Together with you, we at inpro carry out optimizations using the robust bionic optimization method Evolution Strategy. Bionics describes the transfer of results of biological evolution into technology. The Evolution Strategy represents the transfer of the optimization process of biology, biological evolution, into technology. Evolutionary algorithms can also help with problems that are considered to be non-optimizable or difficult to optimize. Previous applications of the Evolution Strategy range from the optimization of coffee blends and the optimization of elastomer material models to the optimization of sequence problems and discrete problems.

Optimizing according to a natural model? Does nature also need to be searched for models? Is it worth it? Is there any optimization at all? Aren’t the many optimization methods already invented by mathematicians sufficient? These and similar questions are frequently asked in lectures. And the answer is: It’s worth it! In the process of evolution, for example, the one-photon measuring device “eye” and the one-molecule measuring device “nose” were developed. For physical reasons, it cannot be built any better.

If evolution is able to do this, then it should be worthwhile to take a closer look at the biological “optimization method”. Ingo Rechenberg and Hans-Paul Schwefel from the Technical University of Berlin did this in the 1960s and developed what they called an Evolution Strategy. In the USA at that time John Holland had designed the Genetic Algorithms and Lawrence Fogel the Evolutionary Programming.

Since their creation, both the Genetic Algorithms and Evolutionary Programming have become more and more similar to the Evolution Strategy of Ingo Rechenberg and Hans-Paul Schwefel. For example, for genetic algorithms, which originally worked on 0-1 images of variables, there also exist real coded genetic algorithms. The concept of adaptive adaptation of the step sizes to control the mutation size was also integrated.

Today, these methods are referred to as Evolutionary Algorithms. Common to all these methods is the reference to evolutionary principles, some of which were first formulated by Charles Darwin – the most relevant of which are mutation and selection. However, recombination, i.e. sexual reproduction, is also a component of all algorithms.

Optimization tasks in the area of production control, mixture optimization of chemical substances, positioning of components in deep-drawing presses and optimization of the geometry of self-pierce rivets have shown the potential of the Evolution Strategy in industrial applications. But, also components of looms, coffee blends, glaze blends for tiles and sanitary ceramics and the shape of headlight mirrors as well as formulas for the description of rubber seals have been optimized by inpro employees. In many of these questions, the usual mathematical optimization methods proved to be less suitable. The Evolution Strategy often finds better solutions with greater certainty.

When planning optimization, the effort involved in realizing and evaluating the individual variants must be considered. This applies to optimizations in the computer as well as to those where real models are built. If, for example, the intake manifold of a vehicle is to be optimized, it would be too expensive to build a new intake manifold for each variant. An adjustable intake manifold, on which the most important influencing variables can be changed, is the answer. In the computer model, it is not a solution to change every node of a finite-element network. Since a component can have several millions of such nodes, optimization is not possible without further effort. Here it helps to change the design of surfaces that are described with a few parameters and thus to obtain an object that can then be optimized.

The evaluation of a variant can take a lot of time. For example, the most accurate method for calculating the properties of a weld seam requires several hours of computing time for a seam length of a few centimetres. This is of course much too long if several meters of weld are to be optimized. But it does not always have to be as accurate. An alternative method developed by inpro now only requires a fraction of this computing time and provides enough prediction accuracy – this now also makes it possible to optimize weld seams. In practice, it is possible and sensible to first work with a simplified method and then switch to a more accurate and more computationally intensive method in the final optimization phase.

When optimizing the mixture of chemical substances, it took one laboratory day per offspring to measure the physical properties of the mixture. An additional bionic process was used to remedy this situation. By means of artificial neural networks – simple replicas of brain structures in the computer – it was possible to predict the physical properties of the offspring without further laboratory measurements. The networks were first taught with examples – if this mixture is present, it has these physical properties; if that mixture is present, it has those properties. Then the networks were able to predict with enough accuracy the properties of mixtures that had never before been perceived.

Optimizations in industry are often time-consuming and expensive. In an example similar in complexity, the optimization process must already function perfectly so that in “reality” no time is wasted on a process that does not work effectively. Here, the optimization of lenses is used as an example for problems with continuous parameters and of Rubik’s cubes as an example for combinatorial problems. The application of the Evolution Strategy with subjective selection of the best offspring is shown by the example of the optimization of a coffee blend. In none of the examples shown was it necessary to apply the concept of recombination, which plays an important role in biological evolution. The basic idea behind the application of Evolutionary Algorithms in practice is always: Why complicated, when it can be simple (without recombination)?

In the process of optimization, a variable glass body, initially a flat glass pane, is to be deformed so that a bundle of parallel light rays is focused on a screen. In addition, the resulting lens should have a minimal volume.

A (1, 10) Evolution Strategy is used: Starting from one parent lens, ten offspring lenses are produced, and the best of the offspring lenses becomes the next generation parent lens. The offspring lenses are created by copying the parent lens and then mutating the lens thickness at 25 given locations. Small changes are more likely than large ones. Thus, all offspring are similar to the parent lens. How strongly the offspring individuals deviate from the parents is determined by one or more step sizes, which are automatically adjusted. The smaller the step sizes, the more similar the individuals are in the population.

To determine the best of the ten offspring lenses, the quality of each offspring lens is calculated. Two objectives are given in the quality function: The lens should concentrate the incoming light and the volume of the lenses should be as small as possible. In the example, the focus has a high weight in the evaluation, so that the focus is very good, but at the same time a minimal volume is created under these circumstances.

When determining the best offspring, if the desired minimum volume is not taken into account in addition to the desired convergence of the light rays, it will only happen by chance that a thinner lens is also selected as the solution.

Often a compromise has to be found between the number of manipulated variables and the possibility of finding new innovative solutions. This becomes clear with lens optimization: initially, the thickness of the glass body was only changed in 25 places. This led to the result of the well-known convex lens. The 25 prisms, of which the lens is composed, merge into each other steplessly. If this condition is dropped and the upper and lower sides of the prisms are released for optimization, the result is the familiar Fresnel lens, a stepped lens that is used in studio spotlights, solar systems, lighthouses and rear walls of SLR cameras due to its small volume. In the example, the Fresnel lens has only about 20% of the volume of the convex lens.