1,181 research outputs found
Fourier Analysis Meets Runtime Analysis: Precise Runtimes on Plateaus
We propose a new method based on discrete Fourier analysis to analyze the
time evolutionary algorithms spend on plateaus. This immediately gives a
concise proof of the classic estimate of the expected runtime of the
evolutionary algorithm on the Needle problem due to Garnier, Kallel, and
Schoenauer (1999).
We also use this method to analyze the runtime of the evolutionary
algorithm on a new benchmark consisting of plateaus of effective size
which have to be optimized sequentially in a LeadingOnes fashion.
Using our new method, we determine the precise expected runtime both for
static and fitness-dependent mutation rates. We also determine the
asymptotically optimal static and fitness-dependent mutation rates. For , the optimal static mutation rate is approximately . The optimal
fitness dependent mutation rate, when the first fitness-relevant bits have
been found, is asymptotically . These results, so far only proven for
the single-instance problem LeadingOnes, are thus true in a much broader
respect. We expect similar extensions to be true for other important results on
LeadingOnes. We are also optimistic that our Fourier analysis approach can be
applied to other plateau problems as well.Comment: 40 page
Elitism Levels Traverse Mechanism For The Derivation of Upper Bounds on Unimodal Functions
In this article we present an Elitism Levels Traverse Mechanism that we
designed to find bounds on population-based Evolutionary algorithms solving
unimodal functions. We prove its efficiency theoretically and test it on OneMax
function deriving bounds c{\mu}n log n - O({\mu} n). This analysis can be
generalized to any similar algorithm using variants of tournament selection and
genetic operators that flip or swap only 1 bit in each string.Comment: accepted to Congress on Evolutionary Computation (WCCI/CEC) 201
Simple Max-Min Ant Systems and the Optimization of Linear Pseudo-Boolean Functions
With this paper, we contribute to the understanding of ant colony
optimization (ACO) algorithms by formally analyzing their runtime behavior. We
study simple MAX-MIN ant systems on the class of linear pseudo-Boolean
functions defined on binary strings of length 'n'. Our investigations point out
how the progress according to function values is stored in pheromone. We
provide a general upper bound of O((n^3 \log n)/ \rho) for two ACO variants on
all linear functions, where (\rho) determines the pheromone update strength.
Furthermore, we show improved bounds for two well-known linear pseudo-Boolean
functions called OneMax and BinVal and give additional insights using an
experimental study.Comment: 19 pages, 2 figure
DROP: Dimensionality Reduction Optimization for Time Series
Dimensionality reduction is a critical step in scaling machine learning
pipelines. Principal component analysis (PCA) is a standard tool for
dimensionality reduction, but performing PCA over a full dataset can be
prohibitively expensive. As a result, theoretical work has studied the
effectiveness of iterative, stochastic PCA methods that operate over data
samples. However, termination conditions for stochastic PCA either execute for
a predetermined number of iterations, or until convergence of the solution,
frequently sampling too many or too few datapoints for end-to-end runtime
improvements. We show how accounting for downstream analytics operations during
DR via PCA allows stochastic methods to efficiently terminate after operating
over small (e.g., 1%) subsamples of input data, reducing whole workload
runtime. Leveraging this, we propose DROP, a DR optimizer that enables speedups
of up to 5x over Singular-Value-Decomposition-based PCA techniques, and exceeds
conventional approaches like FFT and PAA by up to 16x in end-to-end workloads
Behavior of heuristics and state space structure near SAT/UNSAT transition
We study the behavior of ASAT, a heuristic for solving satisfiability
problems by stochastic local search near the SAT/UNSAT transition. The
heuristic is focused, i.e. only variables in unsatisfied clauses are updated in
each step, and is significantly simpler, while similar to, walksat or Focused
Metropolis Search. We show that ASAT solves instances as large as one million
variables in linear time, on average, up to 4.21 clauses per variable for
random 3SAT. For K higher than 3, ASAT appears to solve instances at the ``FRSB
threshold'' in linear time, up to K=7.Comment: 12 pages, 6 figures, longer version available as MSc thesis of first
author at http://biophys.physics.kth.se/docs/ardelius_thesis.pd
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