Online Population Size Adjusting Using Noise and Substructural Measurements TianLi Yu, Kumara Sastry

1
On-line Population Size Adjusting Using Noise and
Substructural MeasurementsTian-Li Yu, Kumara
Sastry, and David E. Goldberg

• Presented by
• Edwin Frankowski

2
Introduction

• Adjusting the population size of a given genetic
  algorithm to one that is more fitting for the
  specific problem is desirable because it allows
  you to minimize the necessary number of
  evaluations.
• It is claimed that the algorithm proposed in this
  paper is both efficient and robust. The proposed
  method reduces the population size if it is too
  large resulting in less evaluations for a high
  quality solution and increases the population
  size if it is to small to avoid premature
  convergence.
• The method is tested using DSMGA(dependency
  structure matrix genetic algorithm) and comparing
  an adjusted on the fly population size to a fixed
  population size on an m-k trap problem.

3
Related Work

• Past work has been done in eliminating selection
  pressure, crossover rate, and population size.
• Past GAs have simulated a set of population sizes
  starting with a base population size with
  subsequent populations being twice the size of
  the previous one. The population is terminated
  when no improvement is expected from it.
• If the optimal population size takes n
  evaluations, parameter-less GAs can be shown to
  take O(nlog(n)) evaluations. This paper
  demonstrates a different method that uses roughly
  the same number of evaluations as a GA with an
  optimal population size.

4
Dependency Structure Matrix Genetic Algorithm

• The GA used is DSMGA, it relates nodes by
  dependency.
• Each entry d is marked with an x in this case to
  show a dependency

5

• An X present in a square means a dependency
  exists between the two elements. The larger the
  dij the higher the dependency between the two
  nodes. The first image is just an example of a
  listing of nodes and their dependencies.
• The second image is the goal state, a set of
  clusters so that nodes within a cluster are
  maximally dependent and minimally interacting.
  The clusters in this case being B,D,G,
  A,C,E,H, F.

6
M-k trap problem

• One can define a trap function as follows. If x
  is a binary string, let x be the number of 1s
  in x. (x is called the unitation of x.) Then let

7
DSMGA Predictions

• Demonstrating that the theory matches results
• Results for DSMGA fit closely to expected results

• m building blocks, k size of building blocks, cn
  is a problem dependent constant, and BB is the
  fitness variance

8
FIX and ADJ

• m-k trap function and two DSMGAs one with a fixed
  population size (FIX) and the other (ADJ) with an
  adjustable population size.
• Which performs better in what situations
• Are any failings of ADJ correctable

9
FIX

• Uses a fixed population size
• Required population size is calculated to be 137
• The least number of evaluations are used when the
  population size is set close to the calculated
  optimum
• If the number is less than 137 it frequently
  finds a local optimum, if its greater it wastes
  evaluations

10
ADJ

• ADJ is able to shrink the population size if the
  initial population size is too large
• After the first generation the population size
  has been reduced to optimum size
• After that point it behaves as an optimum sized
  fixed population

11
Trendlines

• If nfe is the number of function evaluations
  needed, n0 is the initial population size and n
  is the optimum population size

• Where g is number of evaluations before
  convergence

12
Comparison

• When near optimum population size is used FIX out
  performs ADJ
• When a small population size is used both ADJ and
  FIX fail to converge
• When a population size that is too large is used
  ADJ out performs FIX

13
Success Rate Comparison

• When initial population size is sub optimal FIX
  fails
• ADJ on the other hand is slightly more robust and
  has some degree of success
• Both suffer from a lack of BB supply

14
What happens on small populations

• When ADJ encounters a population that is smaller
  than optimal and tries to increase its size it is
  using a small amount of building blocks to create
  a much larger population.
• All of the members of the population will look
  too similar and the GA will converge early due to
  a lack of diversity

15
How can if be fixed?

• Inject randomly initialized members into the
  population to increase diversity
• This works well when done at the beginning of the
  GA, but if it happens at the end it could mess up
  a possible solution
• We dont want the GA to be disturbed when its
  close to an answer

16
Problem with injecting

• This is a run of the GA with introducing new
  individuals switched on all the time
• Proportion of correct BBs decreases when the
  population spikes
• Notice the severe decrease near the end

17
ADJINJECT

• When do we switch over to pure recombination
  rather than injection?
• The first time that the population size is
  decreased
• Indicates that the GA has a good supply of BBs
• If we have an initial population of 10 and the
  next estimate for population size is 1000, create
  990 new random members. As soon as the
  population size is decreased only use mutations
  and crossovers within the population

18
ADJINJECT Performance

• Roughly the same as ADJ in terms of number of
  function evaluations required
• This indicates that we havent lost any
  efficiency from the injections
• FIX not shown in this graph, but it can be seen
  in the previous comparison of FIX and ADJ that it
  is clearly still worse in terms of function
  evaluations

19
Success Rate

• ADJINJECT has a higher success rate when the
  initial population size is low
• Specifically it is much higher when the
  population size is around 10
• Even for n 2 it converges around 66 of the
  time to the global optimum
• ADJINJECT is even more robust than ADJ

20
Conclusion

• Both ADJ and ADJINJECT can yield a savings in
  number of evaluations functions over FIX
• ADJ and ADJINJECT estimate what the optimum
  population size is for the specific m-k trap
  problem using a DSMGA
• ADJINJECT is shown to be efficient and robust
  for this particular problem meaning that it uses
  few evaluations and rarely fails to converge to a
  global optimum