Sisteme de programe pentru timp real

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Sisteme de programepentru timp real

• Universitatea Politehnica din Bucuresti
• 2005-2006
• Adina Magda Florea
• http//turing.cs.pub.ro/sptr_06

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Curs Nr. 11

• 1. Hybrid GA-heuristic search strategy
• 2. Learning decision rules by GA
• 3. Genetic programming

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1. Hybrid GA-heuristic search strategy

• A simple resource planning application
• Solve it using GA first then solve it using
  hybrid GA-heuristic search
• 4 resources A, B, C and D
• Each resource carry out a number of different
  operation types O1, O2 and O3.
• For each resource
• - the time to carry out an operation type
• - the cost of running an operation
• - the available capacity

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1.1 Using GA

• Given 3 requirements (jobs) for 1400 units of
  O1, 1200 units of O2 and 900 units of O3
• Find the optimal resource planning that meets
  the following objectives
• Cheapest production cost
• Delivering the required units of each job
• Not exceeding the available capacity for each
  resource

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• Individuals the number of units of each
  operation assigned to each resource.
• No.O1A No.O2A No.O3A No.O2B No.O3B
  No.O1C No.O1D No.O3D
• Fitness function cost function which consists of
  the total cost of running the resources plus the
  total penalty points for exceeding the available
  capacity of resources.
• Fitness No.O1A230 No.O2A530 ..
  ?(No.O1A No.O2A No.O3A 1000 ) to
  minimize
• ? - a value which reflects the severity of the
  penalty constraint.
• This representation aprox 60 generations of 50
  individuals to evolve a solution which has a cost
  of 99 of the known optimal cost.
• This is quite slow considering the simplicity of
  the problem.

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1.2 Using hybrid GA-heuristic

• Individuals the sequence of jobs to be presented
  to a simple resource planner.
• First break down the three large jobs
  (requirements) into smaller jobs.
• The jobs are broken down as follows
• The job of 1400 O1 was broken down into 5 jobs of
  280 O1 each
• The job of 1200 O2 was broken down into 4 jobs of
  300 O2 each
• The job of 900 O3 was broken down into 3 jobs of
  300 O2 each
• Use 12 sequence genes to represent the order in
  which these jobs are presented to a simple
  planner.
• The simple planner uses very simple heuristics
  take the next job in the queue and allocate to
  the first resource (from A to D) which has
  available capacity.
• This new representation strategy needs only 2
  generations of 50 individuals to evolve a
  solution with a cost of 100 of the known optimal
  cost.
• The evolution time was reduced from minutes in
  the initial strategy to seconds using the new
  methodology.

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1.3 Application

• Methodology used to build an application for
  Channel 4 - the largest commercial TV station in
  the UK.
• Channel 4 had the requirement of optimising the
  sequencing of advertisements within a commercial
  break.
• They have to ensure that different copies
  (versions) of the same advert go out
  simultaneously to different regions of the UK
  whilst satisfying as many of advertisers requests
  for special positions as possible.
• Advertisers can specify a mix of regions, first
  or last position in a break or a 'top tail'
  pair in the same break.
• A break sequencer has to ensure that all the
  requirements are met without overlaps or gaps in
  the break transmitted to each region.
• In a four minute break across 6 regions there are
  144 ten second slots to schedule with up to 50
  adverts.
• A heuristic knowledge based system solution to
  the problem was rather difficult to achieve and a
  GA optimisation approach was considered.

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Application

• GA approach use 144 index genes to represent
  each of the 10 second slots across the six
  regions.
• Each index gene returns a pointer to an advert
  (one of 50).
• This strategy could take hours to optimise.
• Given that there are over 70 breaks a day to
  optimise, the evolution time is unacceptably
  high.
• GA-heuristic use sequence of genes to represent
  the sequence of adverts to be scheduled (up to
  50) by a simple heuristic scheduler.
• This approach reduces the evolution time to
  seconds.
• The simple scheduler works by taking the next
  advert in the sequence and placing it in the
  first available position (across the required
  regions) in the break.
• The optimisation task becomes one of optimising
  the sequence in which the adverts are presented
  to the simple scheduler.
• Major advantage a simple scheduler would always
  produce a valid schedule which satisfies the hard
  constraints while the soft constraints are
  represented in the cost function and are
  satisfied through natural selection.

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2. Learning decision rules by GA

• Rules of the form
• if A1v1
• and x1ltA2ltv2
• then Class C1
• Both discrete and continuous values attributes
• Learning set Ee1,..eM
• e?E is described by N atributes A1, ..AN and
  labeled by a class c(e) ?C
• Discrete value attributes finite set V(Ai)
• Continuous value attributes an interval V(Ai)
  li,ui

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2.1 Decision rules

• A class ck?C
• Positive examples - E(ck) e ?E C(e)ck
• Negative examples - E-(ck) E E(ck)
• A decision rule R
• if t1 and t2 .. and tr then ck
• LHS
• RHS class membership of an example
• Rule set - RS disjunctive set of decision rules
  with the same RHS
• CRS ?C denotes the class on the RHS of an RS
• The GA is called for each class ck ?C to find the
  RS separating E(ck) from E-(ck)
• Fitness function -gt prefers rules consisting of
  fewer conditions, which cover many ex and very
  few ex-

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2.2 Representation

• One chromosome encodes an RS
• The no. of rules in RS is not knwon ? Use
  variable length chromosomes provide operators
  which change the no. of rules
• 1 chromosome concatenation of strings
• Each fixed-length string the LHS of one
  decision rule (no need for RHS)
• 1 string is composed of N sub-strings (LHS) a
  condition for each attribute

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Representation

• Discrete value attributes binary flags
• Continous value attributes li, ui, liltAiltui
  (?, - ?)
• li, ui are selected from a finite set of boundary
  thresholds
• Boundary threshold midpoint between a
  successive pair of examples in the sequence
  sorted by increasing value of Ai, that one is ex
  and the other ex-
• ex ex ex ex- ex- ex- ex ex ex- ex- Ai
• thik-1 thik thik1
• If a condition is not present li - ?, ui ?

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Representation

• Example
• 2 cont val attr Salary, Amount
• 1 disc val attr Purpose (car, house, school)
• Class - Accept
• Salary Amount Purpose
• - ? ? - ? 250 1 1 1 if Amountlt250
  then ACCEPT
• 100 250 - ? 500 1 1 1 if 100ltsalarylt250
  
• and Amount lt500
• then ACCEPT
• 750 ? - ? ? 1 1 0 if Salarygt750
• and Purpose (car or house)
• then ACCEPT

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2.3 Genetic operators

• 4 operators applied to a single rule set
• Changing condition (a)
• Positive example insertion (b)
• Negative example removal (c)
• Rule drop (d)
• 2 operators applied with 2 arguments to RS1 and
  RS2
• Rule copy (e)
• Crossover (f)

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Genetic operators

• (a) Changing condition
• A mutation like operator alters a single
  condition related to an attribute Ai
• If Ai disc randomly chooses a flag and flip
• If Ai cont randomly replaces a threshold (li or
  ui) by a boundary threshold
• (b) Pos ex insertion
• Modifies a single dec rule R in RS to allow to
  cover a new random e?E(CRS) currently uncovered
  by R
• All conditions in the rule, which conflict with
  e have to be altered.
• Ai disc flag set
• Ai cont liltAiltui with uiltAi(ex) smallest
  ui such as uigtAi similar if ligt Ai(ex)

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Genetic operators

• (c) Negative ex removal
• The negative example removal operator alters a
  single rule R from the ruleset RS.
• It selects at random a negative example e- from
  the set of all the negative examples covered by
  R.
• Then it alters a random condition in R in such a
  way, that the modied rule does not cover e-.
• If the chosen condition concerns a discrete
  attribute Ai the flag which corresponds to Ai(e-)
  is cleared.
• If Ai is a continuous-valued attribute then the
  condition li lt Ai lt ui is narrowed down either
  to li lt Ai lt ui or to li lt Ai lt ui, where li
  is the smallest boundary threshold such that
  Ai(e-) gt li and ui is the largest boundary
  threshold such that ui lt Ai(e-).

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Genetic operators

• Rule drop and rule copy operators are the only
  ones capable of changing the number of rules in a
  ruleset.
• (d) Rule drop
• The single argument rule drop removes a random
  rule from a ruleset RS.
• (e) Rule copy
• Rule copy adds to one of its arguments RS1, a
  copy of a rule selected at random from RS2,
  provided that the number of rules in RS1 is lower
  than maxR.
• maxR is an user-supplied parameter, which limits
  the maximal number of rules in the ruleset.
• (f) Crossover
• The crossover operator selects at random two
  rules R1 and R2 from the respective arguments RS1
  and RS2. Then it applies a crossover to the
  strings representing R1 and R2.

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2.4 Fitness

• Uses rank-based fitness asignment
• Goal reduction of the no. of errors
• ERS the set of ex covered by the RS (class of
  RHS CRS)
• ERS ERS ?E(CRS) set of ex correctly
  classified by RS
• E-RS ERS ?E-(CRS) set of ex- covered by RS
• The total no. of ex and ex-
• POS E(CRS)
• NEGE-(CRS) M POS
• The RS correctly classifies
• - pos ERS ex
• and
• - NEG-neg ex- where negE-RS

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Fitness

• Ferror Pr(RS) / Compl(RS)
• Pr(RS) the probability of classifying correctly
  an example from the learning set by RS
• Compl(RS) the complexity of RS
• Pr(RS) (pos NEG neg) / (POSNEG)
• Compl(RS) (L/N1)?
• L total no. of conditions in RS
• N no. of attributes
• ? - user supplied in 0.001..0. 1
• We are interested in maximizing the probability
  and minimizing the complexity to obtain a
  compact rule set and acorrect classification

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2.5 Optimisation strategy to learning decision
rules

• ID3
• Learn order of attributs
• Perform ID3 on that order

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3. Genetic programming

• Genetic programming is a branch of genetic
  algorithms
• Functional programming
• Genetic programming, uses four steps to solve
  problems1) Generate an initial population of
  random compositions of the functions and
  terminals of the problem (computer programs).2)
  Execute each program in the population and assign
  it a fitness value according to how well it
  solves the problem.3) Create a new population
  of computer programs. i) Copy the best existing
  programs ii) Create new computer programs by
  mutation. iii) Create new computer programs by
  crossover4) The best computer program that
  appeared in any generation, the best-so-far
  solution, is designated as the result of genetic
  programming

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Genetic programming
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Fitness function

• The most difficult and most important concept of
  genetic programming is the fitness function.
• It varies greatly from one type of program to the
  next.
• Ex create a genetic program to set the time of a
  clock
• The fitness function - the amount of time that
  the clock is wrong.
• Few problems have such an easy fitness function
  most cases require a slight modification of the
  problem in order to find the fitness.Gun
  Firing Program
• Training a genetic program to fire a gun to hit a
  moving target.
• Fitness function - the distance that the bullet
  is off from the target.
• The program has to learn to take into account a
  number of variables, such as wind velocity, type
  of gun used, distance to the target, height of
  the target, velocity and acceleration of the
  target.
• This problem represents the type of problem for
  which genetic programs are best.
• It is a simple fitness function with a large
  number of variables.

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Fitness function

• Water Sprinkler System
• Consider a program to control the flow of water
  through a system of water sprinklers.
• The fitness function is the correct amount of
  water evenly distributed over the surface.
  Unfortunately, there is no one variable
  encompassing this measurement. Thus, the problem
  must be modified to find a numerical fitness.
• One possible solution is placing
  water-collecting measuring devices at certain
  intervals on the surface.
• The fitness could then be the standard deviation
  in water level from all the measuring devices.
• Another possible fitness measure could be the
  difference between the lowest measured water
  level and the ideal amount of water. Maze
  Solving Program
• If one were to create a program to find the
  solution to a maze, first, the program would have
  to be trained with several known mazes.
• The ideal solution from the start to finish of
  the maze would be described by a path of dots.
• The fitness in this case would be the number of
  dots the program is able to find.
• In order to prevent the program from wandering
  around the maze too long, a time limit is
  implemented along with the fitness function.

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Functions and terminals

• The terminal and function sets are also important
  components of genetic programming.
• The terminal set consists of the variables and
  constants of the programs.
• In the maze example, the terminal set would
  contain three commands forward, right and left.
• The function set consists of the functions of the
  program.
• In the maze example the function set would
  contain
• If "dot" then do x else do y.
• In the gun firing program the terminal set would
  be composed of the different variables of the
  problem.
• Some of these variables could be the velocities
  and accelerations of the gun, the bullet and
  target.
• The functions are several mathematical functions,
  such as addition, subtraction, division,
  multiplication and other more complex functions.

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Selection

• 1) Use probability based on the fitness of the
  solution.
• If f(Si(t)) is the fitness of the solution Si
  and
• is the total sum of all the members of the
  population, then the probability that the
  solution Si will be copied to the next generation
  is
• 2) Use tournament selection

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Crossover

• The creation of the offsprings from the crossover
  operation is accomplish by deleting the crossover
  fragment of the first parent and then inserting
  the crossover fragment of the second parent.
• The second offspring is produced in a symmetric
  manner.

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Crossover
An important improvement that genetic
programming displays over genetic algorithms is
its ability to create two new solutions from the
same solution.
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Mutation

• Two types of mutations are possible.
• In the first kind a function can only replace a
  function or a terminal can only replace a
  terminal.
• In the second kind an entire subtree can replace
  another subtree.

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Benefits

• Genetic programming works best for several types
  of problems.
• The first type is where there is no ideal
  solution for example, a program that drives a
  car.
• There is no one solution to driving a car. Some
  solutions drive safely at the expense of time,
  while others drive fast at a high safety risk.
• Therefore, driving a car consists of making
  compromises of speed versus safety, as well as
  many other variables. In this case genetic
  programming will find a solution that attempts to
  compromise.
• Second, genetic programming is useful in finding
  solutions where the variables are constantly
  changing. In the previous car example, the
  program will find one solution for a smooth
  concrete highway, while it will find a totally
  different solution for a rough unpaved road.

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