Black-box complexity: from complexity theory to playing mastermind

 Together with Frank Neumann and Ingo Wegener, he founded the theory track at GECCO and served as its co-chair 2007-2009.  He is a member of the editorial boards of Evolutionary Computation and Information Processing Letters.  His research area includes theoretical aspects of randomized search heuristics, in particular, run-time analysis and complexity theory.  This is a tutorial on black-box complexity. This is currently one of the hottest topics in the theory of randomized search heuristics.  I shall try my best to..  tell you on an elementary level what black-box complexity is and how it shapes our understanding of randomized search heuristics  give an in-depth coverage of two topics that received much attention in the last few years  stronger upper bounds and the connection to guessing games  alternative black-box models  sketch several open problems  Don't hesitate to ask questions whenever they come up! Agenda  Part 1: Black-box complexity: A complexity theory for randomized search heuristics (RSH)  Introduction/definition  Lower bounds for all RSH (example: needle functions)  Thorn in the flesh: Are there better RSH out there? (example onemax)  Different black-box models – what is the right difficulty measure?  Part 2: Tools and techniques (in the language of guessing games)  From black-box to guessing games  A general lower bound  How to play Mastermind  A new game  Summary, open problems Copyright is held by the author/owner(s).  Why a complexity theory for RSH?  Understand problem difficulty!  How?  Black-box complexity!  What can we do with that?  General lower bounds, thorn in the flesh  Different notions of black-box complexity Why a Complexity Theory for RSH?  Understand problem difficulty!  Randomized search heuristics (RSH) like evolutionary algorithms, genetic algorithms, ant colony optimization, simulated annealing, … are very successful for a variety of problems.  Little general advice which problems are suitable for such general methods  Solution: Complexity theory for RSH  Take a similar successful route as classical algorithmics!  Algorithmics: Design good algorithms and analyze their performance  Complexity theory: Show that certain things are just not possible  The interplay between the two areas proved to be very fruitful for the research on classic algorithms Algorithms vs. Complexity Theory for RSH – An Example  Bottom line: Spanning tree is easy for RSH, the Needle problem …