What is artificial intelligence,Hill Climbing Procedure,Hill Climbing Procedure,State Space Representation and Search,classify problems in AI,AO* ALGORITHM

1. Artificial Intelligence
(AI Study Material)
by Jay Nagar
Email: nagarjay007@gmail.com
Website: https://jaynagarblog.wordpress.com/
Call: 9601957620

2. What is artificial intelligence?
 AI refers to only a computer that is able to "seem"
intelligent by analyzing data and producing a response.
 The science and engineering of making intelligent
machines.
 This concept was founded on the belief that human
intelligence "can be so precisely described that a
machine can be made to simulate it."
 The central goals of AI research include reasoning,
knowledge, planning, learning, natural language
processing (communication), perception and the ability
to move and manipulate objects.
 The AI field is interdisciplinary, including computer
science,
mathematics, psychology, linguistics, philosophy and
neuroscience, as well as other specialized fields such as

3. State Space Representation and
Search
 In this section we examine the concept of a state space and the different
searches that can be used to explore the search space in order to find a
solution. Before an AI problem can be solved it must be represented as a state
space. The state space is then searched to find a solution to the problem. A
state space essentially consists of a set of nodes representing each state of the
problem, arcs between nodes representing the legal moves from one state to
another, an initial state and a goal state. Each state space takes the form of a
tree or a graph. Factors that determine which search algorithm or technique will
be used include the type of the problem and the how the problem can be
represented. Search techniques that will be examined in the course include:
• Depth First Search
• Depth First Search with Iterative Deepening
• Breadth First Search
• Best First Search
• Hill Climbing
• Branch and Bound Techniques
• A* Algorithm

4. Depth First Search
 Depth First Search One of the searches
that are commonly used to search a state
space is the depth first search. The depth
first search searches to the lowest depth
or ply of the tree. Consider the tree in
Figure. In this case the tree has been
generated prior to the search Each node
is not visited more than once.
 A depth first search of the this tree
produces: A, B, E, K, S, L ,T, F, M, C, G,
N, H, O, P, U, D, I, Q, J, R. Although in
this example the tree was generated first
and then a search of the tree was
conducted. However, often there is not
enough space to generate the entire tree
representing state space and then search
it. The algorithm presented below
conducts a depth first search and

5. Depth First Search with Iterative Deepening Algorithm
 Depth First Search with Iterative Deepening Iterative deepening involves
performing the depth first search on a number of different iterations with
different depth bounds or cutoffs. On each iteration the cutoff is increased
by one. There iterative process terminates when a solution path is found.
Iterative deepening is more advantageous in cases where the state space
representation has an infinite depth rather than a constant depth. The
state space is searched at a deeper level on each iteration. DFID is
guaranteed to find the shortest path. The algorithm does retain information
between iterations and thus prior iterations are “wasted”.
 Depth First Iterative Deepening Algorithm
procedure DFID (intial_state, goal_states)
begin
search_depth=1 while (solution path is not found)
begin
dfs(initial_state, goals_states) with a depth bound of search_depth
increment search_depth by 1
endwhile
end

6. Breadth First Search
 Breadth First Search The breadth first search visits
nodes in a left to right manner at each level of the tree.
Each node is not visited more than once. A breadth first
search of the tree in Figure 5.1. produces A, B, C, D, E,
F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U. Although in
this example the tree was generated first and then a
search of the tree was conducted. However, often there
is not enough space to generate the entire tree
representing state space and then search it. The

7. Bayesian network
 Inferring unobserved variables.
Because a Bayesian network is a
complete model for the variables
and their relationships, it can be
used to answer probabilistic
queries about them. ... This
process of computing the posterior
distribution of variables given
evidence is called probabilistic
inference.
 Bayesian probability is an
interpretation of the concept
of probability, in which, instead of
frequency or propensity of some
phenomenon, probability is
interpreted as reasonable
expectation representing a state of
knowledge or as quantification of a

8. Graphs v/s Trees
 If states in the solution space can be
revisited more than once a directed graph is
used to represent the solution space. In a
graph more than one move sequence can
be used to get from one state to another.
Moves in a graph can be undone. In a
graph there is more than one path to a goal
whereas in a tree a path to a goal is more
clearly distinguishable. A goal state may
need to appear more than once in a tree.
Search algorithms for graphs have to cater
for possible loops and cycles in the graph.
Trees may be more “efficient” for
representing such problems as loops and
cycles do not have to be catered for. The
entire tree or graph will not be generated.
Figure illustrates the both a graph a
representation of the same the states.

9. Travelling Salesmen Problem:

10. These characteristics are often used to
classify problems in AI:
 Decomposable to smaller or easier problems
 Solution steps can be ignored or undone
 Predictable problem universe
 Good solutions are obvious
 Uses internally consistent knowledge base
 Requires lots of knowledge or uses knowledge to
constrain solutions
 Requires periodic interaction between human and
computer

11. This is a variety of depth-first (generate - and - test) search. A feedback is used here to decide on the direction of
motion in the search space. In the depth-first search, the test function will merely accept or reject a solution. But
in hill climbing the test function is provided with a heuristic function which provides an estimate of how close a
given state is to goal state. The hill climbing test procedure is as follows :
1. General he first proposed solution as done in depth-first procedure. See if it is a solution. If so quit , else continue.
2. From this solution generate new set of solutions use , some application rules
3. For each element of this set
(i) Apply test function. It is a solution quit.
(ii) Else see whether it is closer to the goal state than the solution already generated. If yes, remember it else discard it.
4. Take the best element so far generated and use it as the next proposed solution. This step corresponds to move through the problem
space in the direction Towards the goal state.
5. Go back to step 2.
Sometimes this procedure may lead to a position, which is not a solution, but from which there is no move that improves things. This will
happen if we have reached one of the following three states.
(a) A "local maximum " which is a state better than all its neighbors , but is not better than some other states farther away. Local
maxim sometimes occur with in sight of a solution. In such cases they are called " Foothills".
(b) A "plateau'' which is a flat area of the search space, in which neighboring states have the same value. On a plateau, it is not
possible to determine the best direction in which to move by making local comparisons.
(c) A "ridge" which is an area in the search that is higher than the surrounding areas, but can not be searched in a
simple move.
To overcome theses problems we can:
(a) Back track to some earlier nodes and try a different direction. This is a good way of dealing with local maxim.
(b) Make a big jump an some direction to a new area in the search. This can be done by applying two more rules of the same rule several
times, before testing. This is a good strategy is dealing with plate and ridges.
Hill climbing becomes inefficient in large problem spaces, and when combinatorial explosion occurs. But it is a useful when combined with
other methods.
Hill Climbing Procedure:

12. The AO* ALGORITHM
The problem reduction algorithm we just described is a simplification of an algorithm
described in Martelli and Montanari, Martelli and Montanari and Nilson. Nilsson calls it the
AO* algorithm , the name we assume.
1. Place the start node s on open.
2. Using the search tree constructed thus far, compute the most promising solution tree T
3. Select a node n that is both on open and a part of T. Remove n from open and place it on
closed.
4. If n is a terminal goal node, label n as solved. If the solution of n results in any of n’s
ancestors being solved, label all the ancestors as solved. If the start node s is solved, exit
with success where T is the solution tree. Remove from open all nodes with a solved
ancestor.
5. If n is not a solvable node (operators cannot be applied), label n as unsolvable. If the start
node is labeled as unsolvable, exit with failure. If any of n’s ancestors become unsolvable
because n is, label them unsolvable as well. Remove from open all nodes with unsolvable
ancestors.
6. Otherwise, expand node n generating all of its successors. For each such successor
node that contains more than one sub problem, generate their successors to give individual
sub problems. Attach to each newly generated node a back pointer to its predecessor.
Compute the cost estimate h* for each newly generated node and place all such nodes that
do not yet have descendents on open. Next, recomputed the values of h* at n and each
ancestor of n.
7. Return to step 2.

13. A* Algorithm2.
A* algorithm: The best first search algorithm that was just presented is a simplification an
algorithm called A* algorithm which was first presented by HART.
Algorithm:
Step 1: put the initial node on a list start
Step 2: if (start is empty) or (start = goal) terminate search.
Step 3: remove the first node from the start call this node a
Step 4: if (a= goal) terminate search with success.
Step 5: else if node has successors generate all of them estimate the fitness number of the
successors by totaling the evaluation function value and the cost function value and sort
the fitness number.
Step 6: name the new list as start 1.
Step 7: replace start with start 1.
Step 8: go to step 2.

14.  A Heuristic technique helps in solving problems, even though there
is no guarantee that it will never lead in the wrong direction. There
are heuristics of every general applicability as well as domain
specific. The strategies are general purpose heuristics. In order to
use them in a specific domain they are coupler with some domain
specific heuristics. There are two major ways in which domain -
specific, heuristic information can be incorporated into rule-based
search procedure.
 - In the rules themselves
 - As a heuristic function that evaluates individual problem states and
determines how desired they are.
 A heuristic function is a function that maps from problem state
description to measures desirability, usually represented as number
weights. The value of a heuristic function at a given node in the
search process gives a good estimate of that node being on the
desired path to solution. Well designed heuristic functions can
provides a fairly good estimate of whether a path is good or not. ( "
The sum of the distances traveled so far" is a simple heuristic
function in the traveling salesman problem) . the purpose of a
heuristic function is to guide the search process in the most
profitable directions, by suggesting which path to follow first when
more than one path is available. However in many problems, the cost
of computing the value of a heuristic function would be more than
the effort saved in the search process. Hence generally there is a
trade-off between the cost of evaluating a heuristic function and the
HEURISTIC FUNCTIONS:

15. Tower of Honai Problem.?

17. Generate and Test Procedure
This is the simplest search strategy. It consists of the following
steps;
 1. Generating a possible solution for some problems; this means
generating a particular point in the problem space. For others it
may be generating a path from a start state.
 2. Test to see if this is actually a solution by comparing the
chosen point at
 the end point of the chosen path to the set of acceptable goal
states.
 3. If a solution has been found, quit otherwise return to step 1.
 The generate - and - Test algorithm is a depth first search
procedure because complete possible solutions are generated
before test. This can be implemented states are likely to appear
often in a tree; it can be implemented on a search graph rather
than a tree.

18. What is the difference between forward and backward chaining in artificial
intelligence?
An AI cannot give proofs somehow thinking and assuming meanings of statements. So to get the proofs there
are set of rules that are fixed for inference logic and within that fixed set of rules we have forward and
backward chaining.
Forward chaining.
It is also known as data driven inference technique.
Forward chaining matches the set of conditions and infer results from these conditions. Basically, forward
chaining starts from a new data and aims for any conclusion.
It is bottom up reasoning.
It is a breadth first search.
It continues until no more rules can be applied or some cycle limit is met.
For example: If it is cold then I will wear a sweater. Here “it is cold is the data” and “I will wear a sweater”is a
decision. It was already known that it is cold that is why it was decided to wear a sweater, This process is
forward chaining.
It is mostly used in commercial applications i.e event driven systems are common example of forward
chaining.
It can create an infinite number of possible conclusions.
Backward chaining.
It is also called as goal driven inference technique.
It is a backward search from goal to the conditions used to get the goal. Basically it starts from possible
conclusion or goal and aims for necessary data.
It is top down reasoning.
It is a depth first search.
It process operations in a backward direction from end to start, it will stop when the matching initial condition is
met.
For example: If it is cold then I will wear a sweater. Here we have our possible conclusion “I will wear a

19.  A technique to find a good solution to an optimization problem by trying random variations of the current
solution. A worse variation is accepted as the new solution with a probability that decreases as the
computation proceeds. The slower the cooling schedule, or rate of decrease, the more likely the
algorithm is to find an optimal or near-optimal solution.
 Simulated annealing is a generalization of a Monte Carlo method for examining the equations of state
and frozen states of n-body systems [Metropolis et al. 1953]. The concept is based on the manner in
which liquids freeze or metals recrystalize in the process of annealing. In an annealing process a melt,
initially at high temperature and disordered, is slowly cooled so that the system at any time is
approximately in thermodynamic equilibrium. As cooling proceeds, the system becomes more ordered
and approaches a "frozen" ground state at T=0. Hence the process can be thought of as an adiabatic
approach to the lowest energy state. If the initial temperature of the system is too low or cooling is done
insufficiently slowly the system may become quenched forming defects or freezing out in metastable
states (ie. trapped in a local minimum energy state).
 The original Metropolis scheme was that an initial state of a thermodynamic system was chosen at
energy E and temperature T, holding T constant the initial configuration is perturbed and the change in
energy dE is computed. If the change in energy is negative the new configuration is accepted. If the
change in energy is positive it is accepted with a probability given by the Boltzmann factor exp -(dE/T).
This processes is then repeated sufficient times to give good sampling statistics for the current
temperature, and then the temperature is decremented and the entire process repeated until a frozen
state is achieved at T=0.
 By analogy the generalization of this Monte Carlo approach to combinatorial problems is straight
forward [Kirkpatrick et al. 1983, Cerny 1985]. The current state of the thermodynamic system is
analogous to the current solution to the combinatorial problem, the energy equation for the
thermodynamic system is analogous to at the objective function, and ground state is analogous to the
global minimum. The major difficulty (art) in implementation of the algorithm is that there is no obvious
analogy for the temperature T with respect to a free parameter in the combinatorial problem.
Furthermore, avoidance of entrainment in local minima (quenching) is dependent on the "annealing
schedule", the choice of initial temperature, how many iterations are performed at each temperature,
and how much the temperature is decremented at each step as cooling proceeds.
 Simulated annealing has been used in various combinatorial optimization problems and has been
particularly successful in circuit design problems
Define simulated annealing?