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.
Why to optimize following a natural example?
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.
One-molecule measuring device nose and one-photon measuring device eye, adapted in the course of biological evolution (pictures: pixabay).
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.
Mutation and selection in industrial application
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.
Planning and implementation of optimization
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.
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Optimize, adapt, improve.
Examples for the application of the Evolution Strategy
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)?
Optimization of an optical lens
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.
Evolutionary optimization of coffee blends
Branded coffee usually consists of several varieties. However, the taste of the individual varieties is not constant. Therefore, depending on climatic conditions during ripening, processing, transport and other factors, the taste of the coffee will vary with each harvest. When optimising coffee blends, the aim is to preserve the old flavour after delivery and roasting of the coffee beans from the previously used or even from additional beans. Another goal could be to create a new coffee blend for which only the developer has an idea in his mind how it should taste. Experienced coffee testers often know which components they must change in order to change the taste of the coffee in the desired direction. An attempt has been made by a coffee roasting plant in Berlin to optimize a coffee with an Evolution Strategy but without this knowledge.
A single parent coffee served as the initial mixture. For this purpose, the five components of a branded coffee were put together in a fantasy blend. For the trained taste buds of the three coffee experts involved, the taste of the blend was far from that of branded coffee.
A (1, 5) Evolution Strategy was used for this optimization because it is very difficult, if not impossible, to remember the taste of ten coffees and then select the best one. Using an automatic blender specially designed for this purpose, the five offspring coffee blends from the five individual brewed varieties could be weighed in fully automated.
The evaluation of the offspring coffees was carried out by experienced experts from the coffee company. The experts decided by tasting which blend is closest to the target coffee and should become the next generation’s parent coffee.
After eleven generations, the solution to the optimization problem was found. The taste of the selected offspring coffee could no longer be distinguished from that of the target coffee. The result was a blend that was very different from the current blend, but still had the same taste. The reason for this could be that, in contrast to the usual expert approach, the Evolution Strategy always varies all components simultaneously and permits temporary deteriorations. A further goal could be to include the prices of the individual types of coffee, for example, in order to achieve a blend that is optimal in terms of taste and cost.
Set-up of Michael Herdy at the TU-Berlin, Department of Bionics and Evolutionary Technology
Optimization of Rubik’s cube
This optimization example is a three-dimensional logical puzzle. You can buy these dice with different numbers of pieces.
The goal is to bring the cube from a multicolored initial state into a state in which either each side of the cube contains only partial cubes of one color or another target pattern is created. In the literature there are solution strategies with exact details on how a cube can be turned into the target position. Here, so-called manoeuvres are specified with which successive turns, for example, two corners can be swapped, or three edges twisted. Such maneuvers have been further developed for the use of the Evolution Strategy from the smallest 2 x 2 x 2 cube to the 7 x 7 x 7 cube.
In contrast to the prefabricated strategies, evolutionary optimization does not first analyze the state of the cube and then work through a fixed strategy. This optimization also works with variation, evaluation and selection.
In variation, for each offspring it is decided by chance which manoeuvre is executed at which position of the cube. The offspring with the fewest false color proportions on each side of the cube is closest to the goal and becomes the parent of the next generation. The optimization begins with ten offspring per generation. In the course of the optimization, values of more than 5000 offspring per generation are achieved for the 7 x 7 x 7 cube.
In industry, paints are needed that are easy to disperse on the one hand and on the other are stable after impact with the body. This is achieved by special binders that make use of the thixotropic effect, i.e. become more viscous under the effect of force. When the load decreases, i.e. after the paint hits the bodywork, the binders in the paint film become thick again. This prevents a high film thickness from running off. However, the surface tension of the material causes a desired flow in the paint layer.
This thixotropic effect was maximized for a customer by the Evolution Strategy. In order to realize and evaluate fewer recipes and to discard the worst recipes after a virtual evaluation, artificial neural networks (KNN) were taught to predict viscosities for different shear rates based on recipes and to derive a prognosis for the ratio of viscosities at different shear rates. The results of this formulation modelling were very positive. The individual predicted viscosities were provided with a high standard deviation. However, the ranking of the formulations with regard to the ratio of viscosities at different shear rates was reproduced so well that the worst offspring of a generation no longer had to be evaluated experimentally.
Finally, a virtual optimization was carried out using the trained neural networks without any laboratory tests. The formulation measured at the end of this optimization showed a significantly improved viscosity ratio.
Adaptation of material models of elastomers
Wherever elastomers are used in technology and their special thermoviscoelastic properties are to be used to advantage (e.g. as damping elements for engine mounts), it is of great importance for the specific design of such components to have quantitative data on the thermoviscoelastic properties. The so-called master curve describes these properties.
The master curve, a data model consisting of a sum of up to 20 exponential functions, is to be adapted to an experimentally determined curve of the temperature behaviour of an elastomer in the time or frequency domain. The experimentally determined curve results from measurements in which the relaxation behaviour of the elastomer to be investigated is determined at specified temperatures (e.g. ten temperatures between -20 °C and +80 °C) during a specified time period (e.g. 10 minutes) with specified elongation (e.g. 1 %).
To evaluate the fit, the sum of the squared errors between model and experimental values is determined. These so-called Prony parameters can be used directly in FEA programs (e.g. MARC or ANSYS) for the simulation of viscoelastic materials.
Optimization process with Evolution Strategies
1. Definition of parents(Initialization of the optimization)
2. Mutation(Realization of descendants)
In the case of mutation, the offspring settings are generated from the parent settings by adding random numbers in the case of continuous manipulated variables. Small changes are more likely than large ones. The offspring are therefore mostly similar to the parents. In combinatorial optimizations, more or less large changes are made per individual offspring, the magnitude of these changes can be automatically adjusted in the process of optimization.
3. Selection(evaluation of offspring)
The evaluation determines which offspring have come closest to the optimization goal and become parents of the next generation. All goals that are to be achieved by optimization must be included in the evaluation. Otherwise, it is left to chance whether they are met in the solution. In the quality function, the different goals are balanced against each other.
4. Adaptation of the mutation distribution
The random distribution with which the offspring have been varied is adjusted, taking into account the difference between the best offspring and their parents. With this adjusted distribution, the offspring of the next generation are produced in the next generation. In combinatorial optimization examples this distribution does not exist. There it is advantageous to regulate the number of offspring per generation depending on how many offspring have a better quality than the parent.
The most important facts about the Evolution Strategy
- The Evolution Strategy originally conceived by Ingo Rechenberg and Hans-Paul Schwefel belongs mathematically speaking to the class of stochastic search methods, it works according to the model of biological evolution.
- With a population of individuals, each representing possible solutions to the optimisation problem, the goals formulated in the quality function are progressively achieved better in the process of simulated evolution.
Optimization can start without much prior knowledge. In comparison, some mathematical optimization methods require a very good initial setup.
No analytical description of the optimization task is required. It must only be possible to determine which of several offspring variants is the best and becomes the parent of the next generation.
It can also be judged subjectively by looking, smelling, tasting, hearing or feeling which is the best offspring.
- If you do not want to give sensitive data from the house, an optimization is also possible by e-mail:
- You send us a starting data record.
- We will send you the descendant data records for each generation by e-mail.
- You send us by e-mail the information which of the descendants is the best.
2. and 3. are repeated until the goal is reached.
Cooperation with your company
If you now believe that one of your optimization challenges could be solved with the Evolution Strategy, please contact us. We look forward to assisting you! The support can take the form of consulting and/or the creation of customized software.
Get in contact either directly by telephone
Prof. Dr.-Ing. Michael Herdy
Seniorexperte für Bionik
T. +49 30 399 97–183