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ARTIFICIAL INTELLIGENCE [INTELLIGENT AGENTS PARADIGM]

ARTIFICIAL INTELLIGENCE [INTELLIGENT AGENTS PARADIGM]. PROBLEM SOLVING BY SEARCHING. Professor Janis Grundspenkis Riga Technical University Faculty of Computer Science and Information Technology Institute of Applied Computer Systems Department of Systems Theory and Design

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ARTIFICIAL INTELLIGENCE [INTELLIGENT AGENTS PARADIGM]

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  1. ARTIFICIAL INTELLIGENCE[INTELLIGENT AGENTS PARADIGM] PROBLEM SOLVING BY SEARCHING Professor Janis Grundspenkis Riga Technical University Faculty of Computer Science and Information Technology Institute of Applied Computer Systems Department of Systems Theory and Design E-mail: Janis.Grundspenkis@rtu.lv

  2. Problem Solving by Searching (1) • Problem Solving Agent(one kind of a Goal-Based Agent) • Relevant feature:Decision making what to do by finding sequence of actions that leads to desired states

  3. Problem Solving by Searching (2) • How problem is solved? Step 1. Goal formulation Step 2. Problem formulation – a process of deciding what actions and states to consider Step 3. Search – systematic exploration of the sequence of alternative states that appear in a problem solving process Step 4. Solution – an action sequence Step 5. Execution – recommended actions can be accomplished

  4. Simple-Problem-Solving Agent > Percept Update-State(state, percept) > Goal Formulate-Goal(state) > Problems Formulate-Problem(state, goal) > Current state Search(problem) > Action Recommendation(state, action) Return: action

  5. Problem Types (1) • Single-state problem • Percepts give enough information to tell exactly which state is it • Agent knows exactly what each of its actions does • Agent can calculate exactly which state it will be in after any sequence of actions

  6. Problem Types (2) • Multiple-state problem • Percepts give not enough information to tell which state is it • Agent knows all the effects of itsactions • Agent must reason about sets of states that it might get to

  7. Basic Elements of a Problem Definition • A problem is a collection of information that the agent can use to decide what to do • Information specification for single-state problem definition Basic elements: • States • Actions

  8. State Space of the Problem • State space is the set of all states reachable from the initial state by any sequence of actions • The initial state is the state that the agent knows itself to be in • The goal state corresponds to the solution of the problem • The operator describes an action in terms of which state will be reached by carrying out the action in a particular state

  9. State Space Representation of the Problem Using Graph • The nodes of a graph corresponds to particular problem solution states • The arcs correspond to steps in a problem-solving process • Initial states form root of the graph and correspond to the given information in a problem instance • Goal states of the problem corresponds to the solutions to a problem instance

  10. Formal State Space Representation of the Problem (1) • A state space is represented by a four-tuple [N, A, IS, GS], where N is the set of nodes or states of the graph A is the set of arcs between nodes

  11. Formal State Space Representation of the Problem (2) • A state space is represented by a four-tuple [N, A, IS, GS], where ISis the non-empty set that contains the initial states of the problem (IS N) GS is the non-empty set that contains the goal states of the problem (GS N)

  12. Testing the Goal States • Agent can apply the goal test to a single-state description to determine if it is a goal state • Description of the goal states: • Explicit set of possible goal states • A measurable property of the states encountered in the search • A property of the path developed in the search

  13. Paths in the State Space • Each path that does reach the goal is called a complete path • Each path that does no reach the goal is called a partial path • A solution path is a complete path through the graph from a node in IS to a node in GS • A path cost function g is a function that assigns a cost to a path • The cost of a path is the sum of the costs of the individual actions along the path

  14. Measuring Problem-Solving Performance • Three ways to measure the effectiveness of a search: • Does a search find a solution at all? • Is a solution good (one with a low path cost)? • What is the search cost associated with the time and memory required to find a solution? • The total cost of the search:Total cost = Path cost + Search cost

  15. Searching for Solutions (1) • Search process builds up a search tree (subgraph of the state space) • Search starts from the search node that corresponds to the initial state (the root of the search tree) • Determining the children of a state is called expanding the state

  16. Searching for Solutions (2) • At each step, the search algorithm chooses one leaf node to expand • Leaf nodes have not successors (children) Two cases: • They have not been expanded • They were expanded, but generated the empty set • Nodes that are waiting to be expanded are called a frontier

  17. Search Algorithms for Agents • INPUT: instances of data type PROBLEM • OUTPUT: solution path • Data type PROBLEM has four components: • Initial state • Operators • Goal test • Path cost function

  18. Distinction Between Nodes and States • A node is a data structure used to represent the search tree for a particular problem instance as generated by a particular problem • A state represents a configuration of the world and is characterized by a set of features

  19. Data Structure for Search Trees • Node v is data structure with five components: • The corresponding state in the state space • The node that generates node v (the parent node) • The operator that was applied to generate v • The depth of the node v (the number of nodes on the path from the search node to v) • The path cost of the path from the search node to v

  20. Classification of Search Strategies (1) If available information is specified: • Uninformed Search (Blind Search) No information is available about: • the number of steps • the path cost from the current state to the goal • Informed Search (Heuristic Search) Problem-specific knowledge is used

  21. Classification of Search Strategies (2) If the search direction is specified: • Data-Driven Search (Forward Chaining) • Search starts from the node(s) representing the given facts of the problem, applies operators to produce new nodes that lead to a goal • Searching forwards means generating successors successively starting from the initial (root) node

  22. Classification of Search Strategies (3) If the search direction is specified: • Goal-Driven Search (Backward Chaining) • Search starts from the goal, applies operators that could produce the goal, and chains backward to the given facts of the problem • Searching backwards means generating predecessors successively starting from the goal node

  23. UninformedSearch Classification of Search Strategies (4) If the order in which nodes are expanded is specified: • Breadth-First Search • Uniform Cost Search • Depth-First Search • Depth-Limited Search • Iterative DeepeningSearch • Bidirectional Search

  24. InformedSearch Classification of Search Strategies (5) If the order in which nodes are expanded is specified: • Best-First Search • Greedy Search (minimizing theestimate cost to reach the goal) • A* Search (minimizing the totalpath cost)

  25. InformedSearch Classification of Search Strategies (6) If the order in which nodes are expanded is specified: • Memory Bounded Search • IDA* Search (IterativeDeepeningA* search) • SMA* Search (SimplifiedMemory-Bounded A*)

  26. InformedSearch Classification of Search Strategies (7) If the order in which nodes are expanded is specified: • Iterative ImprovementAlgorithms • Hill-Climbing Search • Random-Restart Hill-Climbing • Simulated Annealing • Beam Search

  27. UninformedSearch Strategies (1) • Breadth-First Search • This search expands the shallowest node in the search tree first • This search explores the space in a level-by-level fashion

  28. Breadth-first search A B C D E F G H I J CLOSED  B B D B D F B D F G B D F G I B D F G I J Iteration 0 1 2 3 4 5 6 OPEN B D F G F G I J G I J H I J H J H H Data driven search B- the initial node H – the goal Goal

  29. UninformedSearch Strategies (2) • Uniform-Cost Search • This search expands the lowest-cost node on the frontier first • The path cost must never decreaseg(successor(n))  g(n)for every node n

  30. UninformedSearch Strategies (3) • Depth-First Search • This search expands the deepest node in the search tree first • This search goes deeper into the search space whenever this is possible • Depth-Limited Search • This search places a limit on how deep a depth-first search can go (imposes a cutoff on the maximum depth of a path)

  31. Depth-first search A B C D E F G H I J Iteration 0 1 2 3 4 5 OPEN B D F G I J F G J F G F G H G CLOSED  B B D B D I B D I J B D I J F Data driven search B- the initial node H – the goal Goal

  32. Depth limited search Data driven search A B B- the initial node F- the goal Depth limit - 2 C D E Node depth CLOSED  B B D Iteration 0 1 2 OPEN B0 D1 G1 E1 F2 H2 G1 E1 F G H I J Goal

  33. UninformedSearch Strategies (4) • Iterative Deepening Search • This search call depth-limited search with increasing limits until a goal is found • This search expands many states multiple times • Bidirectional Search • This search goes both forwards from the initial state and backward from the goal, and stop when the two searches meet in the middle

  34. Bidirectional search A B A- the initial node J- the goal C D E F G H Data-driven search Goal-driven search I J CLOSED  J J G CLOSED  A A C Iteration 0 1 2 OPEN J G H H C D Iteration 0 1 2 OPEN A C D D F G Solution is found because the node D is found in both OPEN lists

  35. Evaluation of Uninformed Search Strategies • Four Criteria • Completeness (is a solution guaranteed?) • Time Complexity (time needed for search) • Space Complexity (memory needed for search) • Optimality (is highest-quality solution guaranteed when there are several different solutions?)

  36. Comparing Uninformed Search Strategies (1) b is the branching factor (every state can be expanded toyield b new states), d is the depth of solution, m is the maximum depth of the search tree, andl is the depth limit

  37. Comparing Uninformed Search Strategies (2) b is the branching factor (every state can be expanded toyield b new states) d is the depth of solution m is the maximum depth of the search tree l is the depth limit

  38. Strengths of Uninformed Search Strategies (1) • Breadth-First Search • This search always finds the shortest solution path • Uniform-Cost Search • When the cost of the path never decrease, the first solution that is found is guaranteed to be the cheapest solution

  39. Strengths of Uninformed Search Strategies (2) • Depth-First Search • For problems that have very many solutions, depth-first may actually be faster than breadth-first search, because chances to find a solution after searching only a small part of the whole space is rather good

  40. Strengths of Uninformed Search Strategies (3) • Depth-Limited Search • It avoids the pitfalls of depth-first search • Iterative Deepening Search • It is the preferred search method when there is a large search space and the depth of the solution is not known • Bidirectional Search • Can enormously reduce time complexity

  41. Weaknesses of Uninformed Search Strategies (1) • Breadth-First Search • Impractical in most cases due to the memory requirements • It is optimal only when all operators have the same cost • Uniform-Cost Search • If some operators have negative cost, only an exhaustive search of all nodes would guaranteed the optimal solution

  42. Weaknesses of Uninformed Search Strategies (2) • Breadth-First Search (assume that 1 million nodes can be generated per second and that a node requires 1000 bytes of storage) • At depth 2 there are 110 nodes, time needed is 0,11 milliseconds and 107 kilobytes of memory are needed • At depth 4 there are 11110 nodes, time needed is 11 milliseconds and 10,6 megabytes of memory are needed • At depths 6, 8, 10, 12, 14, and 16 the number of nodes is10 in corresponding power, time needed is 1,1 seconds, 2 minutes, 3 hours, 13 days, 3,5 years, and 350 years, respectively, while 1 gigabyte, 103 gigabites, 10 terabytes, 1 petabyte, 99 petabytes, and 10 exabytes of memory are needed • Exponential-complexity search is a problem!

  43. Weaknesses of Uninformed Search Strategies (3) • Depth-First Search • Impractical in search trees with large or infinite maximum depths (it can get stuck going down the wrong paths) • Depth-Limited Search • In cases when depth limit is too small there is no guarantee that the search will find the goal

  44. Weaknesses of Uninformed Search Strategies (4) • Iterative Deepening Search • It is wasteful, because many states are expanded multiple times • Bidirectional Search • It is not always applicable and its memory requirements may be impractical

  45. InformedSearch Strategies (1) • Best-First Search • This search expands the node that appears to be the best according to the evaluation function * Greedy Search • This is one of the simplest best-first search strategies that uses minimization of the estimated cost of the cheapest path (heuristic functionh(n)) to reach the goal • This search expands the node whose state is judged to be closest to the goal state

  46. Best first search A 10 = 0+10 B 6 =1+5 C 8 =1+7 D 4 =1+3 E 5 =2+3 F 7 =2+5 G 4 =2+2 H 5 =3+2 I 3 =3+0 Node heuristic measures 6 The best measure is the highest value A- the initial node H- the goal Iteration 0 1 2 3 4 5 OPEN A(10) C(8) B(6) D(4) B(6) E(5) D(4) G(4) F(7) E(5) D(4) G(4) E(5) D(4) G(4) I(3) H(5) D(4) G(4) I(3) CLOSED  A(10) A(10) C(8) A(10) C(8) B(6) A(10) C(8) B(6) F(7) A(10) C(8) B(6) F(7) E(5)

  47. InformedSearch Strategies (2) • A* Search • This search expands the node n with the lowest value of the estimated cost of the cheapest solution through n:f(n) = g(n) + h(n)

  48. InformedSearch Strategies (3) • Memory-Bounded Search • This search conserves memory • Iterative Deepening A* Search (IDA*) • In this search each iteration is a depth-first search that is modified to use an f-cost limit (not depth limit) • This search expands all nodes inside the contour for the current f-cost, peeping over the contour to find out where the next contour is (contour in the state space is a set of nodes where all nodes have f(n) less than or equal to f-cost of that contour)

  49. InformedSearch Strategies (4) • Simplified Memory-Bounded A* Search (SMA*) • This search drops nodes that are unpromising (nodes with high f-cost) when it needs to generate a successor but has no memory left

  50. InformedSearch Strategies (5) • Iterative Improvement Algorithms • This search explores the state space trying to find the best valueof the estimated cost, which is the optimal solution • Hill-Climbing Search • This search continually expands nodes that have better estimated costs of the remaining distance to the goal then previous ones

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