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First Steps Towards a Runtime Analysis When Starting with a Good Solution
International audienc
First Steps Towards a Runtime Comparison of Natural and Artificial Evolution
Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired
by natural evolution. In recent years the field of evolutionary computation has
developed a rigorous analytical theory to analyse their runtime on many
illustrative problems. Here we apply this theory to a simple model of natural
evolution. In the Strong Selection Weak Mutation (SSWM) evolutionary regime the
time between occurrence of new mutations is much longer than the time it takes
for a new beneficial mutation to take over the population. In this situation,
the population only contains copies of one genotype and evolution can be
modelled as a (1+1)-type process where the probability of accepting a new
genotype (improvements or worsenings) depends on the change in fitness.
We present an initial runtime analysis of SSWM, quantifying its performance
for various parameters and investigating differences to the (1+1)EA. We show
that SSWM can have a moderate advantage over the (1+1)EA at crossing fitness
valleys and study an example where SSWM outperforms the (1+1)EA by taking
advantage of information on the fitness gradient
Extremal Optimization for Graph Partitioning
Extremal optimization is a new general-purpose method for approximating
solutions to hard optimization problems. We study the method in detail by way
of the NP-hard graph partitioning problem. We discuss the scaling behavior of
extremal optimization, focusing on the convergence of the average run as a
function of runtime and system size. The method has a single free parameter,
which we determine numerically and justify using a simple argument. Our
numerical results demonstrate that on random graphs, extremal optimization
maintains consistent accuracy for increasing system sizes, with an
approximation error decreasing over runtime roughly as a power law t^(-0.4). On
geometrically structured graphs, the scaling of results from the average run
suggests that these are far from optimal, with large fluctuations between
individual trials. But when only the best runs are considered, results
consistent with theoretical arguments are recovered.Comment: 34 pages, RevTex4, 1 table and 20 ps-figures included, related papers
available at http://www.physics.emory.edu/faculty/boettcher
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
An Autonomous Engine for Services Configuration and Deployment.
The runtime management of the infrastructure providing service-based systems is a complex task, up to the point where manual operation struggles to be cost effective. As the functionality is provided by a set of dynamically composed distributed services, in order to achieve a management objective multiple operations have to be applied over the distributed elements of the managed infrastructure. Moreover, the manager must cope with the highly heterogeneous characteristics and management interfaces of the runtime resources. With this in mind, this paper proposes to support the configuration and deployment of services with an automated closed control loop. The automation is enabled by the definition of a generic information model, which captures all the information relevant to the management of the services with the same abstractions, describing the runtime elements, service dependencies, and business objectives. On top of that, a technique based on satisfiability is described which automatically diagnoses the state of the managed environment and obtains the required changes for correcting it (e.g., installation, service binding, update, or configuration). The results from a set of case studies extracted from the banking domain are provided to validate the feasibility of this propos
Design and Analysis of an Estimation of Distribution Approximation Algorithm for Single Machine Scheduling in Uncertain Environments
In the current work we introduce a novel estimation of distribution algorithm
to tackle a hard combinatorial optimization problem, namely the single-machine
scheduling problem, with uncertain delivery times. The majority of the existing
research coping with optimization problems in uncertain environment aims at
finding a single sufficiently robust solution so that random noise and
unpredictable circumstances would have the least possible detrimental effect on
the quality of the solution. The measures of robustness are usually based on
various kinds of empirically designed averaging techniques. In contrast to the
previous work, our algorithm aims at finding a collection of robust schedules
that allow for a more informative decision making. The notion of robustness is
measured quantitatively in terms of the classical mathematical notion of a norm
on a vector space. We provide a theoretical insight into the relationship
between the properties of the probability distribution over the uncertain
delivery times and the robustness quality of the schedules produced by the
algorithm after a polynomial runtime in terms of approximation ratios
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