Project Title:

"Evolutionary Global Optimization in Highly Multimodal Landscapes"

FWF Project Number: P 33702

Project Summary:

Wider research context/theoretical framework

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.

Hypotheses/research questions/objectives

Evolution Strategies - algorithms gleaned from nature - are a promising alternative for solving such challenging problems. However, unlike the promising successes 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 comes as a surprise that rather simple Evolution Strategies are able to locate the global optima of objective functions with exponentially (with respect to search space dimensionality) many local optima. It is a first goal of this project to push forward the theoretical understanding of these algorithms in highly multimodal real-valued optimization landscapes. Important research questions are:

* How do these algorithms explore the search space?

* How do these algorithms locate the global optimum?

* How does the population size influence the convergence behavior?

* How does the structure of the optimization landscape influence the search behavior of the Evolution Strategy?

Finding answers to these questions will pave the way for a principled design of Evolution Strategies and the hybridization with classical non-linear optimization techniques. Being based on the expected findings, special purpose algorithms will be developed for selected real-world optimization problems.


Progress rate theory and - if suitable - information geometry will be used in conjunction with landscape analyses to analyze, understand, and predict the dynamics of the underlying evolutionary processes. The investigations will be done both on the theoretical and the empirical level. New algorithms will be designed and empirically evaluated on synthetic test problems and also on real-world optimization problems.

Level of originality/innovation

The envisioned theory approach will be the first to tackle problems with objective functions comprising a vast number of local optima. The findings will pave the way for the design of improved Evolution Strategies and its hybridization with classical non-linear optimization techniques for notoriously difficult nonlinear optimization problems.

last change: 13.11.2020