AI_Session 10 Local search in continious space.pptx

1. ARTIFICAL INTELLIGENCE
(R18 III(II Sem))
Department of computer science and
engineering (AI/ML)
Session 10
by
Asst.Prof.M.Gokilavani
VITS
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2. 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.
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3. Topics covered in session 10
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• Problem solving by search-I: Introduction to AI, Intelligent Agents.
• Problem solving by search-II: Problem solving agents, searching for
solutions
• Uniformed search strategies: BFS, Uniform cost search, DFS,
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
• Searching with non-deterministic Actions, searching with partial
observations, online search agents and unknown environments.

4. 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 in a continuum.
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5. Local search in continuous spaces
• 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.
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6. 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.
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7. 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.
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8. Local search in continuous spaces
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10. 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.
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11. Working of a Local search algorithm
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12. 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.
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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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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.

15. Conclusion
• Local search often works well on large problems
– optimality
– Always has some answer available (best found so
far)
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16. Topics to be covered in next session 11
• Searching with non-deterministic Actions,
searching with partial observations, online
search agents and unknown environments.
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Thank you!!!