3. Generate a new set of designs (new generation) by performing statistical evaluations (selection, cross- over, mutation)
4. Repeat this procedure for the user-defined number of generations
The optimization cycle terminates when the stopping crite- rion, i.e. the total number of generations, is reached. The flow chart of the above described optimization procedure is depicted in Figure 1.
Multi Objective Optimization Problem (MOOP)
Most engineering design activities require a solution of multi-objective and multi-disciplinary optimization prob- lems that in many cases deal with conflicting objectives. When considering these objectives, a number of alternative trade-off solutions, referred to as Pareto-optimal solutions, have to be evaluated. None of these Pareto designs can be said to be better than the other without any additional infor- mation about the problem under consideration. In order to define the Pareto set, one has to apply the concept of domi- nation, which allows comparing solutions with multiple ob- jectives. Most multi-objective optimization algorithms use the domination concept to search for non-dominated solu- tions, i.e. the ones that constitute the Pareto-optimal set,18 which is schematically shown in Figure 2. Since the Pareto
set includes numerous designs, from an engineering view- point it is more practical to select only a few or even one solution among them. The selection of the “most optimal” design depends on the user’s preference of importance of the different design criteria (e.g. porosity-free casting is more important than having the highest casting yield).
Genetic algorithms work with a set of solutions (popula- tion) instead of a single point, as in gradient based (clas- sical) methods. This gives an opportunity to attack a com- plex problem (discontinuous, noisy, multi-modal, etc.) in different directions, allowing the algorithm to explore as well as exploit the search space. This capability gives a more robust search strategy compared to traditional al- gorithms. Since genetic algorithms do not need any gra- dient information, they are suitable for black-box (e.g. commercial software) optimization applications. More- over, compared with classical optimization strategies based on gradient methods, genetic algorithms can ef- fectively utilize distributed computing facilities because all individuals (designs) can be computed independently. Besides that, they are typically able to provide a larger spectrum of Pareto-optimal designs without requiring ad- ditional problem definition. The availability of trade-off solutions, representing varying preference levels between chosen objectives, makes it easier for a user to choose a particular solution for subsequent implementation.17-20
Figure 1. Flow chart of the optimization process. International Journal of Metalcasting/Fall 10
Figure 2. Design and objective space related to a multi- objective optimization problem, taken from reference.17
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