Evolutionary computation and genetic algorithms

Evolution

For evolution to work (either the real-life biological kind or some more abstract kind), we need at least the following.

• There need to be "creatures" which give birth to other creatures, passing on their traits to their offspring, and which ultimately die. ("Creatures" is in quotes because these don't really have to be biological entities. All they really need to be is combinations of features of some sort. And they only need to reproduce, die, etc. in our program, not in "real life".)
• There must be a way for traits to be passed on: an inherited genome. In interaction with the environment, this results in a phenome, an actual "body" and set of traits.
• There must be a way of evaluating the creatures' traits: some traits aid in survival or reproduction, others are harmful, and still others may be irrelevant. This is "survival of the fittest", but it requires a function of some sorty that takes the creatures and returns a fitness for each one, either directly (by providing a number) or indirectly (by permitting the creatures to mate
• There needs to be a way of generating new traits, mutation, a process by which some of the elements of the genome are randomly changed.

How it works

• Each creature is born with some combination of traits; it may not be possible to simply figure out what combination works best for the environment of the creatures. Thus this is a "hard" problem, one which requires some sort of search procedure to solve.
• Creatures live their lives. Some survive long enough to reproduce and have offspring.
• If a particular trait or combination of traits helps creatures reproduce or live longer, creatures with that trait (those traits) will tend to have more offspring.
• Creatures pass on (at least some of) their traits to their offspring. In sexual reproduction, they pass on a combination of their parents' traits.
• As the fit creatures have a chance to reproduce, or at least reproduce more often than the unfit creatures, the percentage of creatures with the good traits should increase on each generation.
• There is a small probability that a new creature will end up with some random traits which it did not inherit from its parent(s) through mutation. In this way new traits or combinations of traits which were not part of the original population and are not possible through combinations of existing individuals' genomes can be tried out in the world.

Genetic algorithms

(Here is another site where you can learn about genetic algorithms.)

• Genetic algorithms (GAs) are a search technique, a way of solving problems using a form of reinforcement learning based on (biological) evolution.
• GAs are used for
  • Parameter-oriented search problems

    These are problems in which the candidate solutions consist of the settings of multiple parameters. Consider an old-style television with dials labeled with things like "vertical hold" and "contrast". Some combination of settings for these dials results in a good picture, but the viewer is clueless about what combination is the right one. The parameters in this case are the dials, and the search problem is to find the right combination of settings. To apply a GA to a problem like this, we treat each candidate solution as a genome in a population and evaluate each in terms of its fitness, in this case, in terms of the quality of the TV picture that results from the settings.

  • Modeling biological evolution

    GAs may be used to study biological evolution itself. An artificial life simulation is set up in which the behavior of creatures depends (at least in part) on their genomes and in which creatures pass on their traits to their offspring. The researcher observes how the fitness of the population varies over different generations and what sorts of solutions the creatures evolve.

  • Designing a suitable initial architecture for cognition (say, a neural network)

    Neural networks learn by adjusting their weights on their connections, but where do the connections come from in the first place? That is, what wires up the neural architecture in which neural network learning takes place? In real life, much of this is apparently the job of evolution: some neural structure is innate. One area of research combines GAs with neural networks: the neural network architecture (numbers of units, patterns of connectivity joining them, learning algorithms, etc.) is coded for in the genome, and neural network learning adjusts the weights on the connections in the network.

• The basics: how GAs work
  • Genetic encoding
    First, there must be a way of representing the relevant traits in the genome.
    • The genome is usually a binary string. Features which are not binary may be encoded in sets of positions. For example, if we want to represent the settings of five TV dials and each dial has eight possible settings, we could use genomes consisting of 15 bits (0s or 1s). There would be three bits for each dial because it takes to three bits to represent eight different numbers.
    • The genome is a code. There must be a way for it to be translated into something that is relevant for fitness. The most direct approach is to have a fitness function that takes the genome itself and returns a fitness value. This is what happens in the simple example below. A less direct approach, more like real life, is to have the genome code for the behavior of the creature that contains it, that is, to distinguish between the genome and the phenome. Fitness is then evaluated on the basis of the behavior rather than the genome itself. This is what we will do in Smarts.
  • Fitness function: How are individuals evaluated?
    • In most GAs, the fitness function assigns a numerical score to each genome (or to the behavior of the phenome). Of course the fitness function is not known or understood by the designer of the GA; if it were, there would be nothing to search for since the solution would obvious.
    • Alternately the function may be built into the environment, allowing some creatures (at least in part because of their traits) to survive long enough to reproduce and preventing others (again because of their traits) from reproducing.
  • Selection procedure: How are individuals selected for reproduction (crossover) on the basis of their fitness?
    • Selection is usually indirect: individuals' chance of reproducing depends directly on their fitness. One possibility: weighted roulette wheel. Parents are selected probabilistically on the basis of their proportion of the total fitness of the population.
      • After fitnesses are calculated for each individual in the population, each fitness is converted to a proportion of the total fitness.
      • The fitness proportions are used to create sections of different sizes in a "roulette wheel", each associated with a single individual.
      • The roulette wheel is spun as many times as there are individuals in the population. Each time the ball lands in a section, a copy of the individual for that section is added to the pool of parents.
      • Pairs of parents are selected from the pool to reproduce, each producing two offspring.
    • Direct selection: more successful individuals are able to "find" mates.
  • How does reproduction work?
    • For each pair of parents, crossover point is selected randomly within their genomes.
    • One of the offspring gets the first part of the genome (everything before the crossover point) from parent A and the second part of the genome from parent B. The other offspring gets the first part of the genome from parent B and the second part from parent A.
  • Mutation: How are new traits created?
    • With a small probability (say, 0.001) each of the bits in the newly created genomes is flipped (1 changed to 0 or 0 changed to 1).
    • Mutation can create a feature that would not exist otherwise and prevent the population from converging too soon.
  • Question: When are GA's a good idea?
• An example
  Fitness for this example is assigned on the basis of how much the bits in the genome vary. Thus the lowest fitness is assigned to genomes in which all bits are the same, the highest to genomes with an equal number of 0s and 1s.

  Generation	Genomes	Fitness	Fitness proportion	Individuals selected for mating with crossover points
  1	01011110 10111000 00001010 00000100	3 4 2 1	0.3 0.4 0.2 0.1	01|011110 10|111000 10111|000 00001|010
  2	10011110 01111000 00001000 10111010	3 4 1 3	0.27 0.36 0.09 0.27	01111|000 10111|010 0111|1000 1011|1010
  3	10111000 01111010 10111000 01111010	4 3 4 3	0.29 0.21 0.29 0.21	10|111000 01|111010 10111|000 01111|010

• If there's time: example animation of parameters... adapting the search parameters... Lamarck and the Baldwin effect...

© 2004. Indiana University and Michael Gasser. www.indiana.edu/~gasser/Q530/Notes/ga1.html 17 Oct 2004