"Evolutionary Global Optimization in Highly Multimodal Landscapes"
FWF Project Number: P 33702
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.
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:
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.
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.