Multidimensional scaling as a technique for the presentation of high-dimensional data with standard visualization techniques is presented. The technique used is often known as Sammon mapping. We explain the mathematical foundations of multidimensional scaling and its robust calculation. We also demonstrate the use of this technique in the area of evolutionary algorithms. First, we present the visualization of the path through the search space of the best individuals during an optimization run. We then apply multidimensional scaling to the comparison of multiple runs regarding the variables of individuals and multi-criteria objective values (path through the solution space).

Evolutionary algorithms (EAs) are widely employed to solve a broad range of optimization problems. Even though they work in an algorithmically simple manner, it is not always easy to understand what is going on during a particular optimization run. It is especially desirable to gain further insight into the state and course of the algorithm if the optimization does not yield the expected results or if we are not sure whether the result achieved is really the best result possible. During an optimization run an EA produces a vast amount of data. The extraction of useful information is a nontrivial task. In this article, we review visualization methods used to extract this useful information. We also demonstrate the application of visualization techniques and explain how they help us to understand the course and state of the EA. This extra information gained by the use of visualization techniques is often the difference between a good result and a very good result. In complex real-world applications, merely achieving a good result often means that the approach has failed. On the other hand, a success means large gains in productivity or safety or a decrease in costs.

Real-world applications generally distinguish themselves from theoretical developments in that they are much more complex and varied. As a consequence, better models require more details, new methods and, finally, more complexity. By confronting a benchmark evolutionary algorithm with an automotive gearbox with hundreds of parameters to optimize, we were able to observe new requirements which led us to an additional procedure that uses specific knowledge upon gene-objective relations to guide cross-over mechanisms

For real-time systems, correct system functionality depends on logical as well as on temporal correctness. Static analysis alone is not sufficient to verify the temporal behavior of real-time systems. Since existing test methods are not specialized for the verification of temporal correctness, we have developed a new testing method, namely evolutionary testing. This paper illustrates results of the first industrial application of the evolutionary test.