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## Problem Solving

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**1. **Problem Solving

**2. **Definition of Machine Intelligence

**3. **Models of Reasoning State Space Searching with Heuristics
Rule Base Systems
Evolution and adaptation

**5. **Main feature of rules - acquisition

**7. **Other aspects of Intelligence Researchers in AI have constructed models of other aspects of intelligence such as CBR
Neural Networks
Probably many more great ideas to be discovered.
Swarm Intelligence, Ant Intelligence

**8. **Problem Solving Logic Deductive Reasoning
Inductive Reasoning
Abductive Reasoning
Analogical Reasoning

**9. **Analogy and Experience

**10. **Case-based Reasoning A type of analogical reasoning

**11. **Underlying Model of CBR
Humans are robust problem solvers
Humans reason from cases in a wide variety of contexts
Studies abound in how humans do this

**12. **What is CBR? Case-based reasoning is [...] reasoning by remembering.
A case-based reasoner solves new problems by adapting solutions that were used to solve old problems.
Case-based reasoning is a recent approach to problem solving and learning
Case-based reasoning is both the ways people use cases to solve problems and the ways we can make machines use them.

**13. **Analogical Reasoning (CBR) Case-based reasoning (CBR) is a certain technique which was based on analogical reasoning.
The main intention is to reuse previous experiences for actual problems.
The difficulty arises when the actual situation is not identical to the previous one: There is an inexactness involved.
Its main aspect is that CBR-techniques allow inexact (approximate) reasoning in a controlled manner.
Here we will shortly describe its main features.
Major applications include fault diagnosis, help desk systems, eCommerce

**14. **Could be calledSimilarity Based Reasoning The central notion in CBR is the concept of similarity.
The methods in CBR have been extended in a way which allows applications to other problems rather than reusing previous experiences:
in electronic commerce e.g. to product selection.
This is due to an abstract formulation of the similarity concept.
In particular, the main algorithms of CBR can still be applied to these new situations.
We will first describe the original technique informally and then proceed to the extensions.

**15. **Research in CBR ECCBR 2010 - European Conference on Case-Based Reasoning
ICCBR 2011 - International Conference on Case based Reasoning

**16. **Case-Based Reasoning (CBR) Basic Ideas:
Store previous experience (case)
Solve new Problems by selecting and reusing cases
Store new experience again
Replaces 0-1-logic by approximation
Is a well-founded technology:
Mathematically
Algorithmically
With respect to software technology
Supported by experiments and applications
Business success
Most successful recent branch of AI

**17. **What is a Case ? A case has two parts:
Description of a problem or a set of problems (generalized case)
Description of the solution of this problem (formally or informally)
Possibly additions like explanations, comments on the quality of the solution etc.
Cases represent experiences : They record how a problem was solved in the past

**18. **Different Case Representations

**19. **Structured Case Representation Many different case representations are used Depend on requirements of domain and task
Structure of already available case data
Flat feature-value list
Simple case structure is sometimes sufficient for problem solving
Easy to store and retrieve in a CBR system
Object-oriented representations
Case: collection of objects (instances of classes)
Required for complex and structured objects Genauer im Teil III.
Genauer im Teil III.

**20. **How to Use a Case

**21. **How to Use a Case-Base A case base is a data base of cases
If a new problem arises one will use a case from the case base in order to solve the problem
If we have many cases then the chance is higher to find one with a suitable solution
Because the given problem is usually not exactly in the base one wants to retrieve a case which solved a problem which is „similar enough to be useful“
Hence, the notion of similarity is central to CBR
The concept of similarity based retrieval is compared with data base retrieval

**22. **Components of CBR

**23. **The Classical CBR Algorithm

**24. **Typical Problems Handled with CBR: Classification and Diagnosis A class is a certain subset of some universe and a classification assigns to each element one or more classes to which it belongs.
In fault diagnosis the classification is only the first step:

**25. **An Example OverviewTypical Scenario: Call Center Technical Diagnosis of Car Faults:
symptoms are observed (e.g., engine doesn’t start) and values are measured (e.g., battery voltage = 6.3V)
goal: Find the cause for the failure (e.g., battery empty) anda repair strategy (e.g., charge battery)
Case-Based Diagnosis:
a case describes a diagnostic situation and contains:
description of the symptoms
description of the failure and the cause
description of a repair strategy
store a collection of cases in a case base
find case similar to current problem and reuse repair strategy

**26. **A Simple Example (II)What does a Case Look Like? A case describes one particular diagnostic situation
A case records several features and their specific values occurred in that situation
? A case is not a ( general) rule !!

**27. **A Case Base With Two Cases Each case describes one particular situation
All cases are independent of each other

**28. **Solving a New Diagnostic Problem A new problem has to be solved
We make several observations in the current situation
Observations define a new problem
Not all feature values have to be known
Note: The new problem is a “case” without solution part

**29. **You are required to identify between case 1 and case 2 the case that is most similar to to the problem case When are two cases similar?
How to rank the cases according to their similarity?
? Similarity is the most important concept in CBR !!
We can assess similarity based on the similarity of each feature
Similarity of each feature depends on the feature value.
BUT: Importance of different features may be different

**30. **Class Exercise

**31. **A similarity algorithm Assignment of similarities for features values.
Express degree of similarity by a real number between 0 and 1
Examples:
Feature: Problem
Feature: Battery voltage (similarity depends on the difference)
Different features have different importance (weights)!
High importance: Problem, Battery voltage, State of light, ...
Low importance: Car, Year, ...

**32. **Compare Similarity Similarity computation by weighted average
similarity(new,case 2) = 1/20 * [ 6*0.8 + 1*0.8 + 1*0.4 + 6*0.95 + 6*0 ] = 0.585
Case 1 is more similar: due to feature “State of lights”

**33. **Assign similarity values to each feature pair and a weight to each feature Similarity computation by weighted average
similarity(new,case 1) = 1/20 * [ 6*0.8 + 1*0.4 + 1*0.6 + 6*0.9 + 6* 1.0 ] = 0.86

**34. **Case adaption algorithm

**35. **New case inserted into the case library ??

**36. **The Classical CBR R4-Cycle

**37. **Retrieve: Modeling Similarity The similarity based retrieval realizes an inexact match which is still useful:
Useful solutions from a case base
Useful products from a product base
Different approaches depending on case representation
Similarity measures:
Are functions to compare two cases sim: Case x Case ® [0..1]
Local similarity measure: similarity on feature level
Global similarity measure: similarity on case or object level

**38. **Similarities (1) Similarities are described by measures with numerical values
They operate on
problem descriptions, demands, products ,...

**39. **Similarities and Inexact Reasoning
The similarity measure controls the utility when inexact solutions are employed or the desired product is not exactly as desired available.

**40. **A Typical Similarity Measure

**41. **Nearest Neighbor Problem: Should a person be granted a load or not (Ian Watson Slide)
Depends on Monthly income and loan amount.
The loan decisions will be clustered

**42. **Retrieval: Finding The Nearest Neighbor For a new problem C the nearest neighbor in the case base is the case (D,L) for which problem D has the greatest similarity to C.
Its solution L is intended to be most useful and is then the best solution the case base can offer (or best available product).
Classical databases use always total similarity (i.e. equality).
The access to data in databases is in similarity based systems replaced by the search for the nearest neighbor. It can be regarded as an optimization process.

**43. **Thresholds The nearest neighbor (in the given case base) is not always sufficient for providing an acceptable solution.
On the other hand, a case which is not the nearest neighbor may be sufficient enough.
For this purpose one can introduce two thresholds a and b, 0 < a < b < 1 with the intention
If sim(newproblem, caseproblem) < a then the case is not accepted;
If sim(newproblem, caseproblem) > b then the case is accepted.
This partitions this case base (for the actual problem into three parts: accepted cases, unaccepted cases and an uncertainty set. The same works for product bases.

**44. **Retrieve: Efficiency Issues Efficient case retrieval is essential for large case bases and large product spaces.
Different approaches depending
on the representation
complexity of similarity computation
size of the base
Organization of the base:
Linear lists, only for small bases
Index structures for large bases, e.g., kd-trees,
How to store cases or products:
Databases: for large bases or if shared with other applications
Main memory: for small bases, not shared

**45. **Reuse: How to Adapt the Solution No modification of the solution: just copy. Manual/interactive solution adaptation by the user.
Automatic solution adaptation :
Transformational Analogy: transformation of the solution
Rules or operators to adjust solution w.r.t. differences in the problems
Knowledge required about the impact of differences
Compositional adaptation: combine several cases to a single solution

**46. **Summary CBR is a technique for solving problems based on experience
CBR problem solving involves four phases:
Retrieve, Reuse, Revise, Retain
CBR systems store knowledge in four containers:
Vocabulary, Case Base,
Similarity Concept, Solution Adaptation
Large variety of techniques for:
representing the knowledge, in particular, the cases
realizing the different phases
CBR has several advantages over traditional KBS
The basic techniques of CBR can be extended to the needs of E-Commerce.