27 research outputs found
Self-adaptation of Mutation Rates in Non-elitist Populations
The runtime of evolutionary algorithms (EAs) depends critically on their
parameter settings, which are often problem-specific. Automated schemes for
parameter tuning have been developed to alleviate the high costs of manual
parameter tuning. Experimental results indicate that self-adaptation, where
parameter settings are encoded in the genomes of individuals, can be effective
in continuous optimisation. However, results in discrete optimisation have been
less conclusive. Furthermore, a rigorous runtime analysis that explains how
self-adaptation can lead to asymptotic speedups has been missing. This paper
provides the first such analysis for discrete, population-based EAs. We apply
level-based analysis to show how a self-adaptive EA is capable of fine-tuning
its mutation rate, leading to exponential speedups over EAs using fixed
mutation rates.Comment: To appear in the Proceedings of the 14th International Conference on
Parallel Problem Solving from Nature (PPSN
On Non-Elitist Evolutionary Algorithms Optimizing Fitness Functions with a Plateau
We consider the expected runtime of non-elitist evolutionary algorithms
(EAs), when they are applied to a family of fitness functions with a plateau of
second-best fitness in a Hamming ball of radius r around a unique global
optimum. On one hand, using the level-based theorems, we obtain polynomial
upper bounds on the expected runtime for some modes of non-elitist EA based on
unbiased mutation and the bitwise mutation in particular. On the other hand, we
show that the EA with fitness proportionate selection is inefficient if the
bitwise mutation is used with the standard settings of mutation probability.Comment: 14 pages, accepted for proceedings of Mathematical Optimization
Theory and Operations Research (MOTOR 2020). arXiv admin note: text overlap
with arXiv:1908.0868
Fast Mutation in Crossover-based Algorithms
The heavy-tailed mutation operator proposed in Doerr, Le, Makhmara, and
Nguyen (GECCO 2017), called \emph{fast mutation} to agree with the previously
used language, so far was proven to be advantageous only in mutation-based
algorithms. There, it can relieve the algorithm designer from finding the
optimal mutation rate and nevertheless obtain a performance close to the one
that the optimal mutation rate gives.
In this first runtime analysis of a crossover-based algorithm using a
heavy-tailed choice of the mutation rate, we show an even stronger impact. For
the genetic algorithm optimizing the OneMax benchmark
function, we show that with a heavy-tailed mutation rate a linear runtime can
be achieved. This is asymptotically faster than what can be obtained with any
static mutation rate, and is asymptotically equivalent to the runtime of the
self-adjusting version of the parameters choice of the
genetic algorithm. This result is complemented by an empirical study which
shows the effectiveness of the fast mutation also on random satisfiable
Max-3SAT instances.Comment: This is a version of the same paper presented at GECCO 2020 completed
with the proofs which were missing because of the page limi
Self-adaptation of mutation rates in non-elitist populations
The runtime of evolutionary algorithms (EAs) depends critically on their parameter settings, which are often problem-specific. Automated schemes for parameter tuning have been developed to alleviate the high costs of manual parameter tuning. Experimental results indicate that self-adaptation, where parameter settings are encoded in the genomes of individuals, can be effective in continuous optimisation. However, results in discrete optimisation have been less conclusive. Furthermore, a rigorous runtime analysis that explains how self adaptation can lead to asymptotic speedups has been missing. This paper provides the first such analysis for discrete, population-based EAs. We apply level-based analysis to show how a self-adaptive EA is capable of fine-tuning its mutation rate, leading to exponential speedups over EAs using fixed mutation rates
A Self-adaptive Coevolutionary Algorithm
Coevolutionary algorithms are helpful computational abstractions of adversarial behavior and they demonstrate multiple ways that populations of competing adversaries influence one another. We introduce the ability for each competitor's mutation rate to evolve through self-adaptation. Because dynamic environments are frequently addressed with self-adaptation, we set up dynamic problem environments to investigate the impact of this ability. For a simple bilinear problem, a sensitivity analysis of the adaptive method's parameters reveals that it is robust over a range of multiplicative rate factors, when the rate is changed up or down with equal probability. An empirical study determines that each population's mutation rates converge to values close to the error threshold. Mutation rate dynamics are complex when both populations adapt their rates. Large scale empirical self-adaptation results reveal that both reasonable solutions and rates can be found. This addresses the challenge of selecting ideal static mutation rates in coevolutionary algorithms. The algorithm's payoffs are also robust. They are rarely poor and frequently they are as high as the payoff of the static rate to which they converge. On rare runs, they are higher
Analysing Equilibrium States for Population Diversity
Population diversity is crucial in evolutionary algorithms as it helps with
global exploration and facilitates the use of crossover. Despite many runtime
analyses showing advantages of population diversity, we have no clear picture
of how diversity evolves over time. We study how population diversity of
algorithms, measured by the sum of pairwise Hamming distances,
evolves in a fitness-neutral environment. We give an exact formula for the
drift of population diversity and show that it is driven towards an equilibrium
state. Moreover, we bound the expected time for getting close to the
equilibrium state. We find that these dynamics, including the location of the
equilibrium, are unaffected by surprisingly many algorithmic choices. All
unbiased mutation operators with the same expected number of bit flips have the
same effect on the expected diversity. Many crossover operators have no effect
at all, including all binary unbiased, respectful operators. We review
crossover operators from the literature and identify crossovers that are
neutral towards the evolution of diversity and crossovers that are not.Comment: To appear at GECCO 202