The document outlines a course on Artificial Intelligence, focusing on search algorithms and optimization methods, particularly the hill-climbing algorithm. It details various types of hill climbing, including simple, steepest-ascent, stochastic, and random-restart hill climbing, alongside the concept of simulated annealing. The document also explains the importance of heuristics and evaluation functions in navigating search spaces effectively.

1. 09/26/2024 Department of CSE (AI/ML) 1
22PCOAM11
INTROUCTION TO ARTIFICAL
INTELLIGENCE (R22 – II (Sem 3)
Department of computer science and
engineering (AIML)
Session 5
by
Asst.Prof.M.Gokilavani
GNITC

2. 09/26/2024 Department of CSE (AI & ML)
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 Unit 1
09/26/2024 Department of CSE (AI & ML) 3
• Introduction to AI : Intelligent Agent
• Problem-Solving Agents
• Searching for Solutions : Breadth-first search
• Depth-first search
• Hill-climbing search
• Simulated annealing search
• Local Search in Continuous Spaces.

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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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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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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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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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Types of Hill Climbing Algorithm
• Simple hill Climbing
• Steepest-Ascent hill-climbing
• Stochastic hill Climbing
• Random-restart hill climbing
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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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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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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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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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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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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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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.

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Simulated Annealing
• 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.
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State-space Diagram for Hill Climbing
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• 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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20. 09/26/2024 Department of CSE (AI/ML)
Topics to be covered in next session 6
• Local Search in Continuous Spaces
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Thank you!!!