Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, December 05, 2023, 12:15 pm

Duration: 30 minutes

Location: OAT X (floor 19), open area

Speaker: Johannes Lengler

Population Diversity in Neutral Fitness Landscape

One one the major advantages of population-based optimization heuristics like genetic algorithms is that we can recombine two or more solutions into a new. This operation is called crossover. In practice, crossover is known to be extremely helpful, and we would also like to understand how much it helps in theoretical benchmarks. However, there is one obstacle: The effectiveness of crossover depends on the population diversity (e.g., measured by average Hamming distance of the solutions), so we need to understand how the diversity of a population evolves over time.

We answer this question under a seemingly very strong assumption: for a flat objective function, i.e., in absence of fitness signals. We show that in this case, surprisingly, the details of algorithm have almost no influence on the diversity. Specifically, for the (\mu+1) Genetic Algorithm we show that diversity approaches an equilibrium which (almost) does not depend on the used mutation or crossover operators. The equilibrium point increases linearly with the population size.

Although flat objective functions are seemingly uninteresting, the result turned out to be surprisingly useful. I will give one application: for LeadingOnes, a standard hillclimbing benchmark, the runtime of the (\mu+1) GA is reduced by a constant factor if \mu = \Omega(\sqrt n), because in this range the diversity is large enough to speed up optimization, but not for smaller values of \mu.

Upcoming talks     |     All previous talks     |     Talks by speaker     |     Upcoming talks in iCal format (beta version!)

Previous talks by year:   2023  2022  2021  2020  2019  2018  2017  2016  2015  2014  2013  2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  1998  1997  1996  

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M   |   admin login