- The document discusses various problem solving techniques in artificial intelligence including search strategies like BFS, DFS, A*, heuristic search, and beyond classical search methods. - It describes local search algorithms like hill climbing, simulated annealing, and genetic algorithms that are used for large search spaces and optimization problems. - Various hill climbing techniques - simple, steepest ascent, stochastic, and random restart hill climbing - are explained along with state space diagrams and concepts like local maxima. - The next session will cover local search in continuous spaces.

1. ARTIFICAL INTELLIGENCE
(R18 III(II Sem))
Department of computer science and
engineering (AI/ML)
Session 9
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 9
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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. Beyond classical search
• We have seen methods that systematically
explore the search space, possibly using
principled pruning (e.g., A*)
What if we have much larger search spaces?
• Search spaces for some real-world problems
may be much larger e.g., 1030,000 states as in
certain reasoning and planning tasks.
• Some of these problems can be solved by
Iterative Improvement Methods
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5. Local Search Algorithms and
Optimization Problems
• In many optimization problems the goal state itself is the
solution.
• The state space is a set of complete configurations.
• Search is about finding the optimal configuration (as in
TSP) or just a feasible configuration (as in scheduling
problems).
• In such cases, one can use iterative improvement, or
local search, methods.
• An evaluation, or objective, function h must be available
that measures the quality of each state.
• Main Idea: Start with a random initial configuration and
make small, local changes to it that improve its quality.
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6. Hill Climbing Algorithm
• In Hill-Climbing technique, starting at the base of a
hill, we walk upwards until we reach the top of the
hill.
• In other words, we start with initial state and we keep
improving the solution until its optimal.
• It's a variation of a generate-and-test algorithm which
discards all states which do not look promising or
seem unlikely to lead us to the goal state.
• To take such decisions, it uses heuristics (an
evaluation function) which indicates how close the
current state is to the goal state.
• Hill-Climbing = generate-and-test + heuristics
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7. Features of Hill Climbing
Following are some main features of Hill Climbing
Algorithm:
• Generate and Test variant: Hill Climbing is the
variant of Generate and Test method. The Generate and
Test method produce feedback which helps to decide
which direction to move in the search space.
• Greedy approach: Hill-climbing algorithm search
moves in the direction which optimizes the cost.
• No backtracking: It does not backtrack the search
space, as it does not remember the previous states.
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8. Types of Hill Climbing Algorithm
• Simple hill Climbing
• Steepest-Ascent hill-climbing
• Stochastic hill Climbing
• Random-restart hill climbing
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9. Simple Hill Climbing
• Simple hill climbing is the simplest way to implement a
hill climbing algorithm.
• It only evaluates the neighbor node state at a time and
selects the first one which optimizes current cost and
set it as a current state.
• It only checks it's one successor state, and if it finds better
than the current state, then move else be in the same state.
• This algorithm has the following features:
• Less time consuming
• Less optimal solution and the solution is not
guaranteed
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10. Algorithm
• Define the current state as an initial state
• Loop until the goal state is achieved or no more operators
can be applied on the current state:
– Apply an operation to current state and get a new state
– Compare the new state with the goal
– Quit if the goal state is achieved
– Evaluate new state with heuristic function
and compare it with the current state
– If the newer state is closer to the goal compared to
current state, update the current state
• As we can see, it reaches the goal state with iterative
improvements. In Hill-Climbing algorithm, finding goal
is equivalent to reaching the top of the hill.
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11. Example
• Key point while solving any
hill-climbing problem is to
choose an
appropriate heuristic
function.
• Let's define such function h:
• h(x) = +1 for all the blocks
in the support structure if
the block is correctly
positioned otherwise -1 for
all the blocks in the
support structure.
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13. Steepest-ascent Hill climbing
• Steepest-ascent hill climbing is different from
simple hill climbing search.
• Unlike simple hill climbing search, It considers
all the successive nodes, compares them, and
choose the node which is closest to the solution.
• Steepest hill climbing search is similar to best-
first search because it focuses on each node
instead of one.
• Note: Both simple, as well as steepest-ascent hill
climbing search, fails when there is no closer
node.
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14. Algorithm
• Create a CURRENT node and a GOAL node.
• If the CURRENT node=GOAL node,
return GOAL and terminate the search.
• Loop until a better node is not found to reach
the solution.
• If there is any better successor node present,
expand it.
• When the GOAL is attained,
return GOAL and terminate.
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15. Simulated Annealing
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• A hill-climbing algorithm which never makes a move towards a
lower value guaranteed to be incomplete because it can get stuck on
a local maximum.
• And if algorithm applies a random walk, by moving a successor,
then it may complete but not efficient.
• Simulated Annealing is an algorithm which yields both efficiency
and completeness.
• In mechanical term Annealing is a process of hardening a metal or
glass to a high temperature then cooling gradually, so this allows the
metal to reach a low-energy crystalline state.
• The same process is used in simulated annealing in which the
algorithm picks a random move, instead of picking the best move.
• If the random move improves the state, then it follows the same
path.
• Otherwise, the algorithm follows the path which has a probability of
less than 1 or it moves downhill and chooses another path.

16. Stochastic hill climbing
• Stochastic hill climbing does not focus on all the nodes.
• It selects one node at random and decides whether it
should be expanded or search for a better one.
Random-restart hill climbing
• Random-restart algorithm is based on try and try
strategy.
• It iteratively searches the node and selects the best one
at each step until the goal is not found.
• The success depends most commonly on the shape of
the hill.
• If there are few plateaus, local maxima, and ridges, it
becomes easy to reach the destination.
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17. State-space Diagram for Hill Climbing
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18. • Local Maximum: Local maximum is a state
which is better than its neighbor states, but there
is also another state which is higher than it.
• Global Maximum: Global maximum is the best
possible state of state space landscape. It has the
highest value of objective function.
• Current state: It is a state in a landscape diagram
where an agent is currently present.
• Flat local maximum: It is a flat space in the
landscape where all the neighbor states of current
states have the same value.
• Shoulder: It is a plateau region which has an
uphill edge.
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19. Genetic Algorithm
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22. Topics to be covered in next session 10
• Local Search in Continuous Spaces
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Thank you!!!