20,226 research outputs found
On-line Search History-assisted Restart Strategy for Covariance Matrix Adaptation Evolution Strategy
Restart strategy helps the covariance matrix adaptation evolution strategy
(CMA-ES) to increase the probability of finding the global optimum in
optimization, while a single run CMA-ES is easy to be trapped in local optima.
In this paper, the continuous non-revisiting genetic algorithm (cNrGA) is used
to help CMA-ES to achieve multiple restarts from different sub-regions of the
search space. The CMA-ES with on-line search history-assisted restart strategy
(HR-CMA-ES) is proposed. The entire on-line search history of cNrGA is stored
in a binary space partitioning (BSP) tree, which is effective for performing
local search. The frequently sampled sub-region is reflected by a deep position
in the BSP tree. When leaf nodes are located deeper than a threshold, the
corresponding sub-region is considered a region of interest (ROI). In
HR-CMA-ES, cNrGA is responsible for global exploration and suggesting ROI for
CMA-ES to perform an exploitation within or around the ROI. CMA-ES restarts
independently in each suggested ROI. The non-revisiting mechanism of cNrGA
avoids to suggest the same ROI for a second time. Experimental results on the
CEC 2013 and 2017 benchmark suites show that HR-CMA-ES performs better than
both CMA-ES and cNrGA. A positive synergy is observed by the memetic
cooperation of the two algorithms.Comment: 8 pages, 9 figure
Efficient regularized isotonic regression with application to gene--gene interaction search
Isotonic regression is a nonparametric approach for fitting monotonic models
to data that has been widely studied from both theoretical and practical
perspectives. However, this approach encounters computational and statistical
overfitting issues in higher dimensions. To address both concerns, we present
an algorithm, which we term Isotonic Recursive Partitioning (IRP), for isotonic
regression based on recursively partitioning the covariate space through
solution of progressively smaller "best cut" subproblems. This creates a
regularized sequence of isotonic models of increasing model complexity that
converges to the global isotonic regression solution. The models along the
sequence are often more accurate than the unregularized isotonic regression
model because of the complexity control they offer. We quantify this complexity
control through estimation of degrees of freedom along the path. Success of the
regularized models in prediction and IRPs favorable computational properties
are demonstrated through a series of simulated and real data experiments. We
discuss application of IRP to the problem of searching for gene--gene
interactions and epistasis, and demonstrate it on data from genome-wide
association studies of three common diseases.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS504 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Recent Advances in Graph Partitioning
We survey recent trends in practical algorithms for balanced graph
partitioning together with applications and future research directions
Incorporating Road Networks into Territory Design
Given a set of basic areas, the territory design problem asks to create a
predefined number of territories, each containing at least one basic area, such
that an objective function is optimized. Desired properties of territories
often include a reasonable balance, compact form, contiguity and small average
journey times which are usually encoded in the objective function or formulated
as constraints. We address the territory design problem by developing graph
theoretic models that also consider the underlying road network. The derived
graph models enable us to tackle the territory design problem by modifying
graph partitioning algorithms and mixed integer programming formulations so
that the objective of the planning problem is taken into account. We test and
compare the algorithms on several real world instances
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