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Motivation
(2016)

Since human beings started to work consciously with their environment, they have tried to improve the world they were living in. Early use of tools, increasing quality of these tools, use of new materials, fabrication of clay pots, and heat treatment of metals: all these were early steps of optimization. But even on lower levels of life than human beings or human society, we find optimization processes. The organization of a herd of buffalos to face their enemies, the coordinated strategies of these enemies to isolate some of the herd’s members, and the organization of bird swarms on their long flights to their winter quarters: all these social interactions are optimized strategies of long learning processes, most of them the result of a kind of collective intelligence acquired during long selection periods.

In this chapter we introduce methods to improve mechanical designs by bionic methods. In most cases we assume that a general idea of the part or system is given by a set of data or parameters. Our task is to modify these free parameters so that a given goal or objective is optimized without violation of any of the existing restrictions.

We have seen that bionic optimization can be a powerful tool when applied to problems with non-trivial landscapes of goals and restrictions. This, in turn, led us to a discussion of useful methodologies for applying this optimization to real problems. On the other hand, it must be stated that each optimization is a time consuming process as soon as the problem expands beyond a small number of free parameters related to simple parabolic responses. Bionic optimization is not a quick approach to solving complex questions within short times. In some cases it has the potential to fail entirely, either by sticking to local maxima or by random exploration of the parameter space without finding any promising solutions. The following sections present some remarks on the efficiency and limitations users must be aware of. They aim to increase the knowledge base of using and encountering bionic optimization. But they should not discourage potential users from this promising field of powerful strategies to find good or even the best possible designs.

Application to CAE systems
(2016)

Due to the broad acceptance of CAD-systems based on 3D solids, the geometric data of all common CAE (Computer-Aided Engineering) software, at least in mechanical engineering, are based on these solids. We use solid models, where the space filled by material is defined in a simple and easily useable way. Solid models allow for the development of automated meshers that transform solid volumes into finite elements. Even after some unacceptable initial trials, users are able to generate meshes of non-trivial geometries within minutes to hours, instead of days or weeks. Once meshing had no longer been the cost limiting factor of finite element studies, numerical simulation became a tool for smaller industries as well.
Due to the broad acceptance of CAD-systems based on 3D solids , the geometric data of all common CAE (Computer-Aided Engineering) software, at least in mechanical engineering, are based on these solids. We use solid models , where the space filled by material is defined in a simple and easily useable way. Solid models allow for the development of automated meshers that transform solid volumes into finite elements. Even after some unacceptable initial trials, users are able to generate meshes of non-trivial geometries within minutes to hours, instead of days or weeks. Once meshing had no longer been the cost limiting factor of finite element studies, numerical simulation became a tool for smaller industries as well.
In the early days of automated meshing development, there were discussions over the use of tetragonal (Fig. 4.1) or hexagonal based meshes. But, after a short period of time, it became evident, that there were and will always be many problems using automated meshers to generate hexagonal elements . So today nearly all automated 3D-meshing systems use tetragonal elements .

To illustrate the power and the pitfalls of Bionic Optimization, we will show some examples spanning classes of applications and employing various strategies. These applications cover a broad range of engineering tasks. Nevertheless, there is no guarantee that our experiences and our examples will be sufficient to deal with all questions and issues in a comprehensive way. As general rule it might be stated, that for each class of problems, novices should begin with a learning phase. So, in this introductory phase, we use simple and quick examples, e.g., using small FE-models, linear load cases, short time intervals and simple material models. Here beginners within the Bionic Optimization community can learn which parameter combinations to use. In Sect. 3.3 we discuss strategies for optimization study acceleration. Making use of these parameters as starting points is one way to set the specific ranges, e.g., number of parents and kids, crossing, mutation radii and, numbers of generations. On the other hand, these trial runs will doubtless indicate that Bionic Optimization needs large numbers of individual designs, and considerable time and computing power. We recommend investing enough time preparing each task in order to avoid the frustration should large jobs fail after long calculation times.

Current fields of interest
(2016)

If we review the research done in the field of optimization, the following topics appear to be the focus of current development:
– Optimization under uncertainties, taking into account the inevitable scatter of parts, external effects and internal properties. Reliability and robustness both have to be taken into account when running optimizations, so the name Robust Design Optimization (RDO) came into use.
– Multi-Objective Optimization (MOO) handles situations in which different participants in the development process are developing in different directions. Typically we think of commercial and engineering aspects, but other constellations have to be looked at as well, such as comfort and performance or price and consumption.
– Process development of the entire design process, including optimization from early stages, might help avoid inefficient efforts. Here the management of virtual development has to be re-designed to fit into a coherent scheme.
...
There are many other fields where interesting progress is being made. We limit our discussion to the first three questions.

Broad acceptance of finite-element-based analysis of structural problems and the increased availability of CAD-systems for structural tasks, which help to generate meshes of non-trivial geometries, have been setting a standard for the evaluation of designs in mechanical engineering in the last few decades. The development of automated or semi-automated optimizers, integrated into the Computer-Aided Engineering (CAE)-packages or working as outer loop machines, requiring the solver to do the analysis of the specific designs, has been accepted by most advanced users of the simulation community as well. The availability and inexpensive processing power of computers is increasing without any limitations foreseen in the coming years. There is little doubt that virtual product development will continue using the tools that have proved to be so successful and so easy to handle.

Today the optimization of metal forming processes is done using advanced simulation tools in a virtual process, e.g. FEM-studies. The modification of the free parameters represents the different variants to be analysed. So experienced engineers may derive useful proposals in an acceptable time if good initial proposals are available. As soon as the number of free parameters growths or the total process takes long times and uses different succeeding forming steps it might be quite difficult to find promising initial ideas. In metal forming another problem has to be considered. The optimization using a series of local improvements, often called a gradient approach may find a local optimum, but this could be far away from a satisfactory solution. Therefore non-deterministic approaches, e.g. Bionic Optimization have to be used. These approaches like Evolutionary Optimization or Particle Swarm Optimization are capable to cover a large range of high dimensional optimization spaces and discover many local optima. So the chance to include the global optimum increases when using such non-deterministic methods. Unfortunately these bionic methods require large numbers of studies of different variants of the process to be optimized. The number of studies tends to increase exponentially with the number of free parameters of the forming process. As the time for one single study might be not too small as well, the total time demand will be inacceptable, taking weeks to months even if high performance computing will be used. Therefore the optimization process needs to be accelerated. Among the many ideas to reduce the time and computer power requirement Meta- and Hybrid Optimization seem to produce the most efficient results. Hybrid Optimization often consists of global searches of promising regions within the parameter space. As soon as the studies indicate that there could be a local optimum, a deterministic study tries to identify this local region. If it shows better performance than other optima found until now, it is preserved for a more detailed analysis. If it performs worse than other optima the region is excluded from further search. Meta-Optimization is often understood as the derivation of Response Surfaces of the functions of free parameters. Once there are enough studies performed, the optimization is done using the Response Surfaces as representatives e.g. for the goal and the restrictions of the optimization problem. Having found regions where interesting solutions are to be expected, the studies available up to now are used to define the Response Surfaces. In many cases low degree polynomials are used, defining their coefficients by least square methods. Both proposals Hybrid Optimization and Meta-Optimization, sometimes used in combination often help to reduce the total optimization processes by large numbers of variants to be studied. In consequence they are highly recommended when dealing with time consuming optimization studies.

Bionic optimisation is one of the most popular and efficient applications of bionic engineering. As there are many different approaches and terms being used, we try to come up with a structuring of the strategies and compare the efficiency of the different methods. The methods mostly proposed in literature may be classified into evolutionary, particle swarm and artificial neural net optimisation. Some related classes have to be mentioned as the non-sexual fern optimisation and the response surfaces, which are close to the neuron nets. To come up with a measure of the efficiency that allows to take into account some of the published results the technical optimisation problems were derived from the ones given in literature. They deal with elastic studies of frame structures, as the computing time for each individual is very short. General proposals, which approach to use may not be given. It seems to be a good idea to learn about the applicability of the different methods at different problem classes and then do the optimisation according to these experiences. Furthermore in many cases there is some evidence that switching from one method to another improves the performance. Finally the identification of the exact position of the optimum by gradient methods is often more efficient than long random walks around local maxima.

To prevent high buildings in endangered zones suffering from seismic attack, TMD are applied successfully. In many applications the dampers are placed along the height of the edifice to reduce the damage during the earthquake. The dimensioning of TMD is a multidimensional optimisation problem with many local maxima. To find the absolute best or a very good design, advanced optimisation strategies have to be applied. Bionic optimization proposes different methods to deal with such tasks but requires many repeated studies of the buildings and dampers design. To improve the speed of the analysis, the authors propose a reduced model of the building including the dampers. A series of consecutive generations shows a growing capacity to reduce the impact of an earthquake on the building. The proposals found help to dimension the dampers. A detailed analysis of the building under earthquake loading may yield an efficient design.