page 74
Artificial Intelligence Lecture 7-12Page 25 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
Artificial Intelligence Lecture 7-12Page 26 Best First Search f’ = g + h’ g: cost from initial state to current state h’: 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.
Artificial Intelligence Lecture 7-12Page 27 Best First Search Algorithm page 75-76
Artificial Intelligence Lecture 7-12Page 28 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. 1 level 2 level 3 level f ’ (E) = f ’ (C) = 5 f’ = g + h’
Artificial Intelligence Lecture 7-12Page 29 A* algorithm f’ = g + h’ 1 level 2 level 3 level Overestimate : Suppose the solution is under D : we will not generate D because F ’ (D) = 6 > f ’ (G) = 4.
Artificial Intelligence Lecture 7-12Page 32 Agenda Agenda : a list of tasks a system could perform. a list of reasons a rating representing overall weight of evidence suggesting that the task would be useful When a new task is created, insert into the agenda in its proper place, we need to re- compute its rating and move it to the correct place in the list find the better location put at the end of agenda need a lot more time to compute a new rating
Artificial Intelligence Lecture 7-12Page 33 Not acceptable dialog agenda is not good for when interacting with people page person China computer person Italy computer person computer China something reasonable now may not be continue to be so after the conversation has processed for a while.
Artificial Intelligence Lecture 7-12Page 35 And-Or Graph / Tree can be solved by decomposing them into a set of smaller problems And arcs are indicated with a line connecting all the components
Artificial Intelligence Lecture 7-12Page 36 And-Or Graph / Tree each arc with the successor has a cost of choose lowest value = f ’ (B) = 5 ABEF =
Artificial Intelligence Lecture 7-12Page 37 And-Or Graph / Tree Futility : some value use to compare the result/ threshold value If... the estimate cost of a solution > Futility then.....abandon the search
Artificial Intelligence Lecture 7-12Page 38 Problem Reduction
Artificial Intelligence Lecture 7-12Page 39 Problem Reduction E come from J not C
Artificial Intelligence Lecture 7-12Page 40 Problem Reduction Can not find a solution from this algorithm because of C
Artificial Intelligence Lecture 7-12Page 42 Problem Reduction : AO* Algorithm use a single structure GRAPH we will not store g algorithm will insert all ancestor nodes into a set path C will always be better than path B
Artificial Intelligence Lecture 7-12Page 43 Problem Reduction : AO* Algorithm change G from 5 to 10 no backward propagationneed backward propagation