G52AIM Artificial Intelligence Methods

1
G52AIMArtificial Intelligence Methods
Andrew Parkes (ajp)

• Course Introduction

2
Course Web Page

• Follow link from http//www.cs.nott.ac.uk/ajp/
• Contains (or will contain)
• Course schedule
• will be updated during the course
• Resources
• Slides, handouts, notes
• Exercises, extra reading materials
• Coursework
• My contact details

3
Course Assessment

• Coursework 25 of the assessment
• 5 essay/report
• 20 Implementation required!
• Exam
• 75 of the assessment
• Covering all materials in the lectures, and the
  associated reading

4
Course work

• Will provide full details later, but outline is
• Coursework ONE 5
• 2-3 page report/essay about basics of
  optimisation
• deadline in last two weeks of spring term
• Coursework TWO 20
• Implementation required
• Some optimization algorithms on some domain
• Prefer Java/C/C, but no GUI needed!
• deadline during first weeks of summer term

5
Primary Course Topic

• Finding needles in haystacks
• Many systems have many different solutions
• Not all solutions are equal
• Want to find the best solutions
• Best solutions are very very very rare
• E.g. 1 part in 10100

6
Example Subset Sum

• Given
• a set S of n numbers x1, x2, ... , xn
• a target number K
• Question Is there a subset S of S such that the
  sum of the elements of S is precisely K?
• Purely Academic problem?
• subset sum can be a part of many real-world
  problems

7
Splitting Problem

• Suppose that you have
• a module with K students
• a set R of rooms of different sizes x1, x2, ...
  , xn
• Class is too large for any one room, so want to
• split class into different sections
• assign sections to rooms
• Want rooms that are used to be fully used
• i.e. divide K into sections using a subset of set
  R
• This is subset sum! Part of current research
  project here in Nott. with a company doing
  commercial work on planning space utilisation
  within universities (See my web page)

8
Example Subset Sum

• 6, 10, 4, 16, 34, 2
• target K 22
• Is there a solution?
• ()
• Yes 16, 4, 2
• What about K21 ?
• ()
• No solution! Why?

9
Example Subset Sum

• Why is this hard?
• How many possible subset are there of n numbers?
• Answer 2n
• It might be that only one of these achieves the
  target
• One needle in an exponentially sized haystack
• Best algorithms are still exponential time
• For such NP-hard problems often need to solve
  heuristically and approximately

10
Subset Sum for Cryptography(?)

• S 165 383 953 588 625 169 438 537 247 593
  
• target 1310
• Decode
• find the subset that gives target
• read as a binary string
• 1 if number used
• 0 if number not used

11
Subset Sum for Cryptography(?)

• S 165 383 953 588 625 169 438 537 247 593
  
• target 1310
• Answer 625438247
• Encoded String 0000101010

12
Subset Sum for Cryptography(?)

• Proposed for cryptography but not used
• Subset sum is hard in the worst case
• with good design can be hard on average
• but some instances might be easy
• For cryptography, the instances need to be hard
  in the best case as well as worst case
• Cryptography is a very difficult topic

13
Course Topic

• Usually each solution is given a quality, a
  number, called
• evaluation function, or
• objective, or
• fitness, etc
• The aim is to either minimise or maximise this
  objective
• Often the objective corresponds to monetary cost
• there are many situations in which one wants to
  find solutions with the minimum cost!
• This module is about methods to perform such
  optimization
• We do not cover all such methods
• Focus on heuristic and meta-heuristic methods

14
Methods to find a needle in a haystack

• Local Search
• Run uphill and hope you find the top
• Run downhill and hope you find the bottom
• Simulated Annealing
• Shake it up a lot and then slowly let it settle
• Tabu Search
• Dont look under the same lamp-post twice
• Genetic Algorithms
• survival of the fittest
• Ant Algorithms
• wander around a lot

15
Expectations

• Keep up-to-date with
• the course web page
• email sent to the g52aim mailing list
• Keep current with the terminology and ideas in
  the lectures so that you can join in discussions
• Ask questions!
• Give appropriate feedback!