22PEOIT4C Session 9 Local search in continuous space.pptx

22PEOIT4C Session 9 Local search in continuous space.pptx

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  12/06/2025 DEPARTMENT OF SPECIALBATCH (ET) IV B. Tech -I Semester ARTIFICAL INTELLIGENCE SUBJECT CODE: 22PEOIT4C AcademicYear : 2024-2025 by Dr.M.Gokilavani GNITC Department of SB-ET 1
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  12/06/2025 Department ofSB-ET TEXTBOOK: • Artificial Intelligence A modern Approach, Third Edition, Stuart Russell and Peter Norvig, Pearson Education. REFERENCES: • Artificial Intelligence, 3rd Edn, E. Rich and K.Knight (TMH). • Artificial Intelligence, 3rd Edn, Patrick Henny Winston, Pearson Education. • Artificial Intelligence, Shivani Goel, Pearson Education. • Artificial Intelligence and Expert Systems- Patterson, Pearson Education. 2
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  12/06/2025 Department ofSB-ET 22PEOIT4C ARTIFICAL INTELLIGENCE UNIT – I Syllabus Introduction to AI, Intelligent Agents, problem-Solving Agents, Searching for Solutions, Uninformed Search Strategies: Breadth- first search, Uniform cost search, Depth-first search, Iterative deepening Depth-first search, Bidirectional search, Informed (Heuristic) Search Strategies: Greedy best-first search, A* search, Heuristic Functions, Beyond Classical Search: Hill-climbing search, Simulated annealing search, Local Search in Continuous Spaces. 3
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  12/06/2025 Department ofSB-ET Local search in continuous spaces • The distinction between discrete and continuous environments pointing out that most real-world environments are continuous. • A discrete variable or categorical variable is a type of statistical variable that can assume only fixed number of distinct values. • Continuous variable, as the name suggest is a random variable that assumes all the possible values. • Which leads to a solution state required to reach the goal node. • But beyond these “classical search algorithms," we have some “local search algorithms” where the path cost does not matters, and only focus on solution-state needed to reach the goal node. • Example: Greedy BFS* Algorithm. 4
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  12/06/2025 Department ofSB-ET Local search in continuous spaces • A local search algorithm completes its task by traversing on a single current node rather than multiple paths and following the neighbors of that node generally. • Example: Hill climbing and simulated annealing can handle continuous state and action spaces, because they have infinite branching factors. 5
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  12/06/2025 Department ofSB-ET Solution for Continuous space • One way to avoid continuous problems is simply to discretize the neighborhood of each state. • Many methods attempt to use the gradient of the landscape to find a maximum. The gradient of the objective function is a vector f that gives the magnitude and direction of the ∇ steepest slope. 6
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  12/06/2025 Department ofSB-ET Local search in continuous spaces 7
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  12/06/2025 Department ofSB-ET 8 Local search in continuous spaces
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  12/06/2025 Department ofSB-ET Does the local search algorithm work for a pure optimized problem? • Yes, the local search algorithm works for pure optimized problems. • A pure optimization problem is one where all the nodes can give a solution. But the target is to find the best state out of all according to the objective function. • Unfortunately, the pure optimization problem fails to find high- quality solutions to reach the goal state from the current state. • Note: An objective function is a function whose value is either minimized or maximized in different contexts of the optimization problems. • In the case of search algorithms, an objective function can be the path cost for reaching the goal node, etc. 9
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  12/06/2025 Department ofSB-ET Working of a Local search algorithm 10
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  12/06/2025 Department ofSB-ET Problems in Hill Climbing Algorithm 1. Local Maximum: A local maximum is a peak state in the landscape which is better than each of its neighboring states, but there is another state also present which is higher than the local maximum. Solution: Backtracking technique can be a solution of the local maximum in state space landscape. Create a list of the promising path so that the algorithm can backtrack the search space and explore other paths as well. 11
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  12/06/2025 Department ofSB-ET 12 2. Plateau: A plateau is the flat area of the search space in which all the neighbor states of the current state contains the same value, because of this algorithm does not find any best direction to move. A hill-climbing search might be lost in the plateau area. Solution: The solution for the plateau is to take big steps or very little steps while searching, to solve the problem. Randomly select a state which is far away from the current state so it is possible that the algorithm could find non-plateau region.
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  12/06/2025 Department ofSB-ET 13 3. Ridges: A ridge is a special form of the local maximum. It has an area which is higher than its surrounding areas, but itself has a slope, and cannot be reached in a single move. Solution: With the use of bidirectional search, or by moving in different directions, we can improve this problem.
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  12/06/2025 Department ofSB-ET Conclusion • Local search often works well on large problems – optimality – Always has some answer available (best found so far) 14
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  12/06/2025 Department ofSB-ET Topics to be covered in next session 10 • Searching with non-deterministic Actions, searching with partial observations, online search agents and unknown environments. 15 Thank you!!!