Pengantar Kecerdasan Buatan Penyelesaian Masalah dengan Pencarian 2
Pengantar Kecerdasan Buatan Penyelesaian Masalah dengan Pencarian
2 Problem-solving Agent • Problem-solving agent decide what to do by finding sequences of action that lead to a desirable state • Problem-solving agent is a kind of goal-based agent OSCAR KARNALIM, S. T. , M. T.
3 How do We Solve Problem ? Define the problem Look for solution Solve the problem Evaluate the result OSCAR KARNALIM, S. T. , M. T.
4 How does Agent Work ? • Goal Formulation • • Problem Formulation • • Finding solution Solution • • • The process of deciding what actions and states to consider and follow goal formulation Search • • Know what to do / where to go. The result of Search Process Execution Remember: “Formulate, Search, Execute” OSCAR KARNALIM, S. T. , M. T.
5 Problem Example • The Road to Bucarest An agent enjoying his holiday in the city of Arad, Romania. • The agent’s home flight leaves tomorrow from Bucarest (the flight ticket is nonrefundable) • OSCAR KARNALIM, S. T. , M. T.
6 Romania OSCAR KARNALIM, S. T. , M. T.
7 The Road to Bucharest • Formulate goal: • • be in Bucharest Formulate problem: states: various cities • actions: drive between cities • • Find solution: sequence of cities, • e. g. , Arad, Sibiu, Fagaras, Bucharest • OSCAR KARNALIM, S. T. , M. T.
8 Simplified Road Map to Bucarest OSCAR KARNALIM, S. T. , M. T.
9 Problem Definition A problem is defined by four items: Initial state e. g. , In(Arad) Possible actions available or successor function S(x) = set of action–state pairs e. g. , S(Arad) = {<Arad Zerind, Zerind>, … } Goal test, can be explicit, e. g. , x = "at Bucharest" implicit, e. g. , Checkmate(x) Path cost (additive) e. g. , sum of distances, number of actions executed, etc. c(x, a, y) is the step cost, assumed to be ≥ 0 A solution is a sequence of actions leading from the initial state to a goal state OSCAR KARNALIM, S. T. , M. T.
10 Problem Definition (Cont) • A Problem can be defined by four component Initial State, e. g. In (Arad) • Action or Successor function, a description of the possible actions available to the agent • <action, successor> • e. g. {<Go(Sibiu), In(Sibiu)>, <Go(Timisoara), In(Timisoara)>, …} • Goal Test, e. g. In (Bucharest) • Path Cost, a function that assigns a numeric cost to each path • OSCAR KARNALIM, S. T. , M. T.
11 Selecting a State Space • Real world is absurdly complex state space must be abstracted for problem solving • (Abstract) state = set of real states • (Abstract) action = complex combination of real actions • e. g. , "Arad Zerind" represents a complex set of possible routes, detours, rest stops, etc. • (Abstract) solution = set of real paths that are solutions in the real world • Each abstract action should be "easier" than the original problem OSCAR KARNALIM, S. T. , M. T.
12 The Vacuum World Goal: Clean up all dirt Problem Formulation: 8 possible states as shown 3 possible actions {Left, Right, Suck} Solution: State {7, 8} OSCAR KARNALIM, S. T. , M. T.
13 Vacuum World State Space • States? dirt and robot location • Initial state? Any state • Actions? Left, Right, Suck • Goal test? no dirt at all locations • Path cost? 1 per action OSCAR KARNALIM, S. T. , M. T.
14 The 8 -Puzzle State Space • States? locations of tiles • Initial state? Any state • Actions? move blank left, right, up, down • Goal test? = goal state (given) • Path cost? 1 per move OSCAR KARNALIM, S. T. , M. T.
15 Robotic Assembly State Space • States? real-valued coordinates of robot joint angles parts of the object to be assembled • Actions? continuous motions of robot joints • Goal test? complete assembly • Path cost? time to execute OSCAR KARNALIM, S. T. , M. T.
16 Real World Problems • Route-finding problem • Touring problem • Traveling salesperson problem • Robot Navigation • Automatic assembly sequencing • Protein Design • Internet Searching OSCAR KARNALIM, S. T. , M. T.
17 Searching for A Solution • Finding a solution searching through state space. • Generating action sequence Start with initial state • Check for goal state • Expand state • • The process of choosing which state to expand first is called search strategy OSCAR KARNALIM, S. T. , M. T.
18 The Search Tree • It is helpful to think of the search process as building up a search tree. • We explore problem space with a search tree Tree Nodes represent states • Edges represent operators • The root of the tree is the initial state • The node is expanded to generate its children • OSCAR KARNALIM, S. T. , M. T.
19 Implementation: States vs. Nodes • A state is a (representation of) a physical configuration • A node is a data structure constituting part of a search tree includes state, parent node, action, path cost g(x), depth OSCAR KARNALIM, S. T. , M. T.
20 Konversi Masalah ke Pohon OSCAR KARNALIM, S. T. , M. T.
21 Contoh Pohon Pencarian OSCAR KARNALIM, S. T. , M. T.
22 Contoh Pohon Pencarian (Cont) OSCAR KARNALIM, S. T. , M. T.
23 Contoh Pohon Pencarian (Cont) OSCAR KARNALIM, S. T. , M. T.
24 Strategi Pencarian • A search strategy is defined by picking the order of node expansion • Strategies are evaluated along the following dimensions: • completeness: does it always find a solution if one exists? • time complexity: number of nodes generated • space complexity: maximum number of nodes in memory • optimality: does it always find a least-cost solution? • Time and space complexity are measured in terms of • b: maximum branching factor of the search tree • d: depth of the least-cost solution • m: maximum depth of the state space (may be ∞) OSCAR KARNALIM, S. T. , M. T.
25 Uninformed Search • It have no information about the number of step or the path cost from the current state to the goal, can only distinguish between goal and non-goal state. • For the same reason it is also called blind search OSCAR KARNALIM, S. T. , M. T.
26 Uninformed Search Strategies • Breadth-first search • Uniform-cost search • Depth-first search • Depth-limited search • Iterative deepening search OSCAR KARNALIM, S. T. , M. T.
27 Breadth-first Search • Expand shallowest unexpanded node • fringe is a FIFO queue, i. e. , new successors go at end OSCAR KARNALIM, S. T. , M. T.
28 Breadth-first Search (Cont) OSCAR KARNALIM, S. T. , M. T.
29 Properties of Breadth-first Search • Complete? Yes (if b is finite) • Time? 1+b+b 2+b 3+… +bd + b(bd-1) = O(bd+1) • Space? O(bd+1) (keeps every node in memory) • Optimal? Yes (if cost = 1 per step) • Space is the bigger problem (more than time) OSCAR KARNALIM, S. T. , M. T.
30 Uniform-cost Search • Expand least-cost unexpanded node • Implementation: • fringe = queue ordered by path cost • Equivalent to breadth-first if step costs all equal • Complete? Yes, if step cost ≥ ε • Time? # of nodes with g ≤ cost of optimal solution, O(bceiling(C*/ ε)) where C* is the cost of the optimal solution • Space? # of nodes with g ≤ cost of optimal solution, O(bceiling(C*/ ε)) • Optimal? Yes – nodes expanded in increasing order of g(n) OSCAR KARNALIM, S. T. , M. T.
31 Uniform-cost Search (Cont) OSCAR KARNALIM, S. T. , M. T.
32 Depth-first Search • Expand deepest unexpanded node • Implementation: • fringe = LIFO queue, i. e. , put successors at front OSCAR KARNALIM, S. T. , M. T.
33 Depth-first Search (Cont) OSCAR KARNALIM, S. T. , M. T.
34 Depth-first Search (Cont) OSCAR KARNALIM, S. T. , M. T.
35 Properties of Depth-first Search • Complete? No: fails in infinite-depth spaces, spaces with loops • Modify to avoid repeated states along path complete in finite spaces • Time? O(bm): terrible if m is much larger than d • but if solutions are dense, may be much faster than breadth-first • Space? O(bm), i. e. , linear space! • Optimal? No OSCAR KARNALIM, S. T. , M. T.
36 Depth-limited Search • Depth-first search with depth limit • i. e. , nodes at depth l have no successors OSCAR KARNALIM, S. T. , M. T.
37 Iterative Deepening Search • Depth-first search by trying all possible depth limits. First depth=0, then depth=1, then depth=2, and so on. • Combines the benefits of BFS and DFS OSCAR KARNALIM, S. T. , M. T.
38 Iterative Deepening Search with i=0 OSCAR KARNALIM, S. T. , M. T.
39 Iterative Deepening Search with i=1 OSCAR KARNALIM, S. T. , M. T.
40 Iterative Deepening Search with i=2 OSCAR KARNALIM, S. T. , M. T.
41 Iterative Deepening Search with i=3 OSCAR KARNALIM, S. T. , M. T.
42 Iterative Deepening Search • 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, NDLS = 1 + 100 + 1, 000 + 100, 000 = 111, 111 • NIDS = 6 + 50 + 400 + 3, 000 + 20, 000 + 100, 000 = 123, 456 • • Overhead = (123, 456 - 111, 111)/111, 111 = 11% OSCAR KARNALIM, S. T. , M. T.
43 Properties of Iterative Deepening Search • Complete? Yes • Time? (d+1)b 0 + d b 1 + (d-1)b 2 + … + bd = O(bd) • Space? O(bd) • Optimal? Yes, if step cost = 1 OSCAR KARNALIM, S. T. , M. T.
44 Summary of Algorithms OSCAR KARNALIM, S. T. , M. T.
45 Bidirectional Search OSCAR KARNALIM, S. T. , M. T.
46 Repeated States • Failure to detect repeated states can turn a linear problem into an exponential one! OSCAR KARNALIM, S. T. , M. T.
47 Avoiding Repeated States Three ways to deal with repeated states, in increasing order of effectiveness and computational overhead: Do not return to the state you just came from Do not create paths with cycles in the space state Do not generate any state that was ever generated before [this require every generated state to be kept in memory, resulting in space complexity O(bd)] OSCAR KARNALIM, S. T. , M. T.
48 Referensi • Russell, Stuart J. & Norvig, Peter. Artificial Intelligence: A Modern Approach (3 rd ed. ). Prentice Hall. 2009 • Luger, George F. Artificial Intelligence: Structures and Strategies for Complex Problem Solving. 6 th Edition. Addison Wesley. 2008. • Watson, Mark. , Practical Artificial Intelligence Programming in Java, Open Content – Free e. Book (CC License), 2005. OSCAR KARNALIM, S. T. , M. T.
49 Kuis 2 1. Apakah agent itu? 2. Apakah yang dimasudkan dengan PEAS? 3. Berikan contoh sebuah agent lengkap dengan PEAS-nya. 4. Berikan penjelasan singkat tentang 4 macam jenis agent. OSCAR KARNALIM, S. T. , M. T.
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