unit iv
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unit iv of AI IN MSC IT IN BgsbuTRANSCRIPT
Slide 1
Artificial IntelligenceUnit IV
Problem SolvingIn problem solving, we sometimes have to search through many possible ways.We may know all the possible actions our robot can do, but we have to consider various sequences to find a sequence of action to achieve a goal.We may know all possible moves in chess game, but we must consider many possibilities to find a good move.Effectiveness of SearchThe effectiveness of search can be measured in at least three ways:Does it finds solution at all.Is it an optimal solution(with low cost)?What is the search cost associated with the time and memory required to find a solution?Problem Solving AgentA Problem Solving Agent is a kind of Goal Based Agent that decides what to do by finding sequences of action to get desired goal.Example : (i) Find the shortest path between two cities in given country. (ii) Find the shortest path for salesman to travel, visiting each city once, and then returning to the starting city.Problem Solving AgentsIntelligent agents can solve problems by searching a state-space
State-space Modelthe agents model of the world usually a set of discrete statese.g., in driving, the states in the model could be towns/cities
Goal State(s)a goal is defined as a desirable state for an agentthere may be many states which satisfy the goal teste.g., drive to a town with a ski-resortor just one state which satisfies the goale.g., drive to Mammoth
Operators (actions, successor function)operators are legal actions which the agent can take to move from one state to another
State Space ModelInitial State: The state the agent knows it self to be in. (e.g. Initial Chess Board, Point where to start)Action/Operator: A set of action that moves the problem from one state to another.(e.g. Chess move, Robot Action)Neighbourhood: Set of all possible states reachable from a given state.State Space: The set of all states reachable from initial state by any sequence of actions.Path: Any sequence of action leading from one state to another.Goal Test: A test applicable to a single state problem to determine if it is a goal state.(e.g. Winning Chess position, Target Location)Path Cost: The function that assigns a cost to the path. Eight Queen Problem
Eight Queen Problem
Eight Queen Problem
Eight Queen Problem
Tic-Tac-Toe
Tic-Tac-Toe
Uninformed SearchAlso known as BLIND SEARCH.Uninformed search has no information about the number of steps or the path costs from the current state to the goal.They can only distinguish a goal state from a non-goal state.There is no bias to go to go towards the desire goal.Uninformed SearchBreadth-First-SearchDepth-First-SearchUniform-SearchIterative Deepening SearchBi-Directional Search
Uninformed SearchBreadth-First-SearchDepth-First-SearchUniform-SearchIterative-Deepening-SearchBi-Directional Search
Breadth First SearchExpand root node.Expand all children of root node.Expand all grandchildren.Breadth First Search
Breadth First Search
Breadth First Search
Breadth First Search
Breadth First SearchSSGABDECFADAEBDBFESESBGDFBFADC EACC Breadth First Search
Fringe: Open Queue, List. Fringe contain s the initial node in the beginning.26Breadth First Search
Breadth First SearchTime Complexityassume (worst case) that there is 1 goal leaf at the RHS at depth dso BFS will generate
= b + b2+ ..... + bd + bd+1 - b = O (bd+1)
Space Complexityhow many nodes can be in the queue (worst-case)?at depth d there are bd+1 unexpanded nodes in the Q = O (bd+1) d=0d=1d=2d=0d=1d=2GGDepth-First-Search
Depth-First-Search
Depth-First-Search
Depth-First-Search
Depth-First-Search
Depth-First-Search
Depth-First-Search
Depth-First-Search
Depth-First-Search
Time Complexity of DFS : O(bd) { in Patterson Book}Space Complexity of DFS : O(d) { in Patterson Book}
37BFS vs DFS
Iterative Deepening SearchIt is similar to the DFS but chooses the best depth limit.It tries all possible depth limits: first depth 0, then depth 1, then depth 2 and so on.Linear memory requirement of depth first search.Guarantee for goal node of minimal depth.Iterative Deepening Search
Iterative Deepening Search
Iterative Deepening Search
Iterative Deepening Search
Iterative Deepening Search
Iterative Deepening Search
Bidirectional SearchRun two simultaneous search.One forward from initial state and other backward from goal-hoping that two searches meet in the middle.For problems where branching factor is b and the solution is in depth d, the solution is found after half step of depth first.46Bidirectional Search
Bidirectional Search
Bidirectional SearchThe time and space complexity for Bidirectional search is O(bd/2).Complete : YesOptimal : YesInformed Search StrategiesHere we see how information about the state space can prevent algorithms from blundering about in the dark.Also known as Heuristic Search.
Informed Search StrategiesHill-Climbing.BestFirst Search.Greedy-Best-First Search.A* Search.IDA* Search.Local-Beam SearchInformed Search StrategiesHill-Climbing.BestFirst Search.Greedy-Best-First Search.A* Search.IDA* Search.Local-Beam Search.Heuristic FunctionThe word Heuristic is derived from the Greek verb heuriskein, meaning to find or to discover.A heuristic function at a node n is an estimate of the optimum cost from the current node to a goal. Denoted by h(n).h(n)= Estimated cost of the cheapest path from node n to goal node.Heuristic FunctionHeuristic Function = Cost from start state to current state + Estimated distance from the goal.Heuristic Function
8-Puzzle
8-Puzzle
8-Puzzle
The Manhattan Distance588-PuzzleIn this case only the 3 ,8 and 1 tiles are misplaced by 2, 3 and 3 space respectively.So, the heuristic function evaluates to 8.In other words the heuristic is telling us, that it thinks a solution is available in just 8 more moves.h(n)=8.Greedy Best-First SearchExpand the node that is closest to the goal node.The selection of promising node is based on some heuristic function : f(n)=h(n).Usually it is difficult to compute the exact distance from the goal.Therefore a heuristic function is used to estimate of cost from n to goal.hSLD (n)=STRAIGHT-LINE-DISTANCE from n to BUCHAREST.60Greedy Best-First Search
Greedy Best-First Search
Greedy Best-First Search
Greedy Best-First Search
Greedy Best-First Search
Greedy Best-First Search
Greedy Best-First Search
Greedy Best-First Search
Greedy Best-First Search
Greedy Best-First Search
A*A* include in its evaluation function the cost from the start node to the current node, in addition to the estimated cost from the current node to the goal.Evaluation function: f(n)=g(n)+h(n).Where, g(n) = cost so for to reach n. h(n) =Estimated cost to goal from n. f(n) =Estimated total cost of path from the starting node n0 through n to goal. A*
A*
A*
A*
A*
A*
A*
A*
A*
A*
Optimality of A*
Optimality of A*
Optimality of A*
A* and Depth First
Iterative Deepening A*Like Iterative Deepening Depth-First, but depth bound modified to be an f-Limit.Start with F-Limit= f(Start).Prune any node if f(Node)>F-Limit.Next F-Limit=min-cost of any node pruned.If this Search does not succeed, determine the lowest f-Limit among the nodes that were visited but not expanded.Use this f-Limit as the new limit value-cut off value and do another depth first search.Repeated this procedure Until a goal node is found.Iterative Deepening A*
Iterative Deepening A*
Iterative Deepening A*
Iterative Deepening A*
Iterative Deepening A*
Iterative Deepening A*
Iterative Deepening A*
Iterative Deepening A*
Iterative Deepening A*
Iterative Deepening A*
Iterative Deepening A*
Iterative Deepening A*
Iterative Deepening A*
Iterative Deepening A*
IDA*
Questions from Previous Exams of MITDifference between DFS and BFS with Example?Describe various informed search strategies?What is Iterative Deepening? Write the various steps of IDA*.What do you mean by Heuristic Search Technique. How are they different from informed search techniques.Explain A* algorithm in detail. Also discuss the limitations of this algorithm.Explain Breadth-First Search with Suitable example.Discuss IDA* algorithm in detail.Explain A* in brief. Give its algorithmic complexity.Explain AO* algorithm with suitable example.