scholarly journals Concurrent material and structure optimization of multiphase hierarchical systems within a continuum micromechanics framework

2021 ◽  
Author(s):  
Tarun Gangwar ◽  
Dominik Schillinger
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Structure Optimization ◽  
Material Behavior ◽  
Hierarchical Systems ◽  
Material Optimization ◽  
Continuum Micromechanics ◽  
Benchmark Tests ◽  
Constraint Optimization Problems ◽  
First Time

AbstractWe present a concurrent material and structure optimization framework for multiphase hierarchical systems that relies on homogenization estimates based on continuum micromechanics to account for material behavior across many different length scales. We show that the analytical nature of these estimates enables material optimization via a series of inexpensive “discretization-free” constraint optimization problems whose computational cost is independent of the number of hierarchical scales involved. To illustrate the strength of this unique property, we define new benchmark tests with several material scales that for the first time become computationally feasible via our framework. We also outline its potential in engineering applications by reproducing self-optimizing mechanisms in the natural hierarchical system of bamboo culm tissue.

scholarly journals Optimization of injection molding process for car fender in consideration of energy efficiency and product quality

2014 ◽  
Vol 1 (4) ◽  
pp. 256-265 ◽  
Author(s):  
Hong Seok Park ◽  
Trung Thanh Nguyen
Keyword(s):  
Energy Efficiency ◽  
Energy Consumption ◽  
Injection Molding ◽  
Product Quality ◽  
Process Parameters ◽  
Optimization Problems ◽  
Computational Cost ◽  
Injection Molding Process ◽  
Molding Process ◽  
Nsga Ii

Abstract Energy efficiency is an essential consideration in sustainable manufacturing. This study presents the car fender-based injection molding process optimization that aims to resolve the trade-off between energy consumption and product quality at the same time in which process parameters are optimized variables. The process is specially optimized by applying response surface methodology and using nondominated sorting genetic algorithm II (NSGA II) in order to resolve multi-object optimization problems. To reduce computational cost and time in the problem-solving procedure, the combination of CAE-integration tools is employed. Based on the Pareto diagram, an appropriate solution is derived out to obtain optimal parameters. The optimization results show that the proposed approach can help effectively engineers in identifying optimal process parameters and achieving competitive advantages of energy consumption and product quality. In addition, the engineering analysis that can be employed to conduct holistic optimization of the injection molding process in order to increase energy efficiency and product quality was also mentioned in this paper.

Convergence analysis of online learning algorithm with two-stage step size

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Weilin Nie ◽  
Cheng Wang
Keyword(s):  
Online Learning ◽  
Optimization Problems ◽  
Learning Algorithm ◽  
Computational Cost ◽  
Reproducing Kernels ◽  
Step Size ◽  
Two Stage ◽  
Logarithmic Term ◽  
Convergence Performance ◽  
Online Learning Algorithm

Abstract Online learning is a classical algorithm for optimization problems. Due to its low computational cost, it has been widely used in many aspects of machine learning and statistical learning. Its convergence performance depends heavily on the step size. In this paper, a two-stage step size is proposed for the unregularized online learning algorithm, based on reproducing Kernels. Theoretically, we prove that, such an algorithm can achieve a nearly min–max convergence rate, up to some logarithmic term, without any capacity condition.

Multirow Intersection Cuts Based on the Infinity Norm

2021 ◽  
Author(s):  
Álinson S. Xavier ◽  
Ricardo Fukasawa ◽  
Laurent Poirrier
Keyword(s):  
Optimization Problems ◽  
Valid Inequalities ◽  
Linear Optimization ◽  
Computational Cost ◽  
General Purpose ◽  
Mixed Integer ◽  
Infinity Norm ◽  
Intersection Cuts ◽  
Linear Optimization Problems ◽  
Mixed Integer Linear Optimization

When generating multirow intersection cuts for mixed-integer linear optimization problems, an important practical question is deciding which intersection cuts to use. Even when restricted to cuts that are facet defining for the corner relaxation, the number of potential candidates is still very large, especially for instances of large size. In this paper, we introduce a subset of intersection cuts based on the infinity norm that is very small, works for relaxations having arbitrary number of rows and, unlike many subclasses studied in the literature, takes into account the entire data from the simplex tableau. We describe an algorithm for generating these inequalities and run extensive computational experiments in order to evaluate their practical effectiveness in real-world instances. We conclude that this subset of inequalities yields, in terms of gap closure, around 50% of the benefits of using all valid inequalities for the corner relaxation simultaneously, but at a small fraction of the computational cost, and with a very small number of cuts. Summary of Contribution: Cutting planes are one of the most important techniques used by modern mixed-integer linear programming solvers when solving a variety of challenging operations research problems. The paper advances the state of the art on general-purpose multirow intersection cuts by proposing a practical and computationally friendly method to generate them.

Proactive Quality Control: Observing System Simulation Experiments with the Lorenz ’96 Model

2019 ◽  
Vol 147 (1) ◽  
pp. 53-67 ◽  
Author(s):  
Tse-Chun Chen ◽  
Eugenia Kalnay
Keyword(s):  
Quality Control ◽  
Weather Prediction ◽  
Computational Cost ◽  
Network Size ◽  
Simulation Experiments ◽  
Systematic Testing ◽  
Kalman Gain ◽  
Lorenz 96 ◽  
First Time ◽  
Shed Light

Proactive quality control (PQC) is a fully flow-dependent QC for observations based on the ensemble forecast sensitivity to observations technique (EFSO). It aims at reducing the forecast skill dropout events suffered in operational numerical weather prediction by rejecting observations identified as detrimental by EFSO. Past studies show that individual dropout cases from the Global Forecast System (GFS) were significantly improved by noncycling PQC. In this paper, we perform for the first time cycling PQC experiments in a controlled environment with the Lorenz model to provide a systematic testing of the new method and possibly shed light on the optimal configuration of operational implementation. We compare several configurations and PQC update methods. It is found that PQC improvement is insensitive to the suboptimal configurations in DA, including ensemble size, observing network size, model error, and the length of DA window, but the improvements increase with the flaws in observations. More importantly, we show that PQC improves the analysis and forecast even in the absence of flawed observations. The study reveals that reusing the exact same Kalman gain matrix for PQC update not only provides the best result but requires the lowest computational cost among all the tested methods.

scholarly journals Restricted Boltzmann Machine-Assisted Estimation of Distribution Algorithm for Complex Problems

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Lin Bao ◽  
Xiaoyan Sun ◽  
Yang Chen ◽  
Guangyi Man ◽  
Hui Shao
Keyword(s):  
Optimization Problems ◽  
Probability Model ◽  
Computational Cost ◽  
Evolutionary Process ◽  
Estimation Of Distribution Algorithm ◽  
Restricted Boltzmann Machine ◽  
Model Management ◽  
Boltzmann Machine ◽  
Complex Problems ◽  
Estimation Of Distribution

A novel algorithm, called restricted Boltzmann machine-assisted estimation of distribution algorithm, is proposed for solving computationally expensive optimization problems with discrete variables. First, the individuals are evaluated using expensive fitness functions of the complex problems, and some dominant solutions are selected to construct the surrogate model. The restricted Boltzmann machine (RBM) is built and trained with the dominant solutions to implicitly extract the distributed representative information of the decision variables in the promising subset. The visible layer’s probability of the RBM is designed as the sampling probability model of the estimation of distribution algorithm (EDA) and is updated dynamically along with the update of the dominant subsets. Second, according to the energy function of the RBM, a fitness surrogate is developed to approximate the expensive individual fitness evaluations and participates in the evolutionary process to reduce the computational cost. Finally, model management is developed to train and update the RBM model with newly dominant solutions. A comparison of the proposed algorithm with several state-of-the-art surrogate-assisted evolutionary algorithms demonstrates that the proposed algorithm effectively and efficiently solves complex optimization problems with smaller computational cost.

scholarly journals Beyond Trees: Analysis and Convergence of Belief Propagation in Graphs with Multiple Cycles

2020 ◽  
Vol 34 (05) ◽  
pp. 7333-7340
Author(s):  
Roie Zivan ◽  
Omer Lev ◽  
Rotem Galiki
Keyword(s):  
Graphical Models ◽  
Belief Propagation ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Damping Factor ◽  
Constraint Optimization ◽  
Single Cycle ◽  
Distributed Constraint Optimization ◽  
Multiple Cycles ◽  
Constraint Optimization Problems

Belief propagation, an algorithm for solving problems represented by graphical models, has long been known to converge to the optimal solution when the graph is a tree. When the graph representing the problem includes a single cycle, the algorithm either converges to the optimal solution or performs periodic oscillations. While the conditions that trigger these two behaviors have been established, the question regarding the convergence and divergence of the algorithm on graphs that include more than one cycle is still open.Focusing on Max-sum, the version of belief propagation for solving distributed constraint optimization problems (DCOPs), we extend the theory on the behavior of belief propagation in general – and Max-sum specifically – when solving problems represented by graphs with multiple cycles. This includes: 1) Generalizing the results obtained for graphs with a single cycle to graphs with multiple cycles, by using backtrack cost trees (BCT). 2) Proving that when the algorithm is applied to adjacent symmetric cycles, the use of a large enough damping factor guarantees convergence to the optimal solution.

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