Optimization Problem: Genetic Algorithms

1
Optimization Problem Genetic Algorithms

• Introduction
• GAs and Simulated Annealing
• The Biology of Genetics
• The Logic of Genetic Programmes

2
GAs and Simulated Annealing

• Simulated Annealing is Hill-Climbing with
  occasional reversals
• Genetic Algorithms are parallel Hill-Climbing
• Population of individuals
• Selection based on fitness function
• Crossover
• Mutation

3
GAs

• What are they?
• Programmes which emulate the biological processes
  of genetic recombination, mutation, and natural
  selection to generate solutions to problems.
• When are they used?
• Problems with massive search spaces and many
  parameters resulting in a combinatorial explosion
  of possible solutions

4
Where are They Used?

• Production Management (John Deere, BP).
• Credit Scoring ( UK Banks ).
• Robot Vision/Machine Learning.
• Network Design.
• Financial applications (eg. equity trading and
  asset allocation.)
• Picking Pub Locations (BASS)

5
How do they work?

• function GENETIC-ALGORITHM(population,
  FITNESS-FN)
• returns an individual
• inputs population, a set of individuals
• FITNESS-FN a fn. that measures the fitness
  of an
• individual
• repeat
• parents SELECTION(population, FITNESS-FN)
• population REPRODUCTION(parents)
• until some individual is fit enough
• return the best individual in population,
  according to
• FITNESS-FN

6
GA Procedure

• Individuals are usually represented by a bit
  string
• This is often the tricky bit
• The best individuals contribute most to the next
  generation
• Natural Selection - Culling phenotypes which are
  less fit to survive the environment.
• Recombination - Combining discrete features
  (genes) of different solutions (chromosomes) in
  order to come up with superior solutions.
• Most change is achieved by crossover, little by
  mutation

7
GAs What We Need?

• Decide what constitutes a viable part of a
  solution (what are our genes?).
• Decide how to determine fitness of a solution.
• A method to select chromosomes from population
  for mating or mutation.
• Decide on a data structure to represent the
  chromosome.
• Choose a technique for mutating chromosomes.
• Choose a technique to enable crossover.
• Choose a technique to reinsert children into
  population.

8
Fitness Evaluation

• Maximum of function.
• Magnitude of Y value.
• Schema to Predict the Dow Jones.
• Quality of Match with Historical Values.
• Generating Schedules.
• Complex evaluation function to determine the
  quality of the generated schedule.

9
Consider the Feature Selection problem
10
Knowledge Representation

• Ontology Engineering
• Categories and Objects
• Actions, Situations and Events.
• Study Case Internet Shopping World.
• Reasoning Systems for Categories.
• Reasoning with Default Information.
• Truth Maintenance Systems..

11
Ontology Engineering
A shared ONTOLOGY of minum and food
The List Of Minum
12
What Is An Ontology

• An ontology is an explicit description of a
  domain
• concepts
• properties and attributes of concepts
• constraints on properties and attributes
• Individuals (often, but not always)
• An ontology defines
• a common vocabulary
• a shared understanding

13
Ontology Examples

• Taxonomies on the Web
• Yahoo! Categories
• Catalogs for on-line shopping
• Amazon.com product catalog
• Domain-specific standard terminology
• Unified Medical Language System (UMLS)
• UNSPSC - terminology for products and services

14
The Internet Shopping World

• We will discuss how to create a shopping resaerch
  agent that helps a buyer find product offers on
  the internet.
• Buyergtproduct descriptiongtAgent gt A list of
  web pages that offer such product for sale.
• Shopping Agents environment gt WWW.
• Agents percept ? web pages.
• Human percept gt pages display as an array of
  pixels on a screen.

15
User and Agent Percept

• User Percepts
  Select from our fine line of products
• ? Computers
• ? Cameras
• ? Books
• ? Videos
• ? Music

• Agent Percepts
• lth1gt Generic Online Storelt/h1gt
• ltigt Selectlt/igt from our fine line of products
• ltu1gt
• ltligt lta hrefhttp//gen-store.com/compugtComputerslt
  /agt
• ltligtltltahrefhttp//gentore.com/camergtCameralt/agt
• ltligtltltahrefhttp//gentore.com/booksgtBookslt/agt
• ltligtltltahrefhttp//gentore.com/videogtVideolt/agt
• ltligtltltahrefhttp//gentore.com/musicgtMusiclt/agt

16
What Is Ontology Engineering?

• Ontology Engineering Defining terms in the
  domain and relations among them
• Defining concepts in the domain (classes)
• Arranging the concepts in a hierarchy
  (subclass-superclass hierarchy)
• Defining which attributes and properties (slots)
  classes can have and constraints on their values
• Defining individuals and filling in slot values

17
Why Develop an Ontology?

• To share common understanding of the structure of
  information
• among people
• among software agents
• To enable reuse of domain knowledge
• to avoid re-inventing the wheel
• to introduce standards to allow interoperability

18
More Reasons

• To make domain assumptions explicit
• easier to change domain assumptions (consider a
  genetics knowledge base)
• easier to understand and update legacy data
• To separate domain knowledge from the operational
  knowledge
• re-use domain and operational knowledge
  separately (e.g., configuration based on
  constraints)

19
An Ontology Is Often Just the Beginning
Databases
Declare structure
Ontologies
Knowledge bases
Provide domain description
Domain-independent applications
Software agents
Problem-solving methods
20
Ontology-Development Process

• In this lecture

In reality - an iterative process
21
Ontology Engineering versus Object-Oriented
Modeling

• An ontology
• reflects the structure of the world
• is often about structure of concepts
• actual physical representation is not an issue

• An OO class structure
• reflects the structure of the data and code
• is usually about behavior (methods)
• describes the physical representation of data
  (long int, char, etc.)

22
Categories and Objects

• The organization of objects into categories is a
  vital part of knowledge representation.
• Although interaction with the world takes place
  at the level of individual objects, much
  reasoning takes place at the level of categories.
• Categories serve to make predictions about
  objects once they are classified.
• Also category membership can be inferred from the
  perceived properties of objects.
• Example Fruit has properties green, motled skin,
  large size, and ovoid shape ? watermelon?useful
  for fruit salad.

23
Categories and Objects

• There are two choices for representing categories
  in first-order logic predicates and objects
• In prolog Member (b,Fruit salad).
• Inheritance To organize and simplify the
  knowledge base. Apple?Fruit?Food. All instances
  in food is edible, so the individual apples
  inherit the property of edibility, in this case
  from their membership in the Food category.
• Subclass relations organize categories into a
  taxonomy, or taxonomic hierarchy.

24
Categories with First Order Logic

• First-order logic makes it easy to state facts
  about categories, either by relating objects to
  categories or quantifying over their members
• 1. Water melon ? Fruit ? an object is a
  member of
• category.
• 2. Fruit ? Food ? A category is subclass of
  another
• category.
• 3. Orange(x) ? Round(x) ? (diameter9.5) ? x
  ? Balls
• gt x ? BasketBalls.
• Please see pp. 324-328 for further examples of
  the use of First-order logic.

25
Intrinsic and Extrinsic Properties

• Intrinsic Properties they belong to the very
  substance of the object, rather than to the
  object as a whole. Examples density, boiling
  point, flavor, color, ownership and so on.
• Extrinsic Properties Are not retained under
  subdivision.
• Examples weight, length, shape.

26
Reasoning Systems for Categories

• -gt Organizing
• -gt Reasoning
• of knowledge representation.
• Two Systems
• 1. Semantic Networks.
• 2. Description Logic.

27
Semantic Networks

• Semantic networks are knowledge representation
  schemes involving nodes and links (arcs or
  arrows) between nodes.
• The nodes represent objects or concepts and the
  links represent relations between nodes.
• The links are directed and labeled thus, a
  semantic network is a directed graph.

In semantic networks then, structure is
everything
28
Semantic NetworksThe Market Dynamics of
Microsoft and Netscape Inc.
29
Semantic NetworksMarket Dynamics at Work in the
Rivalrybetween CocaCola and PepsiCo.
30
Figures Explanations

• Figure 1 illustrates a sub-section or domain of
  semantic memory reachable from the concept node
  Microsoft.
• Figure 2 illustrates the structurally similar
  domain of CocaCola.
• Note how the connectivity of the concept
  Microsoft means that concepts relating to
  NetscapeInc are also included in this domain.
• The connectivity of the CocaCola domain causes
  the concept PepsiCo and its associates to
  likewise be included there.
• The domain of Microsoft thus comprises all those
  concept nodes and relations that can be reached
  by starting at the node Microsoft and its
  immediate neighbours, visiting the neighbours of
  each new node in turn until no new nodes can be
  reached

31
Source Description Logics Tutorial, Ian Horrocks
and Ulrike Sattler, ECAI-2002, Lyon, France, July
23rd, 2002
32
(No Transcript)
33
(No Transcript)
34
Reasoning with Default Information

• Suppose you were looking at a bulletin board in a
  university computer science department and saw a
  notice saying
• The following courses will be offered CS
  101, CS 102, CS 106, EE 101.
• How many courses will be offered?
• Human and Database system will give the answer
  4.
• The (First) Order Logic system would answer
  somewhere between one and infinity not four.
  why?
• Because the Course assertions do not deny the
  possibility that other unmentioned courses are
  also offered, nor do they say the courses
  mentioned are different from each other.

35
Two Ways Assumptions

• The previous example shows that database systems
  and human communication conventions differ from
  first-order logic in at least two ways
  assumptions.
• 1. Database systems and Human assume that the
  information
• provided is complete, so that ground
  atomic sentences not
• asserted to be true are assumed to be
  false.
• This is called closed-world assumption
  (CWA).
• 2. We usually assume that distinct names
  refer to distinct objects.
• This is the Unique names assumption
  (UNA).
• First Order logic does not does not assume these
  conventions, and thus needs to be more explicit.

36
The First Order Logic Notation

• To say that only the four distinct courses
  offered, we would write
• Course(d,n) ? d,nCS,101 v d,nCS,102
• V d,n CS,106 v
  d,nEE,101.
• The above notation is completion form of the
  statement in the previous slides.

37
The Completion Form

• In general, the completion is constructed as
  follows
• 1. Gather up all the clauses with the same
  predicate (P) and the same arity (n).
• 2. Translate each clause to Clark Normal Form
  replace
• P(t1,,tn) ? Body
• where ti are terms, with
• P(v1,,vn) ? ?w1,w2,.,wm
  v1,,v2t1,t2,,tn ? Body.
• P(v1,,vn) ? B1
• P(v1,,vn) ? Bk.
• Combine these together into one big disjunctive
  clause
• P(v1,,vn) ? B1 ? ?Bk.
• Form the completion by replacing the ? with an
  equivalence
• P(v1,,vn) ? B1 ? ? Bk.