An Adaptive Elastic Net Method for Edge Linking of Images

2015 ◽  
Vol 7 (2) ◽  
pp. 7-19
Author(s):  
Junyan Yi ◽  
Gang Yang ◽  
Xiaoxuan Ma ◽  
Xiaoyun Shen
Keyword(s):  
Optimization Problem ◽  
Dynamic Parameter ◽  
Elastic Net ◽  
Stochastic Noise ◽  
Optimal Solutions ◽  
Local Minima ◽  
Constrained Optimization Problem ◽  
Edge Linking ◽  
Net Method ◽  
Adaptive Elastic Net

In this paper, the authors propose an adaptive Elastic Net method for edge linking of images. Edge linking is a fundamental computer-vision task, which is a constrained optimization problem. In the proposed method, an adaptive dynamic parameter strategy and a stochastic noise strategy are introduced into the Elastic Net, which enables the network to have superior ability for escaping from local minima and converge sooner to optimal or near-optimal solutions. Simulations confirm that the proposed method could produce more meaningful contours than the original Elastic Net in shorter time.

scholarly journals An Adaptive Elastic Net Method for Edge Linking of Images

2016 ◽  
pp. 921-930
Author(s):  
Junyan Yi ◽  
Gang Yang ◽  
Xiaoxuan Ma ◽  
Xiaoyun Shen
Keyword(s):  
Computer Vision ◽  
Dynamic Parameter ◽  
Elastic Net ◽  
Stochastic Noise ◽  
Optimal Solutions ◽  
Local Minima ◽  
Adaptive Dynamic ◽  
Edge Linking ◽  
Net Method ◽  
Adaptive Elastic Net

In this chapterr, the authors propose an adaptive Elastic Net method for edge linking of images. Edge linking is a fundamental computer-vision task, which is a constrained optimization problem. In the proposed method, an adaptive dynamic parameter strategy and a stochastic noise strategy are introduced into the Elastic Net, which enables the network to have superior ability for escaping from local minima and converge sooner to optimal or near-optimal solutions. Simulations confirm that the proposed method could produce more meaningful contours than the original Elastic Net in shorter time.

New Dynamic Multi-Objective Constrained Optimization Evolutionary Algorithm

2015 ◽  
Vol 32 (05) ◽  
pp. 1550036 ◽  
Author(s):  
Chun-An Liu ◽  
Yuping Wang ◽  
Aihong Ren
Keyword(s):  
Constrained Optimization ◽  
Evolutionary Algorithm ◽  
Optimization Problem ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Constrained Optimization Problem ◽  
Multi Objective ◽  
Time Period ◽  
Pareto Fronts

For dynamic multi-objective constrained optimization problem (DMCOP), it is important to find a sufficient number of uniformly distributed and representative dynamic Pareto optimal solutions. In this paper, the time period of the DMCOP is first divided into several random subperiods. In each random subperiod, the DMCOP is approximately regarded as a static optimization problem by taking the time subperiod fixed. Then, in order to decrease the amount of computation and improve the effectiveness of the algorithm, the dynamic multi-objective constrained optimization problem is further transformed into a dynamic bi-objective constrained optimization problem based on the dynamic mean rank variance and dynamic mean density variance of the evolution population. The evolution operators and a self-check operator which can automatically checkout the change of time parameter are introduced to solve the optimization problem efficiently. And finally, a dynamic multi-objective constrained optimization evolutionary algorithm is proposed. Also, the convergence analysis for the proposed algorithm is given. The computer simulations are made on four dynamic multi-objective optimization test functions and the results demonstrate that the proposed algorithm can effectively track and find the varying Pareto optimal solutions or the varying Pareto fronts with the change of time.

scholarly journals Optimal Design of Coatings for Mirrors of Gravitational Wave Detectors: Analytic Turbo Solution via Herpin Equivalent Layers

2021 ◽  
Vol 11 (24) ◽  
pp. 11669
Author(s):  
Vincenzo Pierro ◽  
Vincenzo Fiumara ◽  
Francesco Chiadini
Keyword(s):  
Analytical Solution ◽  
Gravitational Wave ◽  
Optimization Problem ◽  
Optimized Design ◽  
Brute Force ◽  
Optimal Solutions ◽  
Constrained Optimization Problem ◽  
Type Design ◽  
Gravitational Wave Detectors ◽  
Coating Design

In this paper, an analytical solution to the problem of optimal dielectric coating design of mirrors for gravitational wave detectors is found. The technique used to solve this problem is based on Herpin’s equivalent layers, which provide a simple, constructive, and analytical solution. The performance of the Herpin-type design exceeds that of the periodic design and is almost equal to the performance of the numerical, non-constructive optimized design obtained by brute force. Note that the existence of explicit analytic constructive solutions of a constrained optimization problem is not guaranteed in general, when such a solution is found, we speak of turbo optimal solutions.

A HYBRID ELASTIC NET METHOD FOR SOLVING THE TRAVELING SALESMAN PROBLEM

2005 ◽  
Vol 15 (02) ◽  
pp. 447-453
Author(s):  
WENDONG ZHANG ◽  
YANPING BAI
Keyword(s):  
Hybrid Algorithm ◽  
Elastic Net ◽  
The Self ◽  
Self Organization ◽  
Local Minima ◽  
Gradient Ascent ◽  
Net Method ◽  
Two Phases ◽  
The Traveling Salesman Problem ◽  
Ascent Phase

The purpose of this paper is to present a new hybrid Elastic Net (EN) algorithm, by integrating the ideas of the Self Organization Map (SOM) and the strategy of the gradient ascent into the EN algorithm. The new hybrid algorithm has two phases: an EN phase based on SOM and a gradient ascent phase. We acquired the EN phase based on SOM by analyzing the weight between a city and its converging and non-converging nodes at the limit when the EN algorithm produces a tour. Once the EN phase based on SOM stuck in local minima, the gradient ascent algorithm attempts to fill up the valley by modifying parameters in a gradient ascent direction of the energy function. These two phases are repeated until the EN gets out of local minima and produces the short or better tour through cities. We test the algorithm on a set of TSP. For all instances, the algorithm is showed to be capable of escaping from the EN local minima and producing more meaningful tour than the EN.

scholarly journals Efficiency of quantum vs. classical annealing in nonconvex learning problems

2018 ◽  
Vol 115 (7) ◽  
pp. 1457-1462 ◽  
Author(s):  
Carlo Baldassi ◽  
Riccardo Zecchina
Keyword(s):  
Nonconvex Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Transverse Field ◽  
Learning Problems ◽  
Optimal Solutions ◽  
Local Minima ◽  
Quantum Annealing ◽  
Nonconvex Optimization Problems ◽  
Classical Energy

Quantum annealers aim at solving nonconvex optimization problems by exploiting cooperative tunneling effects to escape local minima. The underlying idea consists of designing a classical energy function whose ground states are the sought optimal solutions of the original optimization problem and add a controllable quantum transverse field to generate tunneling processes. A key challenge is to identify classes of nonconvex optimization problems for which quantum annealing remains efficient while thermal annealing fails. We show that this happens for a wide class of problems which are central to machine learning. Their energy landscapes are dominated by local minima that cause exponential slowdown of classical thermal annealers while simulated quantum annealing converges efficiently to rare dense regions of optimal solutions.

Sparse damage detection via the elastic net method using modal data

2021 ◽  
pp. 147592172110219
Author(s):  
Rongrong Hou ◽  
Xiaoyou Wang ◽  
Yong Xia
Keyword(s):  
Damage Detection ◽  
Structural Damage ◽  
Damage Identification ◽  
Measurement Data ◽  
Elastic Net ◽  
Sensitivity Matrix ◽  
Regularization Technique ◽  
Modal Data ◽  
Regularization Techniques ◽  
Net Method

The l1 regularization technique has been developed for damage detection by utilizing the sparsity feature of structural damage. However, the sensitivity matrix in the damage identification exhibits a strong correlation structure, which does not suffice the independency criteria of the l1 regularization technique. This study employs the elastic net method to solve the problem by combining the l1 and l2 regularization techniques. Moreover, the proposed method enables the grouped structural damage being identified simultaneously, whereas the l1 regularization cannot. A numerical cantilever beam and an experimental three-story frame are utilized to demonstrate the effectiveness of the proposed method. The results showed that the proposed method is able to accurately locate and quantify the single and multiple damages, even when the number of measurement data is much less than the number of elements. In particular, the present elastic net technique can detect the grouped damaged elements accurately, whilst the l1 regularization method cannot.

scholarly journals A Fast and Exact Greedy Algorithm for the Core–Periphery Problem

Symmetry ◽  
2020 ◽  
Vol 12 (1) ◽  
pp. 94 ◽  
Author(s):  
Dario Fasino ◽  
Franca Rinaldi
Keyword(s):  
Structural Analysis ◽  
Optimization Problem ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Combinatorial Optimization Problem ◽  
Connected Subgraph ◽  
Optimal Solutions ◽  
The Core ◽  
Core Set ◽  
Key Concepts

The core–periphery structure is one of the key concepts in the structural analysis of complex networks. It consists of a partitioning of the node set of a given graph or network into two groups, called core and periphery, where the core nodes induce a well-connected subgraph and share connections with peripheral nodes, while the peripheral nodes are loosely connected to the core nodes and other peripheral nodes. We propose a polynomial-time algorithm to detect core–periphery structures in networks having a symmetric adjacency matrix. The core set is defined as the solution of a combinatorial optimization problem, which has a pleasant symmetry with respect to graph complementation. We provide a complete description of the optimal solutions to that problem and an exact and efficient algorithm to compute them. The proposed approach is extended to networks with loops and oriented edges. Numerical simulations are carried out on both synthetic and real-world networks to demonstrate the effectiveness and practicability of the proposed algorithm.

scholarly journals Nonconvex constrained optimization by a filtering branch and bound

2020 ◽  
Author(s):  
Gabriele Eichfelder ◽  
Kathrin Klamroth ◽  
Julia Niebling
Keyword(s):  
Constrained Optimization ◽  
Optimization Problem ◽  
Feasible Solution ◽  
Constrained Optimization Problem ◽  
Numerical Tests ◽  
Nonconvex Constrained Optimization ◽  
Objective Value ◽  
Feasible Solutions ◽  
Quality Guarantee ◽  
Single Objective

AbstractA major difficulty in optimization with nonconvex constraints is to find feasible solutions. As simple examples show, the $$\alpha $$ α BB-algorithm for single-objective optimization may fail to compute feasible solutions even though this algorithm is a popular method in global optimization. In this work, we introduce a filtering approach motivated by a multiobjective reformulation of the constrained optimization problem. Moreover, the multiobjective reformulation enables to identify the trade-off between constraint satisfaction and objective value which is also reflected in the quality guarantee. Numerical tests validate that we indeed can find feasible and often optimal solutions where the classical single-objective $$\alpha $$ α BB method fails, i.e., it terminates without ever finding a feasible solution.

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