Title: Scalability of evolved online bin packing heuristics

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Title Scalability of evolved on-line bin packing
heuristics

• Grant Title An Investigation of the role of
  Genetic Programming in a Hyper-Heuristic Framework

ASAP Automated Scheduling Optimisation and
Planning The University of Nottingham (with Essex
University) Prof. Edmund Burke, Prof. Graham
Kendall Matthew Hyde and John Woodward
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Outline

• Hyper-heuristics
• Genetic Programming
• The on-line bin packing problem
• Scalability of evolved heuristics

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Hyper-heuristics

• Move away from tackling a problem directly
  (conventional search approaches).
• We operate on a meta or hyper level (or
  intermediary layer), which acts on the problem.
• A method of abstraction and therefore possible
  unification.
• Possibly a problem independent methodology.
• Instead of finding a solution to a problem (short
  term view), we search for a solution method to
  solve a set (or class) of problems (long term
  view). Reuse is our goal.

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Comparison of Search Spaces

• If we tackle a problem instance directly, e.g.
  Travelling Salesman Problem, we get a
  combinatorial explosion. The search space
  consists of solutions, and therefore explodes as
  we tackle larger problems.
• If we tackle a generalization of the problem, we
  do not get an explosion as the distribution of
  functions expressed in the search space tends to
  a limiting distribution (Bill Langdon 99). The
  search space consists of algorithms to produces
  solutions to a problem instance of any size.

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Genetic Programming

• A way to write programs, not by telling the
  computer how to do it, but what we would like ?
• The biologically inspired search of the space of
  computer programs (Genetic Algorithms,
  Evolutionary Computation).
• A population of programs is generated and tested
  and better programs are promoted to future
  generations (survival of the fittest)
• John Koza 1992
• Human competitive solutions have been generated
  for some problem domains.
• We are using standard genetic programming

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On-line Bin Packing
A sequence of pieces is to be packing into as few
a bins or containers as possible. Bin size is 150
units, pieces uniformly distributed between
20-100. Different to the off-line bin packing
problem where the set of pieces to be packed is
available for inspection at the start. The best
fit heuristic, puts the current piece in the
space it fits best (leaving least slack). It has
the property that this heuristic does not open a
new bin unless it is forced to.
Array of bins
Range of piece size 20-100
150 Bin capacity
Pieces packed so far
Sequence of pieces to be packed
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Genetic Programming applied to on-line bin
packing
Not immediately obvious how to link Genetic
Programming to apply to combinatorial
problems. See previous paper. The GP tree is
applied to each bin with the current piece put in
the bin which gets maximum score
Terminals supplied to Genetic Programming Initial
representation C, F, S Replaced with E, S,
EC-F We can possibly reduce this to one
variable!!
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Parameters Settings
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The Best Fit Heuristic
Best fit 1/(E-S). Point out features. Pieces of
size S, which fit well into the space remaining
E, score well. Best fit applied produces a set of
points on the surface, The bin corresponding to
the maximum score is picked.
Piece size
emptiness
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Our best heuristic.
Similar shape to best fit but curls up in one
corner. Note that this is rotated, relative to
previous slide.
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Performance of Heuristics on problems of much
larger size
Table shows probability that results are
different from the results obtained using the
best fit heuristic, for heuristics trained on
different size problems, when applied to
different sized problems 1. As number of problem
instances trained on increases, the probability
decreases (see next slide). 2. As the number of
pieces packed increases, the probability
decreases (see next slide).
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Compared with Best Fit
Amount evolved heuristics beat best fit by.
Number of pieces packed so far.

• Averaged over 30 heuristics over 20 problem
  instances
• Performance does not deteriorate
• The larger the training problem size, the better
  the bins are packed.

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Compared with Best Fit
Zoom in of previous slide
Amount evolved heuristics beat best fit by.

• The heuristic seems to learn the number of pieces
  in the problem
• Analogy with sprinters running a race
  accelerate towards end of race.
• The break even point is approximately half of
  the size of the training problem size
• If there is a gap of size 30 and a piece of size
  20, it would be better to wait for a better piece
  to come along later about 10 items (similar
  effect at upper bound?).

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Conclusions

• Evolved on line bin packing heuristics do
  continue to perform well on problem instances
  larger than the size of the training instances.
• The larger the size of the training problems, the
  more the heuristic beats best fit by.
• We would like to establish similar results for
  other combinatorial problem domains.
• If we used a direct method, it would fail on
  larger problems, where as this method can produce
  solutions.
• We have not reported on the time complexity of
  our solutions. This can be improved.

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Work in Progress and Further work

• Can we improve results by including information
  about the index of the current piece.
• Other combinatorial problems (e.g. packing in
  higher dimensions 2D, 3D).
• Reducing the number of test cases and,
• Reducing the size of the problem.

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Thank you for your attention

• Comments?
• Questions?
• Criticisms?
• ?