Evolutionary Global Optimization

Finding global optimal solutions to problems in science, technology, and economics is becoming of increasing importance. However, certain optimization problems from fields as diverse as structure prediction in chemistry and material science, machine learning, data-driven portfolio management are often highly multimodal. That is, these problems comprise a vast number of local optimal solutions. Yet, one is interested in searching for the best among these local optima, i.e. the global optimum. For such problems, classical numerical optimization algorithms are not well-suited since these strategies yield usually only local optima. Evolution Strategies - algorithms gleaned from nature - are a promising alternative for solving such challenging problems. However, unlike the practical success in applying such algorithms to real-world problems, the theoretical understanding of the working principles of such evolutionary approaches is still in its infancy. It is a first goal of this project to push forward the theoretical understanding of these algorithms in highly multimodal real-valued fitness landscapes. This will pave the way for a principled design methodology for evolutionary global optimization algorithms. Furthermore, hybrid techniques will be developed to connect classical numerical optimization with evolutionary computation techniques. The findings of these investigations will be used to tackle selected real-world problems taken from the field of structure prediction in chemistry and applications in machine learning.

Finding global optimal solutions to problems in science, technology, and economics is becoming of increasing importance. However, certain optimization problems from fields as diverse as structure prediction in chemistry and material science, machine learning, data-driven portfolio management are often highly multimodal. That is, these problems comprise a vast number of local optimal solutions. Yet, one is interested in searching for the best among these local optima, i.e. the global optimum. For such problems, classical numerical optimization algorithms are not well-suited since these strategies yield usually only local optima. Evolution Strategies - population based algorithms gleaned from Darwinian evolution - are a promising alternative for solving such challenging problems. However, unlike the practical success in applying such algorithms to real-world problems, the theoretical understanding of the working principles of such evolutionary methods in highly multimodal landscapes was in the dark for a long time. In this project we were able to push forward a theory that explains how and why these algorithms perform so well, how to choose the populations in these algorithms in highly multimodal real-valued fitness landscapes, how to perform restarts, and what are the conditions for a global search. These results pave the way for improved and more efficient Evolution Strategies.