Friday, April 27, 2007

A (15, 100)-ES Following A Moving Optimum

Here you are a nice video, which I took from EvoWeb Flying Circus, that shows us an Evolution Strategy (ES) following a moving optimum. The ES applied is the so-called Comma ES or (μ, λ)-ES. The Comma word has to do with the mechanism of selection that happens and it is done through a simple way:

There are, in the current generation, μ parents that generate (via mutation and/or recombination) λ offsprings. Then, we select among the λ offsprings the μ best ones which will be the parents for the next generation, even though those λ are worse than their parents. Let me show you an example:

Say that we have 5 parents (μ = 5) and we want to generate 20 offsprings (λ = 20) - so, our evolution strategy is (5, 20)-ES. When the 5 parents have already generated the 20 offsprings, we select the top 5 from those 20 ones. This kind of selection mechanism is interesting because allows us to escape local optima or do hill-climbing to seek better places inside the space defined by the fitness function. Despite the fact that that type of selection procedure permits a temporary deterioration related to the quality of the individuals (offsprings' fitnesses) which will replace their parents in the subsequent generation, it is well suited to problems that have a moving optimum.

The turquoise (or cyan) star is the moving optimum and the function being optimized is the Fletcher-Powell function, see below.


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