problem solving AI

1. PROBLEM
SOLVING AND
CREATIVITY

2. OUTLINE
1.
2.
1. The Problem-Solving Cycle/problem solving process
2. T
ypes ofProblems
Well-Structured Problems
Ill-Structured Problems and the Role of Insight

3. 1.THE PROBLEM-SOLVING CYCLE
 Problem Solving
 The process of overcoming obstacles to answer a question
or to achieve a goal
The problem Solving Cycle
1.Problem Identification
 We have to recognize that we have a goal or that the
solution we had in mind does not work
2.Problem definition and representation
 We have to define and represent the problem well enough
to understand how to solve it

4. 1.THE PROBLEM-SOLVING
CYCLE
3.Strategy formulation
 We have to plan a strategy for solving the problem which may involve
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Analysis – breaking down the whole of a complex problem into manageable elements
Synthesis – putting together various elements to arrange them into something useful
Divergent thinking – you try to generate a diverse assortment of possible alternative solutions to
a problem
Convergent thinking – you narrow down the multiplepossibilities to converge on asingle,best
answer

5. 1.THE PROBLEM-SOLVING
CYCLE
4.O rganization of Information
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You have to organize the available information in a way that
enables you to implement the strategy
You organize the information strategically,finding a the most
suitable representation
5.Resource allocation
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We have limited resources (time,money
,equipment,space,…)
We have to decide how much we want to invest into the
problem solving

6. 1.THE PROBLEM-SOLVING
CYCLE
6.Monitoring
 It is necessary to monitor the process of solving the
problem to make sure that we are getting closer to the goal
 We need to reassess what we are doing to be able to
compensate for possible flaws
7.Evaluation
 You need to evaluate your solution after you have finished
 New problems can be recognized,the problem may be
redefined,new strategies may come to light,and new
resources may become available

7. 1.THE PROBLEM-SOLVING
CYCLE
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8. 2.TYPES OF PROBLEMS
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9. 2.TYPES OF PROBLEMS
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10. General problem solving
• Problem solving is a process of generating solutions from observed
data.
• • a ‘problem’ is characterized by a set of goals,
• • a set of objects, and
• • a set of operations.
• These could be ill-defined and may evolve during problem solving.
 A ‘problem space’ is an abstract space.
• A problem space encompasses all valid states that can be generated
by the application of any combination of operators on any combination
of objects.
• The problem space may contain one or more solutions. A solution is
a combination of operations and objects that achieve the goals.
 A ‘search’ refers to the search for a solution in a problem space.
• Search proceeds with different types of ‘search control strategies’.
• The depth-first search and breadth-first search are the two common
search strategies.

11. DEFINING PROBLEM AS A STATE SPACE SEARCH
• To solve the problem of playing a game, we require the rules of the game
and targets for winning as well as representing positions in the game. The
opening position can be defined as the initial state and a winning position as
a goal state. Moves from initial state to other states leading to the goal state
follow legally. However, the rules are far too abundant in most games—
especially in chess, where they exceed the number of particles in the
universe. Thus, the rules cannot be supplied accurately and computer
programs cannot handle easily. The storage also presents another problem
but searching can be achieved by hashing.
• The number of rules that are used must be minimized and the set can be
created by expressing each rule in a form as possible. The representation of
games leads to a state space representation and it is common for well-
organized games with some structure. This representation allows for the
formal definition of a problem that needs the movement from a set of initial
positions to one of a set of target positions. It means that the solution
involves using known techniques and a systematic search. This is quite a
common method in Artificial Intelligence.

12. State Space Search
A state space represents a problem in terms of states and operators that
change states.
A state space consists of:
 A representation of the states the system can be in. For example, in a
board game, the board represents the current state of the game.
 A set of operators that can change one state into another state. In a
board game, the operators are the legal moves from any given state. Often
the operators are represented as programs that change a state
representation to represent the new state.
 An initial state.
 A set of final states; some of these may be desirable, others undesirable.
This set is often represented implicitly by a program that detects terminal
states.

13. The Water Jug Problem
• In this problem, we use two jugs called four and three; four holds a maximum of
four gallons of water and three a maximum of three gallons of water. How can
we get two gallons of water in the four jug?
• The state space is a set of prearranged pairs giving the number of gallons of
water in the pair of jugs at any time, i.e., (four, three) where four = 0, 1, 2, 3 or 4
and three = 0, 1, 2 or 3.
• The start state is (0, 0) and the goal state is (2, n) where n may be any but it is
limited to three holding from 0 to 3 gallons of water or empty. Three and four
shows the name and numerical number shows the amount of water in jugs for
solving the water jug problem. The major production rules for solving this
problem are shown below:

14. PRODUCTION RULES

15. One Solution to the Water Jug Problem
The problem solved by using the production rules in
combination with an appropriate control strategy,
moving through the problem space until a path from
an initial state to a goal state is found.
In this problem solving process, search is the
fundamental concept. For simple problems it is easier
to achieve this goal by hand but there will be cases
where this is far too difficult.

16. One possible solution
• 1. Current state = (0, 0)
• 2. Loop until the goal state (2, 0) reached
• – Apply a rule whose left side matches the current state
• – Set the new current state to be the resulting state
• (0, 0) – Start State
• (0, 3) – Rule 2, Fill the 3-liter jug
• (3, 0) – Rule 9, Pour all the water from the 3-liter jug into the 4-liter jug.
• (3, 3) – Rule 2, Fill the 3-liter jug
• (4, 2) – Rule 7, Pour water from the 3-liter jug into the 4-liter jug until the 4-liter jug is full.
• (0, 2) – Rule 5, Empty the 4-liter jug on the ground
• (2, 0) – Rule 9, Pour all the water from the 3-liter jug into the 4-liter jug.
• Goal State reached

17. Another solution to Water Jug Problem in Artificial
Intelligence
• (0, 0) – Start State
• (4, 0) – Rule 1, Fill the 4-liter jug
• (1, 3) – Rule 8, Pour water from the 4-liter jug into the 3-liter jug until the 3-liter jug is
full.
• (1, 0) – Rule 6, Empty the 3-liter jug on the ground
• (0, 1) – Rule 10, Pour all the water from the 4-liter jug into the 3-liter jug.
• (4, 1) – Rule 1, Fill the 4-liter jug
• (2, 3) – Rule 8, Pour water from the 4-liter jug into the 3-liter jug until the 3-liter jug is
full.
• Goal State reached