A natural approach to multilevel optimization in engineering design
In many design optimization problems, the designer is faced with the dilemma of how to simulate the problem at hand using a number of different models. Some models maybe quite elaborate in their representation of the problem and hence tend to be computationally expensive. Other models may be far less elaborate and hence computationally cheaper. The computationally chap models tend to be less accurate than the expensive ones. The designer uses his/her experience, and understanding of the problem domain to switch between different models. S/He goes through a few iterations till a satisfactory design is found. Designs created in such a fashion are not necessarily optimal and they could be improved upon, given more design iterations and an adequate search technique. It is hence important to develop techniques that make maximal use of the many models available within a limited computational budget. Conducting search on such an environment where there are multiple models for evaluation fitness is what is meant by the term Multilevel optimization (MLO). Suitable methods for conduction MLO maybe sought using algorithms and techniques gleaned from natural process, mainly Evolutionary Algorithms and Artificial Neural Networks. In this thesis, an exposition is made of the issues to be considered when carrying out multilevel optimization. This is followed by a comparison of how various optimization algorithms perform in a multilevel problem using three simple model selection strategies. Having established that evolutionary inspired search methods work well in such an environment a topological mapping based model selection approach is then presented. Finally, Gaussian processes based metamodeling and model fusion approaches are explored. Results suggest that there are significant gains to be made in the synthesis between evolutionary and neural computation techniques for MLO.