Well, both genetic algorithms and differential evolution are examples of evolutionary computation.
Genetic algorithms keep pretty closely to the metaphor of genetic reproduction. Even the language is mostly the same-- both talk of chromosomes, both talk of genes, the genes are distinct alphabets, both talk of crossover, and the crossover is fairly close to a low-level understanding of genetic reproduction, etc.
Differential evolution is in the same style, but the correspondences are not as exact. The first big change is that DE is using actual real numbers (in the strict mathematical sense-- they're implemented as floats, or doubles, or whatever, but in theory they're ranging over the field of reals.) As a result, the ideas of mutation and crossover are substantially different. The mutation operator is modified so far that it's hard for me to even see why it's called mutation, as such, except that it serves the same purpose of breaking things out of local minima.
On the plus side, there are a handful of results showing DEs are often more effective and/or more efficient than genetic algorithms. And when working in numerical optimization, it's nice to be able to represent things as actual real numbers instead of having to work your way around to a chromosomal kind of representation, first. (Note: I've read about them, but I've not messed extensively with them so I can't really comment from first hand knowledge.)
On the negative side, I don't think there's been any proof of convergence for DEs, yet.
Answer from Novak on Stack OverflowWell, both genetic algorithms and differential evolution are examples of evolutionary computation.
Genetic algorithms keep pretty closely to the metaphor of genetic reproduction. Even the language is mostly the same-- both talk of chromosomes, both talk of genes, the genes are distinct alphabets, both talk of crossover, and the crossover is fairly close to a low-level understanding of genetic reproduction, etc.
Differential evolution is in the same style, but the correspondences are not as exact. The first big change is that DE is using actual real numbers (in the strict mathematical sense-- they're implemented as floats, or doubles, or whatever, but in theory they're ranging over the field of reals.) As a result, the ideas of mutation and crossover are substantially different. The mutation operator is modified so far that it's hard for me to even see why it's called mutation, as such, except that it serves the same purpose of breaking things out of local minima.
On the plus side, there are a handful of results showing DEs are often more effective and/or more efficient than genetic algorithms. And when working in numerical optimization, it's nice to be able to represent things as actual real numbers instead of having to work your way around to a chromosomal kind of representation, first. (Note: I've read about them, but I've not messed extensively with them so I can't really comment from first hand knowledge.)
On the negative side, I don't think there's been any proof of convergence for DEs, yet.
Differential evolution is actually a specific subset of the broader space of genetic algorithms, with the following restrictions:
- The genotype is some form of real-valued vector
- The mutation / crossover operations make use of the difference between two or more vectors in the population to create a new vector (typically by adding some random proportion of the difference to one of the existing vectors, plus a small amount of random noise)
DE performs well for certain situations because the vectors can be considered to form a "cloud" that explores the high value areas of the solution solution space quite effectively. It's pretty closely related to particle swarm optimization in some senses.
It still has the usual GA problem of getting stuck in local minima however.
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Well, both genetic algorithms and differential evolution are examples of evolutionary computation.
Genetic algorithms keep pretty closely to the metaphor of genetic reproduction. Even the language is mostly the same-- both talk of chromosomes, both talk of genes, the genes are distinct alphabets, both talk of crossover, and the crossover is fairly close to a low-level understanding of genetic reproduction, etc.
Differential evolution is in the same style, but the correspondences are not as exact. The first big change is that DE is using actual real numbers (in the strict mathematical sense-- they're implemented as floats, or doubles, or whatever, but in theory they're ranging over the field of reals.) As a result, the ideas of mutation and crossover are substantially different. The mutation operator is modified so far that it's hard for me to even see why it's called mutation, as such, except that it serves the same purpose of breaking things out of local minima.
On the plus side, there are a handful of results showing DEs are often more effective and/or more efficient than genetic algorithms. And when working in numerical optimization, it's nice to be able to represent things as actual real numbers instead of having to work your way around to a chromosomal kind of representation, first. (Note: I've read about them, but I've not messed extensively with them so I can't really comment from first hand knowledge.)
On the negative side, I don't think there's been any proof of convergence for DEs, yet.
Answer from Novak on Stack Overflow
If you're asking for a homework assignment, then I can't really help you, because the answer really depends on how your professor interprets the taxonomy. But if you're asking for your own edification, I can give you my view.
First, the distinctions between the four classes you list (particularly between 1, 3, and 4) are largely historic. There are still some very real differences of course, but we don't view the lines between them as sharply as we once did. This means, for example, that GAs can be real-valued instead of binary and might rely on mutation more than crossover. You can have an evolution strategy for the traveling salesman problem. Really the description in the book isn't terribly well suited for use as a taxonomy for this reason. I teach from this book, and I like it a lot, so that's not really a criticism. I don't think the authors intended for you to try and use it as a well-defined taxonomy either.
If we go with this idea as a rough taxonomy though, then in principle, we have an umbrella term: "Evolutionary Computation" or "Evolutionary Algorithms" that covers all four of the cases you list. In practice though, while if someone says "evolution strategy" or "genetic programming", it's because they intentionally want to highlight that that's what they're doing, people sometimes say "genetic algorithms" when they really mean "evolutionary algorithms". So that term is especially hard to interpret.
So we might be able to call DE a GA with that understanding and be OK, but it really depends on who's asking the question as to whether that's what they had in mind or not.
Looking at the problem another way though, it gets even fuzzier. Right now, you're reading someone else's taxonomy and trying to fit the pieces together. What if you take a step back and try to formally define what a genetic algorithm or evolutionary algorithm is yourself? You might come up with something like "an algorithm that maintains a population of one or more candidate solutions, usually generated randomly, and continually selects the better individuals from the population, produces new individuals from the old ones via some type of variation operators, and favors the better of these new individuals for insertion into the population".
It's hard to get much narrower than that without excluding some things we think are "obviously" evolutionary algorithms, but this definition is really very broad. Certainly things like differential evolution and particle swarm optimization meet this definition, but so does, for example, simulated annealing. You can even take a simple next-descent hill-climber and call it a (1+1)-ES.
Personally then, my answer to your question is "sort of". If I write a paper that proposes a novel DE variant that looks super-awesome, I'd absolutely submit it to a journal like Evolutionary Computation. I know that my algorithm would be viewed as being appropriate for a venue that focused on genetic and evolutionary algorithms. But I probably wouldn't tell people that I used a "genetic algorithm" either, because that term doesn't feel precise enough to capture what it is that I want to express.
I'm not sure this is a particularly helpful answer, but I think it's probably a pretty common view among people in the field.
The wording of the original paper that introduced Differential Evolution is such that the authors consider DE a different thing from Genetic Algorithms or Evolution Strategies. Example:
Choosing a subgroup of parameters for mutation is similiar to a process known as crossover in GAs or ESs.
Another one:
A further disadvantage of GAs is the amount of expertise that is required to operate them, the same holds true for ESs.
Yet the differences remain unclear to me (I am not an expert in the field). Taking Eiben & Smith taxonomy strictly I would say DE is just another class of Evolutionary Algorithms.
