Coevolving Solutions to the Shortest Common Superstring Problem

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Coevolving Solutions to the Shortest Common
Superstring Problem

• Assaf Zaritsky Moshe Sipper
• Ben-Gurion University, Israel
• www.cs.bgu.ac.il/assafza

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Outline

• The Shortest Common Superstring problem.
• DNA sequencing and the input domain.
• Simple genetic algorithm (GA).
• Cooperative coevolutionary algorithm.
• Experimental results.

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The Shortest Common Superstring Problem (SCS)

• Let S s1,,sn be a set of strings (blocks)
  over some alphabet S. A superstring of S is a
  string x such that each si in S is a substring of
  x.
• Problem Find shortest (common) superstring.
• NP-Complete.
• MAX-SNP hard.

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SCS Example

• S ate, half, lethal, alpha, alfalfa
• A trivial superstring is atehalflethalalphaalfalf
  a of length 25 (a simple concatenation of all
  blocks).
• A shortest common superstring is
  lethalphalfalfate of length 17.
• Note that a compressed permutation of the
  blocks is actually a superstring.

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Approximation Algorithms

• Several linear approximations for SCS have been
  proposed, most of which rely on greedy
  approaches.
• GREEDY
• The most widely heuristic used in DNA
  sequencing.
• Conjecture Blum 1994, Sweedyk 1999 Superstring
  produced by GREEDY is of length at most two times
  the optimal.
• We are not aware of any previous evolutionary
  approach to the SCS problem.

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DNA Sequencing
The most common usage of the SCS problem.
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The Input Domain
The input strings used in the experiments were
inspired by DNA sequencing
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Input Generation Setup Parameters
NB increasing number of blocks results in
exponential growth of the problems complexity.
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Simple GA for the SCS Problem

• Given a set of strings as input, generate initial
  population of random candidate solutions.
• The fitness of each individual depends on its
  length and accuracy.
• The GA uses selection, recombination, and
  mutation to create the next generation, each
  individual of which is then evaluated.
• Theses steps are repeated a predefined number of
  times or until the solution is deemed
  satisfactory.

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Simple GA for the SCS Problem (contd)

• Blocks of the input set are atomic components.
• Representation.
• Permutation Representation Good or Bad?
• Evaluation.
• Genetic operators selection, recombination,
  mutation.

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Coevolution

• Simultaneous evolution of two or more species
  with coupled fitness.
• Coevolving species either compete or cooperate.

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Cooperative Coevolution
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Cooperative Coevolution (contd)

• Cooperative Coevolution involves a number of
  independently evolving species.
• Interaction between species occurs via fitness
  function only.
• The fitness of an individual depends on its
  ability to collaborate with individuals from
  other species.

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Cooperative Coevolution (contd)
Source Potter DeJong (1997)
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Cooperative Coevolutionary Algorithm for the SCS
problem

• Two species evolve simultaneously.
• First species contains prefixes of candidate
  solutions to the SCS problem at hand.
• Second species contains candidate suffixes.
• Fitness of an individual in each species depends
  on how good it interacts with representatives
  from other species to construct a global solution.

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Cooperative Coevolutionary Algorithm for the SCS
problem (evaluation process)
Merge
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Cooperative Coevolutionary Algorithm for the SCS
problem (evaluation process)
Evaluate
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Experiments
Compare GREEDY, Simple GA, Cooperative
Coevolution
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Experimental Setup
Each type of GA was executed twice on each
problem instance the better run of the two was
used for statistical purposes.
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Results Experiment I (50 blocks)
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Results Experiment II (80 blocks)
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Results Summary
size of shortest common superstring
Algorithm
Problem size
Greedy
Genetic
Cooperative
50 blocks
80 blocks
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Conclusions

• Evolutionary algorithms can be applied to the SCS
  problem.
• Cooperative Coevolution outperforms simple GA and
  GREEDY.
• The collaboration between the two populations
  results in a good decomposition of the problem
  into two smaller sub-problems.

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Future Work

• Tackle larger problem instances.
• Construct new species on the fly (as suggested by
  Potter and DeJong 2000).
• Improved method the puzzle algorithm.

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Current Work - The Puzzle Algorithm
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Puzzle Algorithm The Idea

• Improve Recombination Operator.
• Preserve good building blocks discovered by GA
  using selection of recombination loci that do not
  destroy good building blocks.
• Result Assembly of good building blocks to
  construct better solutions (as in a puzzle).