493,536 research outputs found
Renormalization for Discrete Optimization
The renormalization group has proven to be a very powerful tool in physics
for treating systems with many length scales. Here we show how it can be
adapted to provide a new class of algorithms for discrete optimization. The
heart of our method uses renormalization and recursion, and these processes are
embedded in a genetic algorithm. The system is self-consistently optimized on
all scales, leading to a high probability of finding the ground state
configuration. To demonstrate the generality of such an approach, we perform
tests on traveling salesman and spin glass problems. The results show that our
``genetic renormalization algorithm'' is extremely powerful.Comment: 4 pages, no figur
Energy Minimization of Discrete Protein Titration State Models Using Graph Theory
There are several applications in computational biophysics which require the
optimization of discrete interacting states; e.g., amino acid titration states,
ligand oxidation states, or discrete rotamer angles. Such optimization can be
very time-consuming as it scales exponentially in the number of sites to be
optimized. In this paper, we describe a new polynomial-time algorithm for
optimization of discrete states in macromolecular systems. This algorithm was
adapted from image processing and uses techniques from discrete mathematics and
graph theory to restate the optimization problem in terms of "maximum
flow-minimum cut" graph analysis. The interaction energy graph, a graph in
which vertices (amino acids) and edges (interactions) are weighted with their
respective energies, is transformed into a flow network in which the value of
the minimum cut in the network equals the minimum free energy of the protein,
and the cut itself encodes the state that achieves the minimum free energy.
Because of its deterministic nature and polynomial-time performance, this
algorithm has the potential to allow for the ionization state of larger
proteins to be discovered
Towards a Theory-Guided Benchmarking Suite for Discrete Black-Box Optimization Heuristics: Profiling EA Variants on OneMax and LeadingOnes
Theoretical and empirical research on evolutionary computation methods
complement each other by providing two fundamentally different approaches
towards a better understanding of black-box optimization heuristics. In
discrete optimization, both streams developed rather independently of each
other, but we observe today an increasing interest in reconciling these two
sub-branches. In continuous optimization, the COCO (COmparing Continuous
Optimisers) benchmarking suite has established itself as an important platform
that theoreticians and practitioners use to exchange research ideas and
questions. No widely accepted equivalent exists in the research domain of
discrete black-box optimization.
Marking an important step towards filling this gap, we adjust the COCO
software to pseudo-Boolean optimization problems, and obtain from this a
benchmarking environment that allows a fine-grained empirical analysis of
discrete black-box heuristics. In this documentation we demonstrate how this
test bed can be used to profile the performance of evolutionary algorithms.
More concretely, we study the optimization behavior of several EA
variants on the two benchmark problems OneMax and LeadingOnes. This comparison
motivates a refined analysis for the optimization time of the EA
on LeadingOnes
Nonconcave Robust Optimization with Discrete Strategies under Knightian Uncertainty
We study robust stochastic optimization problems in the quasi-sure setting in
discrete-time. The strategies in the multi-period-case are restricted to those
taking values in a discrete set. The optimization problems under consideration
are not concave. We provide conditions under which a maximizer exists. The
class of problems covered by our robust optimization problem includes optimal
stopping and semi-static trading under Knightian uncertainty.Comment: arXiv admin note: text overlap with arXiv:1610.0923
On a novel approach for optimizing composite materials panel using surrogate models
This paper describes an optimization procedure to design thermoplastic composite panels under axial compressive load conditions. Minimum weight is the goal. The panel design is subject to buckling constraints. The presence of the bending-twisting coupling and of particular boundary conditions does not allow an analytical solution for the critical buckling load. Surrogate models are used to approximate the buckling response of the plate in a fast and reliable way. Therefore, two surrogate models are compared to study their effectiveness in composite optimization. The first one is a linear approximation based on the buckling constitutive equation. The second consists in the application of the Kriging surrogate. Constraints given from practical blending rules are also introduced in the optimization. Discrete values of ply thicknesses is a requirement. An ad-hoc discrete optimization strategy is developed, which enables to handle discrete variables
Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows
This paper concerns an extension of discrete gradient methods to
finite-dimensional Riemannian manifolds termed discrete Riemannian gradients,
and their application to dissipative ordinary differential equations. This
includes Riemannian gradient flow systems which occur naturally in optimization
problems. The Itoh--Abe discrete gradient is formulated and applied to gradient
systems, yielding a derivative-free optimization algorithm. The algorithm is
tested on two eigenvalue problems and two problems from manifold valued
imaging: InSAR denoising and DTI denoising.Comment: Post-revision version. To appear in SIAM Journal on Scientific
Computin
The Discrete Dantzig Selector: Estimating Sparse Linear Models via Mixed Integer Linear Optimization
We propose a novel high-dimensional linear regression estimator: the Discrete
Dantzig Selector, which minimizes the number of nonzero regression coefficients
subject to a budget on the maximal absolute correlation between the features
and residuals. Motivated by the significant advances in integer optimization
over the past 10-15 years, we present a Mixed Integer Linear Optimization
(MILO) approach to obtain certifiably optimal global solutions to this
nonconvex optimization problem. The current state of algorithmics in integer
optimization makes our proposal substantially more computationally attractive
than the least squares subset selection framework based on integer quadratic
optimization, recently proposed in [8] and the continuous nonconvex quadratic
optimization framework of [33]. We propose new discrete first-order methods,
which when paired with state-of-the-art MILO solvers, lead to good solutions
for the Discrete Dantzig Selector problem for a given computational budget. We
illustrate that our integrated approach provides globally optimal solutions in
significantly shorter computation times, when compared to off-the-shelf MILO
solvers. We demonstrate both theoretically and empirically that in a wide range
of regimes the statistical properties of the Discrete Dantzig Selector are
superior to those of popular -based approaches. We illustrate that
our approach can handle problem instances with p = 10,000 features with
certifiable optimality making it a highly scalable combinatorial variable
selection approach in sparse linear modeling
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