What are the differences between genetic algorithms and evolution strategies?

Just stumbled on this thread when researching Evolution Strategies (ES).

As Paul noticed before, the encoding is not really the difference here, as this is an implementation detail of specific algorithms, although it seems more common in ES.

To answer the question, we first need to do a small step back and look at internals of an ES algorithm. In ES there is a concept of endogenous and exogenous parameters of the evolution. Endogenous parameters are associated with individuals and therefore are evolved together with them, exogenous are provided from "outside" (e.g. set constant by the developer, or there can be a function/policy which sets their value depending on the iteration no).

The individual k consists therefore of two parts:

  • y(k) - a set of object parameters (e.g. a vector of real/int values) which denote the individual genotype
  • s(k) - a set of strategy parameters (e.g. a vector of real/int values again) which e.g. can control statistical properties of mutation)

Those two vectors are being selected, mutated, recombined together.

The main difference between GA and ES is that in classic GA there is no distinction between types of algorithm parameters. In fact all the parameters are set from "outside", so in ES terms are exogenous.

There are also other minor differences, e.g. in ES the selection policy is usually one and the same and in GA there are multiple different approaches which can be interchanged.

You can find a more detailed explanation here (see Chapter 3): Evolution strategies. A comprehensive introduction

In most newer textbooks on GA, real-valued coding is introduced as an alternative to the integer one, i.e. individuals can be coded as vectors of real numbers. This is called continuous parameter GA (see e.g. Haupt & Haupt, "Practical Genetic Algorithms", J.Wiley&Sons, 1998). So this is practically identical to ES real number coding.

With respect to parent selection, there are many different strategies published for GA's. I don't know them all, but I assume selection among all (not only the best has been used for some applications).

The main difference seems to be that a genetic algorithm represents a solution using a sequence of integers, whereas an evolution strategy uses a sequence of real numbers -- reference: http://en.wikipedia.org/wiki/Evolutionary_algorithm#

In evolution strategies, the individuals are coded as vectors of real numbers. On reproduction, parents are selected randomly and the fittest offsprings are selected and inserted in the next generation. ES individuals are self-adapting. The step size or "mutation strength" is encoded in the individual, so good parameters get to the next generation by selecting good individuals.

In genetic algorithms, the individuals are coded as integers. The selection is done by selecting parents proportional to their fitness. So individuals must be evaluated before the first selection is done. Genetic operators work on the bit-level (e.g. cutting a bit string into multiple pieces and interchange them with the pieces of the other parent or switching single bits).

That's the theory. In practice, it is sometimes hard to distinguish between both evolutionary algorithms, and you need to create hybrid algorithms (e.g. integer (bit-string) individuals that encodes the parameters of the genetic operators).