1. X.4 Genetic Algorithms
Understand the basic design architecture underpinning genetic algorithms
Role of the Fitness function
Repopulation based on genetic changes
Cross-over
Site mutation
Scope of use and limitations.
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2. When to consider genetic algorithms
Genetic algorithms are well-suited when a low-dimensional outcome (e.g., discrimination between two components) depends on a high-dimensional input (e.g., the measurement of a spectrum).
Similar to LDA, genetic algorithms are based on training.
Unlike LDA, the outcomes are not deterministic (i.e., the result of the algorithm can be different each time it is calculated for identical inputs).
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3. Overview 1. Build an initial random population
2. Apply a fitness function and identify a small subset that maximizes the output of the fitness function.
3. Using the selected subset, repopulation based on genetic modification
Cross-over
Site mutation
4. Iterate between steps 2 and 3 to convergence.
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4. Example: Digital signal processing
Consider a problem in which we wish to recover the amplitude of a complicated, distorted signal (Sig1) and suppress an interference (Sig2).
Multiplication by what vector F will maximize the amplitude from Sig1 and suppress Sig2?
In this case, the Fitness Function is the scalar product amplitude of the data trace with the test vector F.
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5. Example: Digital signal processing
1. Generate a set of many test populations consisting of zeros and ones (binary) for filter possibilities. Find the two corresponding to the highest value of amplitude.
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6. Example: Digital signal processing
2. Expand the population by cross-over and point mutation.
-Cross-over:
-Point Mutation 1 1 1
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7. Example: Digital signal processing
2. Evaluate each new member of the population by the fitness function [i.e., multiplication by (Sig1-Sig2) to determine the value of amplitude]. Keep the top two.
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8. Example: Digital signal processing
Iterate to convergence (or impatience).
The value of amplitude converges relatively rapidly for the top two candidates.
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