heuristic technique.pptx...............................

Seminar
on
Heuristic Search Techniques
Submitted to:
Mr.Chetan Gupta
POST GRADUATE GOVERNMENT COLLEGE SECTOR 11
CHANDIGARH
Department of Professional Studies
Submitted by:
Arshdeep kaur
Roll no.462023
Msc.it

A heuristic is a technique that is used to
solve a problem faster than the classic
methods. These techniques are used to find
the approximate solution of a problem when
classical methods do not. Heuristics are said
to be the problem-solving techniques that
result in practical and quick solutions.
Heuristics are strategies that are derived
from past experience with similar problems.
Heuristics use practical methods and
shortcuts used to produce the solutions that
may or may not be optimal, but those
solutions are sufficient in a given limited
timeframe.

The following Algorithm make use of
Heuristic evolution:
Hill Climbing
Best First Search
A*
AO*
Constraint Satisfaction
Means-ends Analysis

Hill climbing algorithm is a local search algorithm which continuously
moves in the direction of increasing elevation/value to find the peak of
the mountain or best solution to the problem. It terminates when it
reaches a peak value where no neighbor has a higher value.
Hill climbing algorithm is a technique which is used for optimizing the
mathematical problems. One of the widely discussed examples of Hill
climbing algorithm is Traveling-salesman Problem in which we need to
minimize the distance traveled by the salesman.
It is also called greedy local search as it only looks to its good immediate
neighbor state and not beyond that.
A node of hill climbing algorithm has two components which are state
and value.
HILL
CLIMBING

State space diagram for hill
climbing
The state-space diagram is a graphical
representation of the set of states our search
algorithm can reach vs the value of our
objective function(the function which we
wish to maximize).
X-axis: denotes the state space ie states or
configuration our algorithm may reach.
Y-axis: denotes the values of objective
function corresponding to a particular state.
The best solution will be a state space where
the objective function has a maximum
value(global maximum).

Local maximum: It is a state which is better than its neighboring state however
there exists a state which is better than it(global maximum).
Global maximum: It is the best possible state in the state space diagram.
This is because, at this stage, the objective function has the highest value.
Plateau/flat local maximum: It is a flat region of state space where
neighboring states have the same value.
Ridge: It is a region that is higher than its neighbors but itself
has a slope. It is a special kind of local maximum.
Current state: The region of the state space diagram where
we are currently present during the search.
Shoulder: It is a plateau that has an uphill edge.
Different
region in
state space
diagran

ALGORITHM
FOR SIMPLE
HILL CLIMBING
Step 1: Evaluate the initial state, if it is goal state then
return success and Stop
Step 2: Loop Until a solution is found or there is no new
operator left to apply.
Step 3: Select and apply an operator to
the current state.
Step 4: Check new state:
Step 5: Exit.

BEST FIRST SEARCH
Best first search (BFS) is a search algorithm that functions at a particular rule
and uses a priority queue and heuristic search. It is ideal for computers to
evaluate the appropriate and shortest path through a maze of possibilities.
Suppose you get stuck in a big maze and do not know how and where to
exit quickly. Here, the best first search in AI aids your system program to
evaluate and choose the right path at every succeeding step to reach the
goal as quickly as possible.
For example, imagine you are playing a video game of Super Mario or
Contra where you have to reach the goal and kill the enemy. The best first
search aid computer system to control the Mario or Contra to check the
quickest route or way to kill the enemy. It evaluates distinct paths and
selects the closest one with no other threats to reach your goal and kill the
enemy as fast as possible

step1 • Place the starting node into the OPEN list
step2 • If the OPEN list is empty, Stop and return failure.
ste3p
• Remove the node n, from the OPEN list which has the
lowest value of h(n), and places it in the CLOSED list.
step4
• Expand the node n, and generate the successors of
node n.
step5
• Check each successor of node n, and find whether any node is a goal node
or not. If any successor node is goal node, then return success and terminate
the search, else proceed to Step 6.
step6
• For each successor node, algorithm checks for evaluation function f(n), and
then check if the node has been in either OPEN or CLOSED list. If the node has
not been in both list, then add it to the OPEN list.
BEST FIRST SEARCH ALGORITHM

A* Search Algorithm:
A* search is the most commonly known form of
best-first search. It uses heuristic function h(n),
and cost to reach the node n from the start state
g(n). It has combined features of UCS and
greedy best-first search, by which it solve the
problem efficiently. A* search algorithm finds the
shortest path through the search space using the
heuristic function. This search algorithm expands
less search tree and provides optimal result
faster. A* algorithm is similar to UCS except that it
uses g(n)+h(n) instead of g(n).
In A* search algorithm, we use search heuristic as
well as the cost to reach the node. Hence we
can combine both costs as following, and this
sum is called as a fitness number.

Its an informed search and works as best first search. ● AO* Algorithm is based on problem
decomposition (Breakdown problem into small pieces). ● Its an efficient method to explore
a solution path. ● AO* is often used for the common pathfinding problem in applications
such as video games, but was originally designed as a general graph traversal algorithm. ●
It finds applications in diverse problems, including the problem of parsing using stochastic
grammars in NLP. ● Other cases include an Informational search with online learning. ● It is
useful for searching game trees, problem solving etc.
AND-OR Graph ● AND-OR graph is useful for representing the solution of problems that can
be solved by decomposing them into a set of smaller problems, all of which must then be
solved. Own Mobile Phone Steal It Earn Money Buy mobile phone
AO* ALGORITHM

Algorithm of A* search:
 Step1: Place the starting node in the OPEN list.
 Step 2: Check if the OPEN list is empty or not, if the list is empty then return failure
and stops.
 Step 3: Select the node from the OPEN list which has the smallest value of
evaluation function (g+h), if node n is goal node then return success and stop,
otherwise
 Step 4: Expand node n and generate all of its successors, and put n into the
closed list. For each successor n', check whether n' is already in the OPEN or
CLOSED list, if not then compute evaluation function for n' and place into Open
list.
 Step 5: Else if node n' is already in OPEN and CLOSED, then it should be attached
to the back pointer which reflects the lowest g(n') value.
 Step 6: Return to Step 2.

In this example, we will traverse the given graph using the A* algorithm. The
heuristic value of all states is given in the below table so we will calculate the f(n) of
each state using the formula f(n)= g(n) + h(n), where g(n) is the cost to reach any
node from start state.
Here we will use OPEN and CLOSED list.
EXAMPLE

1. Initialization: {(S, 5)}
2. Iteration1: {(S--> A, 4), (S-->G,
10)}
3. Iteration2: {(S--> A-->C, 4), (S-->
A-->B, 7), (S-->G, 10)}
4. Iteration3: {(S--> A-->C--->G, 6),
(S--> A-->C--->D, 11), (S--> A--
>B, 7), (S-->G, 10)}
5. Iteration 4 will give the final
result, as S--->A--->C--->G it
provides the optimal path with
cost 6.
SOLUTION

 Its an informed search and works as best first search. ● AO* Algorithm is based on
problem decomposition (Breakdown problem into small pieces). ● Its an efficient
method to explore a solution path. ● AO* is often used for the common pathfinding
problem in applications such as video games, but was originally designed as a general
graph traversal algorithm. ● It finds applications in diverse problems, including the
problem of parsing using stochastic grammars in NLP. ● Other cases include an
Informational search with online learning. ● It is useful for searching game trees,
problem solving etc.
AND-OR Graph
 ● AND-OR graph is useful for representing the solution of problems that can be solved
by decomposing them into a set of smaller problems, all of which must then be solved.
 Node in the graph will point both down to its successors and up to its parent nodes. ●
Each Node in the graph will also have a heuristic value associated with it. f(n)=g(n)
+h(n) f(n): Cost function. g(n): Actual cost or Edge value h(n): Heuristic/ Estimated
value of the nodes
AO* Algorithm

 Initialise the graph to start node
 Traverse the graph following the current path
accumulating nodes that have not yet been
expanded or solved
 Pick any of these nodes and expand it and if it has no
successors call this value FUTILITY otherwise calculate
only f` for each of the successors.
 . If f` is 0 then mark the node as SOLVED
 . Change the value of f` for the newly created node
to reflect its successors by back propagation
 . Wherever possible use the most promising routes and
if a node is marked as SOLVED then mark the parent
node as SOLVED.
 If starting node is SOLVED or value greater than
FUTILITY, stop, else repeat from 2.
AO* Algorithm

Constraint Satisfaction Problems (CSP)
• Constraints: The guidelines that control how variables relate to one another are known
as constraints. Constraints in a CSP define the ranges of possible values for variables.
Unary constraints, binary constraints, and higher-order constraints are only a few
examples of the various sorts of constraints. For instance, in a sudoku problem, the
restrictions might be that each row, column, and 3×3 box can only have one instance
of each number from 1 to 9.
CSP REPRESENTATION:
• The finite set of variables V1, V2, V3 ……………..Vn.
• Non-empty domain for every single variable D1, D2, D3 …………..Dn.
• The finite set of constraints C1, C2 …….…, Cm.
• where each constraint Ci restricts the possible values for variables,
• e.g., V1 ≠ V2
• Each constraint Ci is a pair <scope, relation>
• Example: <(V1, V2), V1 not equal to V2>
• Scope = set of variables that participate in constraint.
• Relation = list of valid variable value combinations.
• There might be a clear list of permitted combinations. Perhaps a relation that is
abstract and that allows for membership testing and listing.

The means-ends analysis process can be
applied recursively for a problem. It is a
strategy to control search in problem-solving.
Following are the main Steps which describes
the working of MEA technique for solving a
problem.
First, evaluate the difference between Initial
State and final State.
Select the various operators which can be
applied for each difference.
Apply the operator at each difference, which
reduces the difference between the current
state and goal state.
MEANS ENDS ANALYSIS

ALGORITHM FOR MEANS END ANALYSIS
1. Step 1: Compare CURRENT to GOAL, if there are no differences between both
then return Success and Exit.
2. Step 2: Else, select the most significant difference and reduce it by doing the
following steps until the success or failure occurs.
3. Select a new operator O which is applicable for the current difference, and if
there is no such operator, then signal failure.
4. Attempt to apply operator O to CURRENT. Make a description of two states.
5. i) O-Start, a state in which O?s preconditions are satisfied.
6. ii) O-Result, the state that would result if O were applied In O-start.
7. If
8. (First-Part <------ MEA (CURRENT, O-START)
9. And
10.(LAST-Part <----- MEA (O-Result, GOAL), are successful, then signal Success and
return the result of combining FIRST-PART, O, and LAST-PART.

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