Discrete and Genetic Algorithms in Bioinformatics

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Discrete and Genetic Algorithms in Bioinformatics

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Discrete Algorithms

• Discrete Math. lies in the foundation of modern
  computer science
• Most algorithms we have learned in computer
  science are discrete
• Discrete algorithms emphasize worst case
  analysis
• Many sequence manipulation algorithms in
  bioinformatics are discrete

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Natural Problems (1)

• Natural problems Problems arisen from nature,
  which are guaranteed to have feasible solutions
  if data is collected accurately.
• But because of noises in sampled data, such
  solutions are hard to come by.
• To tackle these problems one should focus on real
  data rather than worst case analysis.

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Natural Problems (2)

• Techniques taking advantage of the natural
  constraints of these problems do not necessarily
  work for general data (especially the worst
  case), but could perform very well for those
  well-structured problems.
• Examples
• many computational problems arisen from biology,
  speech recognition, and image processing

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Constraints with Errors

• In ordinary constraint optimization problems, one
  naturally assumes that the constraints are
  correct.
• What if these constraints are inconsistent?
• There is no feasible solution satisfying them
• What if every constraint is only partially
  correct?

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Explicit Solution Candidates

• In ordinary optimization problems, most
  algorithms do not generate plausible solutions in
  the interim
• However, there are advantages to have some
  solution candidates when there are errors in the
  constraints.

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Plausible Solution Candidates

• For some optimization problems, machine learning
  approaches generate plausible solutions in the
  interim.
• Solutions are getting better while the machine
  learning approach refines solution patterns
  iteratively.
• A better solution emerges from the cooperation of
  plausible solution candidates.

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Fitness Landscape

• Each solution candidate has its fitness score for
  the optimization problem.
• A fitness landscape shows the fitness
  distribution of the whole search space.
• Solution candidates are ranked by fitness
  judgment.

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Genetic Algorithm

• A search technique to find the exact or
  approximate solutions to optimization problems.
• It is based on the principle of evolution
• Survival of the fittest in Natural Selection
• Two basic processes from evolution
• Inheritance (passing of features from one
  generation to the next)
• Competition (survival of the fittest)

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Basic description of GA

• Algorithm is started with a set of solutions
  (represented by chromosomes) called population.
• Solutions from one population are taken and used
  to form a new population.
• The new population (offspring) will be better
  than the old one (parent).
• Solutions which are selected to form new
  solutions are selected according to their fitness
  - the more suitable they are the more chances
  they have to reproduce.

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GA in Pseudo-code

• Choose initial population
• Evaluate the fitness of each individual in the
  population
• Repeat
• Select best-ranking individuals to reproduce
• Breed new generation through crossover and
  mutation (genetic operations) and give birth to
  offspring
• Evaluate the individual fitness of the offspring
• Replace worst ranked part of population with
  offspring
• Until termination

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Building Block Hypothesis

• Building block a short and highly fit schema
  providing benefit for the solution.
• The global optimal solution is made up of
  building blocks.
• Identify, recombine, and resample small building
  blocks to form a new solution with potentially
  higher fitness.
• By working with these particular building blocks,
  we have reduced the complexity of our problem.

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The Fitness Function

• Plays the role of a judge
• Give more scores if the individual owns more
  building blocks
• Refine the fitness function based on the
  evolution results

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Physical Mapping
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Cutting and reassembling for DNA sequence

• Cut a DNA sequence into small pieces in different
  ways and reassemble them together

• the small pieces (called clones) are still too
  large to find complete sequences
• biologically, use probeto mark the clones
• each probe could mark several clones clone could
  contain several probes

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The Physical Mapping Problem with Noisy Genomic
DataJournal of Computational Biology 10(5),
709-735, 2003

• Each row represents a clone Each column
  represents a probe
• Diagram on the left input clone-probe matrix
• Diagram on the right after probe arrangement the
  clones are put in correct positions

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Consecutive Ones with Errors
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False Positives and False Negatives
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A genetic algorithm for physical mapping

• A two-stage genetic algorithm
• First stage generate the neighborhood
  information among probes
• Second stage generate the maximum length of
  connecting probes

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The first stage of GA (GA1)

• Purpose find a probe ordering with the highest
  fitness score for each clone.
• Pseudo Code
• Random generate a population of probe
  permutations
• Evaluate the fitness of each individual in the
  population
• Repeat
• Select best-ranking individuals to reproduce
• Breed new generation through crossover and
  mutation (genetic operations) and give birth to
  offspring
• Evaluate the individual fitnesses of the
  offspring
• Replace worst ranked part of population with
  offspring
• Until termination

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The first stage of GA (GA1)
4 1 2 3 5 8 6 9 11 12 13 14 15 17 18
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Two building blocks that make partial
consecutive ones
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Crossover Operation
2 3 6 8 1 9 10 12 13 5 11 14 15 17 18
P1
9 10 11 12 13 14 8 18 17 6 5 3 2 1 15
P2
Child
2 3 6 8 1 9 10 11 12 13 14 18 17 5 15
2 3 6 8 1 9
2 3 6 8 1 9 10
2 3 6 8 1 9 10 11
2 3 6 8 1 9 10 11 12
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Mutations
2 3 6 8 1 9 10 12 13 5 11 12 15 17 18
2 3 6 8 5 9 10 12 13 1 11 12 15 17 18
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Detection of false Negatives
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
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The first stage of GA (GA1)

• Construct the probe neighboring information
  according to the GA1 results

1 2 3 5 6 8 9 10 11 12 13 14 15 17 18
Probe ordering result for probe segment 1
5 6 7 8 9 10 11 13 14 15 16 17 18 19 20
Probe ordering result for probe segment 2
.
83 85 86 87 88 89 90 91 92 93 95 96 97 98 99
Probe ordering result for probe segment 20
5 3, 6 6 5, 8 8 6, 9 18 17
5 6 6 5, 7 7 6, 8 20 19
5 3, 6 6 5, 7, 8 7 6, 8, 9 20 19
A neighboring probe list

Probe neighboring information
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The second stage of GA (GA2)

• Purpose find the longest connecting probe
  sequence according to the probe neighboring
  information.
• Pseudo Code
• Random generate a population of probe
  permutations
• Evaluate the fitness of each individual in the
  population
• Repeat
• Select best-ranking individuals to reproduce
• Breed new generation through crossover and
  mutation (genetic operations) and give birth to
  offspring
• Evaluate the individual fitnesses of the
  offspring
• Replace worst ranked part of population with
  offspring
• Until termination

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The second stage of GA (GA2)

• Generate a probe ordering according to the probe
  neighboring information

1 2 2 1, 3 3 2, 4, 5 4 3, 5 5 3, 4,
6 6 5, 7, 8 7 6, 8, 9 99 97, 98
2 3 5 4 71 72 73 55 56 57 99 98 97 96
1 2 3 4 5 6 7 93 94 95 96 97 98 99