What are some real world problems that have been solved using a genetic algorithm? What is the problem? What is the fitness test used to solve this problem?
The Lamarckian Genetic Algorithm is used in chemoinformatics to screen for potential new drug compounds that can bind with a particular receptor.
The computational problem is to search through a chemical database for candidates that can orient correctly (wrt the possible orientations of the molecule containing the receptor), and to combine that with a conformational search (i.e., one that considers the possible rotatable torsions of the molecule, which can strongly affect the reaction).
Previously, it was feasible to perform either an orientation search or a conformation search, but not both. LGA takes advantage of computer speedup, and combines the global search of a genetic algorithm with a local search.
Nasa created a genetic algorithm for Antenna Design.
The fitness test is as follows:
The fitness function used to evaluate antennas is a function of the voltage standing wave ratio (VSWR) and gain values on the transmit and receive frequencies. VSWR is a way to quantify reflected-wave interference, and thus the amount of impedance mismatch at the junction. VSWR is the ratio between the highest voltage and the lowest voltage in the signal envelope along a transmission line.
These are often used in finance, especially for portfolio optimization problems. There are many papers on this subject, but see for example Genetic Algorithms in Portfolio Optimization.
I've used GAs to solve scheduling problems in manufacturing and education. The fitness function in the first case was how much of the requested items were manufactured in the given time frame, while in the second case the fitness was based on penalizing schedules with conflicts.
If you're interested in applications, here's a link to 20K+ papers on citeseerx
I can't resist but point out Roger Alsing's work:
Represent the image of Mona Lisa using only 50 semi-transparent triangles.
Antenna design has already been mentioned, and it is an extremely rich domain. (It is, very directly, what started my motion from electrical engineering to computer science (in the late 90's) and more specifically to bio-inspired computation and artificial intelligence (in the last five years or so.))
In the same vein, I'll add antenna array optimization, especially for phased array optimization, which is all of the headaches of antenna design, and more. There are opportunities in the entire field of electromagnetic device design, really: Antennas, antenna arrays, microwave filters, optical gratings, metamaterial device design, all off the top of my head. A dated survey is Electromagnetic Optimization by Genetic Algorithms, and a more recent survey is Genetic Algorithms in Electromagnetics. (I should really buy that second one.
I've seen a lot of good papers on non-electromagnetic circuit design as well: GAs coming up with competitive op-amp or other integrated circuit designs, GAs "learning" to take advantage of the analog imperfections in FPGAs to implement analog functions like clocks, etc. Even something as simple as dumb, discrete element filter design can be a target for GAs: I've seen one that factors in q-factors, tolerances, discrete values and soldering parasitic models to get good, manufacturable filters from the parts you have at hand.
These often involve some novel (to me, anyway) circuit representations to get the genetic operators to fit the paradigm, as well as variable size chromosomes.
recently there was a question about using GAs to evolve wind turbine blade designs using fluid dynamics simulations of physical power generated as the fitness function.
This video shows the use of a genetic algorithm to develop VAWT wind turbine blades. One of the resulting blades is quite different and seems to simulate well. The breeding software was written in Perl, the display software Java, and the CFD software was OpenFoam. More than 672 CPU hours went into the making of this video. Note: I have since discovered I used the wrong viscosity for air on this experiment, so the results aren't valid for use on the earth. (Maybe Jupiter.)
 "Evolving wind turbine blades" on youtube by "sjh7132". cited by/from the TCS.se question: To what extent is it possible to use genetic algorithms to make wind mill turbine blades more efficient?
there is some research into using GAs for wine classification. it accurately classifies the variety of wine and the production place ("origin denomination"). this is a subset of use of GAs in Agricultural Systems of which there are many applications. 
 Feature selection algorithms using Chilean wine chromatograms as examples by N.H.Beltran et al
 State of Art in Genetic Algorithms for Agricultural Systems by Bolboaca et al
there are many papers on use of GAs for flight control in the aerospace field. many of these are published or searchable by IEEE explorer. the fitness function generally measures how well/effectively the algorithm controls the flight.
 Flight control system design and optimisation with a genetic algorithm by Fantinutto et al
 Application of genetic algorithms to hypersonic flight control. Austin, Jacobs.
 Multi-core implementation of F-16 flight surface control system using Genetic Algorithm based adaptive control algorithm, Xiaoru Wang
 Fuzzy logic control based on genetic algorithm to integrated flight control for hypersonic vehicles. by Wang Jian
a remarkable, even extraordinary or paradigm shifting use of GAs, highly cited in later surveys, was pioneered by Koza to solve a video game "problem"— namely Pac Man for a proof of principle, but the concept can likely be applied to possibly almost any video game, and the results are definitely far from trivial or "toy".
that is, he evolved algorithms that implement actual behavior to win at playing the game for extended periods of time. results are on the level of performance of amateur or even advanced human players. a fitness function can be either points scored by the algorithm or length of time played (the later will presumably evolve algorithms that survive without scoring points, such as a classic case of "hunting" spaceships in the game Asteroids). the behavior is implemented with "primitives" (eg sense monsters/act by turning etc) and trees that represent the combinations of primitive strategies.
 Evolving Diverse Ms. Pac-Man Playing Agents Using Genetic Programming by Atif M. Alhejali and Simon M. Lucas
 Learning to Play Pac-Man: An Evolutionary, Rule-based Approach by Gallagher and Ryan
 Learning to Play Using Low-Complexity Rule-Based Policies: Illustrations through Ms. Pac-Man by István Szita András L~orincz
The annual GECCO conference (pretty much the premier venue for evolutionary computation research) has a `Real World Applications' track.
See also this recent presentation: