5,422 research outputs found
A Hybrid MILP and IPM for Dynamic Economic Dispatch with Valve Point Effect
Dynamic economic dispatch with valve-point effect (DED-VPE) is a non-convex
and non-differentiable optimization problem which is difficult to solve
efficiently. In this paper, a hybrid mixed integer linear programming (MILP)
and interior point method (IPM), denoted by MILP-IPM, is proposed to solve such
a DED-VPE problem, where the complicated transmission loss is also included.
Due to the non-differentiable characteristic of DED-VPE, the classical
derivative-based optimization methods can not be used any more. With the help
of model reformulation, a differentiable non-linear programming (NLP)
formulation which can be directly solved by IPM is derived. However, if the
DED-VPE is solved by IPM in a single step, the optimization will easily trap in
a poor local optima due to its non-convex and multiple local minima
characteristics. To exploit a better solution, an MILP method is required to
solve the DED-VPE without transmission loss, yielding a good initial point for
IPM to improve the quality of the solution. Simulation results demonstrate the
validity and effectiveness of the proposed MILP-IPM in solving DED-VPE
Efficient Evolutionary Algorithm for Single-Objective Bilevel Optimization
Bilevel optimization problems are a class of challenging optimization
problems, which contain two levels of optimization tasks. In these problems,
the optimal solutions to the lower level problem become possible feasible
candidates to the upper level problem. Such a requirement makes the
optimization problem difficult to solve, and has kept the researchers busy
towards devising methodologies, which can efficiently handle the problem.
Despite the efforts, there hardly exists any effective methodology, which is
capable of handling a complex bilevel problem. In this paper, we introduce
bilevel evolutionary algorithm based on quadratic approximations (BLEAQ) of
optimal lower level variables with respect to the upper level variables. The
approach is capable of handling bilevel problems with different kinds of
complexities in relatively smaller number of function evaluations. Ideas from
classical optimization have been hybridized with evolutionary methods to
generate an efficient optimization algorithm for generic bilevel problems. The
efficacy of the algorithm has been shown on two sets of test problems. The
first set is a recently proposed SMD test set, which contains problems with
controllable complexities, and the second set contains standard test problems
collected from the literature. The proposed method has been evaluated against
two benchmarks, and the performance gain is observed to be significant
Neural Network Architecture Search with Differentiable Cartesian Genetic Programming for Regression
The ability to design complex neural network architectures which enable
effective training by stochastic gradient descent has been the key for many
achievements in the field of deep learning. However, developing such
architectures remains a challenging and resourceintensive process full of
trial-and-error iterations. All in all, the relation between the network
topology and its ability to model the data remains poorly understood. We
propose to encode neural networks with a differentiable variant of Cartesian
Genetic Programming (dCGPANN) and present a memetic algorithm for architecture
design: local searches with gradient descent learn the network parameters while
evolutionary operators act on the dCGPANN genes shaping the network
architecture towards faster learning. Studying a particular instance of such a
learning scheme, we are able to improve the starting feed forward topology by
learning how to rewire and prune links, adapt activation functions and
introduce skip connections for chosen regression tasks. The evolved network
architectures require less space for network parameters and reach, given the
same amount of time, a significantly lower error on average.Comment: a short version of this was accepted as poster paper at GECCO 201
A Sequential Quadratic Programming Method for Constrained Multi-objective Optimization Problems
In this article, a globally convergent sequential quadratic programming (SQP)
method is developed for multi-objective optimization problems with inequality
type constraints. A feasible descent direction is obtained using a linear
approximation of all objective functions as well as constraint functions. The
sub-problem at every iteration of the sequence has feasible solution. A
non-differentiable penalty function is used to deal with constraint violations.
A descent sequence is generated which converges to a critical point under the
Mangasarian-Fromovitz constraint qualification along with some other mild
assumptions. The method is compared with a selection of existing methods on a
suitable set of test problems.Comment: 19 pages, 11 figure
Embryo staging with weakly-supervised region selection and dynamically-decoded predictions
To optimize clinical outcomes, fertility clinics must strategically select
which embryos to transfer. Common selection heuristics are formulas expressed
in terms of the durations required to reach various developmental milestones,
quantities historically annotated manually by experienced embryologists based
on time-lapse EmbryoScope videos. We propose a new method for automatic embryo
staging that exploits several sources of structure in this time-lapse data.
First, noting that in each image the embryo occupies a small subregion, we
jointly train a region proposal network with the downstream classifier to
isolate the embryo. Notably, because we lack ground-truth bounding boxes, our
we weakly supervise the region proposal network optimizing its parameters via
reinforcement learning to improve the downstream classifier's loss. Moreover,
noting that embryos reaching the blastocyst stage progress monotonically
through earlier stages, we develop a dynamic-programming-based decoder that
post-processes our predictions to select the most likely monotonic sequence of
developmental stages. Our methods outperform vanilla residual networks and
rival the best numbers in contemporary papers, as measured by both per-frame
accuracy and transition prediction error, despite operating on smaller data
than many
Variational Optimization
We discuss a general technique that can be used to form a differentiable
bound on the optima of non-differentiable or discrete objective functions. We
form a unified description of these methods and consider under which
circumstances the bound is concave. In particular we consider two concrete
applications of the method, namely sparse learning and support vector
classification
Positional Cartesian Genetic Programming
Cartesian Genetic Programming (CGP) has many modifications across a variety
of implementations, such as recursive connections and node weights. Alternative
genetic operators have also been proposed for CGP, but have not been fully
studied. In this work, we present a new form of genetic programming based on a
floating point representation. In this new form of CGP, called Positional CGP,
node positions are evolved. This allows for the evaluation of many different
genetic operators while allowing for previous CGP improvements like recurrency.
Using nine benchmark problems from three different classes, we evaluate the
optimal parameters for CGP and PCGP, including novel genetic operators
Genetic algorithms with DNN-based trainable crossover as an example of partial specialization of general search
Universal induction relies on some general search procedure that is doomed to
be inefficient. One possibility to achieve both generality and efficiency is to
specialize this procedure w.r.t. any given narrow task. However, complete
specialization that implies direct mapping from the task parameters to
solutions (discriminative models) without search is not always possible. In
this paper, partial specialization of general search is considered in the form
of genetic algorithms (GAs) with a specialized crossover operator. We perform a
feasibility study of this idea implementing such an operator in the form of a
deep feedforward neural network. GAs with trainable crossover operators are
compared with the result of complete specialization, which is also represented
as a deep neural network. Experimental results show that specialized GAs can be
more efficient than both general GAs and discriminative models.Comment: AGI 2017 procedding, The final publication is available at
link.springer.co
Estimating the Region of Attraction Using Polynomial Optimization: a Converse Lyapunov Result
In this paper, we propose an iterative method for using SOS programming to
estimate the region of attraction of a polynomial vector field, the conjectured
convergence of which necessitates the existence of polynomial Lyapunov
functions whose sublevel sets approximate the true region of attraction
arbitrarily well. The main technical result of the paper is the proof of
existence of such a Lyapunov function. Specifically, we use the Hausdorff
distance metric to analyze convergence and in the main theorem demonstrate that
the existence of an -times continuously differentiable maximal Lyapunov
function implies that for any , there exists a polynomial Lyapunov
function and associated sub-level set which together prove stability of a set
which is within Hausdorff distance of the true region of attraction.
The proposed iterative method and probably convergence is illustrated with a
numerical example
Deep Learning: Our Miraculous Year 1990-1991
In 2020, we will celebrate that many of the basic ideas behind the deep
learning revolution were published three decades ago within fewer than 12
months in our "Annus Mirabilis" or "Miraculous Year" 1990-1991 at TU Munich.
Back then, few people were interested, but a quarter century later, neural
networks based on these ideas were on over 3 billion devices such as
smartphones, and used many billions of times per day, consuming a significant
fraction of the world's compute.Comment: 37 pages, 188 references, based on work of 4 Oct 201
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