Structural Optimization Methods for Large Scale Problems: Status and Limitations

2007 ◽  
Author(s):  
Claude Fleury
Keyword(s):  
Large Scale ◽  
Real Life ◽  
Local Stress ◽  
Positive Definite Matrix ◽  
Optimization Methods ◽  
Practical Applications ◽  
Cpu Time ◽  
Active Constraints ◽  
Design Variables ◽  
Numerical Effort

This paper presents results from recent numerical experiments supported by theoretical arguments which indicate where are the limits of current optimization methods when applied to problems involving a large number of design variables as well as a large number of constraints, many of them being active. This is typical of optimal sizing problems with local stress constraints especially when composite materials are employed. It is shown that in both primal and dual methods the CPU time spent in the optimizer is related to the numerical effort needed to invert a symmetric positive definite matrix of size jact, jact being the effective number of active constraints, i.e. constraints associated with positive Lagrange multipliers. This CPU time varies with jact3. When the number m of constraints increases, jact has a tendency to grow, but there is a limit. Indeed another well known theoretical property is that the number of active constraints jact should not exceed the number of free primal variables iact, i.e. the number of variables that do not reach a lower or upper bound. This number iact is itself of course smaller than the real number of design variables n. This leads to the conclusion that for problems with many active constraints the CPU time could grow as fast as n3. With respect to m the increase in CPU time remains approximately linear. Some practical applications to real life industrial problems will be briefly shown: design optimisation of an aircraft composite wing with local buckling constraints and topology optimization of an engine pylon.

scholarly journals Assessment of Reliability and Quality Performance using the Impact of Shortfall Generation Capacity Index on Power Systems

2019 ◽  
Vol 9 (6) ◽  
pp. 4937-4941
Author(s):  
B. M. Alshammari
Keyword(s):  
Power Systems ◽  
Large Scale ◽  
Real Life ◽  
Power Grids ◽  
Three Dimensions ◽  
Evaluation Methodology ◽  
Practical Applications ◽  
Generation Capacity ◽  
Capacity Index ◽  
The Impact

This paper presents a novel practical technique developed and applied for assessment of reliability and quality in real-life power systems. System-wide integrated performance indices are capable of addressing and revealing areas of deficiencies and bottlenecks as well as shortfalls in the composite generation-transmission-demand structure of large-scale power grids. The new evaluation methodology offers a general and comprehensive framework to assess the harmony and compatibility of generation capacities, transmission and required demand in a power system. The technique used in this paper is evaluated by the shortfall generation capacity index which is based on three dimensions introduced to represent the relationship between certain system generation capacity and demand. Also, practical applications to the Saudi power grid are presented for demonstration purposes.

Global optimization with deep-learning-based acceleration surrogate for large-scale seismic acoustic-impedance inversion

Geophysics ◽  
2021 ◽  
pp. 1-74
Author(s):  
Zhaoqi Gao ◽  
Wei Yang ◽  
Yajun Tian ◽  
Chuang Li ◽  
Xiudi Jiang ◽  
...  
Keyword(s):  
Global Optimization ◽  
Deep Learning ◽  
Acoustic Impedance ◽  
Large Scale ◽  
Optimization Methods ◽  
Inversion Method ◽  
Local Minima ◽  
Practical Applications ◽  
Global Optimization Methods ◽  
Low Efficiency

Seismic acoustic-impedance (AI) inversion, which estimates the AI of the reservoir from seismic and other geophysical data, is a type of nonlinear inverse problem that faces the local minima issue during optimization. Without requiring an accurate initial model, global optimization methods have the ability to jump out of local minima and search for the optimal global solution. However, the low-efficiency nature of global optimization methods hinders their practical applications, especially in large-scale AI inversion problems (AI inversion with a large number of traces). We propose a new intelligent seismic AI inversion method based on global optimization and deep learning. In this method, global optimization is used to generate datasets for training a deep learning network and it is used to first accelerate and then surrogate global optimization. In other words, for large-scale seismic AI inversion, global optimization only inverts the AI model for a few traces, and the AI models of most traces are obtained by deep learning. The deep learning architecture that we used to map from seismic trace to its corresponding AI model is established based on U-Net. Because the time-consuming global optimization inversion procedure can be avoided for most traces, this method has a significant advantage over conventional global optimization methods in efficiency. To verify the effectiveness of the proposed method, we compare its performance with the conventional global optimization method on 3D synthetic and field data examples. Compared with the conventional method, the proposed method only needs about one-tenth of the computation time to build AI models with better accuracy.

scholarly journals Design and Comparative Analysis of New Personalized Recommender Algorithms with Specific Features for Large Scale Datasets

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1106
Author(s):  
S. Bhaskaran ◽  
Raja Marappan ◽  
B. Santhi
Keyword(s):  
Large Scale ◽  
Real Life ◽  
Optimization Methods ◽  
Tuning Parameter ◽  
Computational Time ◽  
Data Set ◽  
Significant Difference ◽  
Minimum Number ◽  
Tremendous Amount ◽  
The Given

Nowadays, because of the tremendous amount of information that humans and machines produce every day, it has become increasingly hard to choose the more relevant content across a broad range of choices. This research focuses on the design of two different intelligent optimization methods using Artificial Intelligence and Machine Learning for real-life applications that are used to improve the process of generation of recommenders. In the first method, the modified cluster based intelligent collaborative filtering is applied with the sequential clustering that operates on the values of dataset, user′s neighborhood set, and the size of the recommendation list. This strategy splits the given data set into different subsets or clusters and the recommendation list is extracted from each group for constructing the better recommendation list. In the second method, the specific features-based customized recommender that works in the training and recommendation steps by applying the split and conquer strategy on the problem datasets, which are clustered into a minimum number of clusters and the better recommendation list, is created among all the clusters. This strategy automatically tunes the tuning parameter λ that serves the role of supervised learning in generating the better recommendation list for the large datasets. The quality of the proposed recommenders for some of the large scale datasets is improved compared to some of the well-known existing methods. The proposed methods work well when λ = 0.5 with the size of the recommendation list, |L| = 30 and the size of the neighborhood, |S| < 30. For a large value of |S|, the significant difference of the root mean square error becomes smaller in the proposed methods. For large scale datasets, simulation of the proposed methods when varying the user sizes and when the user size exceeds 500, the experimental results show that better values of the metrics are obtained and the proposed method 2 performs better than proposed method 1. The significant differences are obtained in these methods because the structure of computation of the methods depends on the number of user attributes, λ, the number of bipartite graph edges, and |L|. The better values of the (Precision, Recall) metrics obtained with size as 3000 for the large scale Book-Crossing dataset in the proposed methods are (0.0004, 0.0042) and (0.0004, 0.0046) respectively. The average computational time of the proposed methods takes <10 seconds for the large scale datasets and yields better performance compared to the well-known existing methods.

Development of Multi-Stage and Hybrid Real-Coded Genetic Algorithms With Active Constraints

2002 ◽  
Author(s):  
Yasunari Mimura ◽  
Shinobu Yoshimura ◽  
Tomoyuki Hiroyasu ◽  
Mitsunori Miki
Keyword(s):  
Genetic Algorithm ◽  
Large Scale ◽  
Initial Point ◽  
Global Optimum ◽  
Feasible Region ◽  
Active Constraints ◽  
Multi Stage ◽  
Design Variables ◽  
Real Coded Genetic Algorithm ◽  
Optimum Solution

In this study, we propose multi-stage and hybrid real-coded genetic algorithm. In the proposed algorithm, there are two stages. In the first stage, Real-coded Genetic Algorithm with Active Constraints (RGAAC) is applied to find a solution that is close to the global optimum. In RGAAC, indviduals who are out of the feasible region are pulled back into feasible region. Therefore, the effective search can be carried out even in the constraints problems. In the second stage, Feasible Region Limiting Method (FRLM) is applied to obtain an optimum solution. FRLM uses the solution that is derived in the first stager as an initial point. In this study, RGAAC is applied to solve the truss structure problems. Through these problems, the effectiveness and the searching mechanism of RGAAC is discussed. The, the proposed algorithm is also applied to 2D problem. In this problem, there are about 1000 design variables. The proposed method can derive the reasonable solution. From these results, it is concluded that the proposed method is effective to solve optimzation problems of large scale structures.

A Literature Review: Solving Constrained Non-Linear Bi-Level Optimization Problems With Classical Methods

2019 ◽  
Author(s):  
Arpan Biswas ◽  
Christopher Hoyle
Keyword(s):  
Literature Review ◽  
Optimization Problems ◽  
Classical Method ◽  
Optimization Methods ◽  
Function Evaluation ◽  
Practical Applications ◽  
Design Variables ◽  
Non Linear ◽  
Upper Level ◽  
Work Done

Abstract Bi-level optimization is an emerging scope of research which consists of two optimization problems, where the lower-level optimization problem is nested into the upper-level problem as a constraint. Bi-level programming has gained much attention recently for practical applications. Bi-level Programming Problems (BLPP) can be solved with classical and heuristic optimization methods. However, applying heuristic methods, though easier to formulate for realistic complex design, are likely to be too computationally expensive for solving bi-level problems, especially when the problem has high function evaluation cost associated with handling large number of constraint functions. Thus, classical approaches are investigated in this paper. As we present, there appears to be no universally best classical method for solving any kind of NP-hard BLPP problem in terms of accuracy to finding true optimal solutions and minimal computational costs. This could cause a dilemma to the researcher in choosing an appropriate classical approach to solve a BLPP in different domains and levels of complexities. Therefore, this motivates us to provide a detailed literature review and a comparative study of the work done to date on applying different classical approaches in solving constrained non-linear, bi-level optimization problems considering continuous design variables and no discontinuity in functions.

Strategic vehicle fleet management–a joint solution of make-or-buy, composition and replacement problems

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Adam Redmer
Keyword(s):  
Management Strategy ◽  
Large Scale ◽  
Real Life ◽  
Optimization Methods ◽  
Solution Procedure ◽  
Fleet Management ◽  
Content Type ◽  
Fleet Size ◽  
Real Life Data ◽  
Management Problems

PurposeThe purpose of this paper is to develop an original model and a solution procedure for solving jointly three main strategic fleet management problems (fleet composition, replacement and make-or-buy), taking into account interdependencies between them.Design/methodology/approachThe three main strategic fleet management problems were analyzed in detail to identify interdependencies between them, mathematically modeled in terms of integer nonlinear programing (INLP) and solved using evolutionary based method of a solver compatible with a spreadsheet.FindingsThere are no optimization methods combining the analyzed problems, but it is possible to mathematically model them jointly and solve together using a solver compatible with a spreadsheet obtaining a solution/fleet management strategy answering the questions: Keep currently exploited vehicles in a fleet or remove them? If keep, how often to replace them? If remove then when? How many perspective/new vehicles, of what types, brand new or used ones and when should be put into a fleet? The relatively large scale instance of problem (50 vehicles) was solved based on a real-life data. The obtained results occurred to be better/cheaper by 10% than the two reference solutions – random and do-nothing ones.Originality/valueThe methodology of developing optimal fleet management strategy by solving jointly three main strategic fleet management problems is proposed allowing for the reduction of the fleet exploitation costs by adjusting fleet size, types of exploited vehicles and their exploitation periods.

Stabilized Column Generation Via the Dynamic Separation of Aggregated Rows

2021 ◽  
Author(s):  
Luciano Costa ◽  
Claudio Contardo ◽  
Guy Desaulniers ◽  
Julian Yarkony
Keyword(s):  
Column Generation ◽  
Large Scale ◽  
Bin Packing ◽  
Time Windows ◽  
Real Life ◽  
Problem Formulation ◽  
Master Problem ◽  
Cpu Time ◽  
Dual Variables ◽  
New Formulation

Column generation (CG) algorithms are well known to suffer from convergence issues due, mainly, to the degenerate structure of their master problem and the instability associated with the dual variables involved in the process. In the literature, several strategies have been proposed to overcome this issue. These techniques rely either on the modification of the standard CG algorithm or on some prior information about the set of dual optimal solutions. In this paper, we propose a new stabilization framework, which relies on the dynamic generation of aggregated rows from the CG master problem. To evaluate the performance of our method and its flexibility, we consider instances of three different problems, namely, vehicle routing with time windows (VRPTW), bin packing with conflicts (BPPC), and multiperson pose estimation (MPPEP). When solving the VRPTW, the proposed stabilized CG method yields significant improvements in terms of CPU time and number of iterations with respect to a standard CG algorithm. Huge reductions in CPU time are also achieved when solving the BPPC and the MPPEP. For the latter, our method has shown to be competitive when compared with a tailored method. Summary of Contribution: Column generation (CG) algorithms are among the most important and studied solution methods in operations research. CG algorithms are suitable to cope with large-scale problems arising from several real-life applications. The present paper proposes a generic stabilization framework to address two of the main issues found in a CG method: degeneracy in the master problem and massive instability of the dual variables. The newly devised method, called dynamic separation of aggregated rows (dyn-SAR), relies on an extended master problem that contains redundant constraints obtained by aggregating constraints from the original master problem formulation. This new formulation is solved in a column/row generation fashion. The efficacy of the proposed method is tested through an extensive experimental campaign, where we solve three different problems that differ considerably in terms of their constraints and objective function. Despite being a generic framework, dyn-SAR requires the embedded CG algorithm to be tailored to the application at hand.

Finite Element Modeling for Steel Cord Analysis in Radial Tires

2013 ◽  
Vol 41 (1) ◽  
pp. 60-79 ◽  
Author(s):  
Wei Yintao ◽  
Luo Yiwen ◽  
Miao Yiming ◽  
Chai Delong ◽  
Feng Xijin
Keyword(s):  
Finite Element ◽  
High Efficiency ◽  
Force Measurement ◽  
Three Dimensional ◽  
Local Stress ◽  
Tension Force ◽  
Center Line ◽  
Element Analysis ◽  
Design Variables ◽  
Steel Cord

ABSTRACT: This article focuses on steel cord deformation and force investigation within heavy-duty radial tires. Typical bending deformation and tension force distributions of steel reinforcement within a truck bus radial (TBR) tire have been obtained, and they provide useful input for the local scale modeling of the steel cord. The three-dimensional carpet plots of the cord force distribution within a TBR tire are presented. The carcass-bending curvature is derived from the deformation of the carcass center line. A high-efficiency modeling approach for layered multistrand cord structures has been developed that uses cord design variables such as lay angle, lay length, and radius of the strand center line as input. Several types of steel cord have been modeled using the developed method as an example. The pure tension for two cords and the combined tension bending under various loading conditions relevant to tire deformation have been simulated by a finite element analysis (FEA). Good agreement has been found between experimental and FEA-determined tension force-displacement curves, and the characteristic structural and plastic deformation phases have been revealed by the FE simulation. Furthermore, some interesting local stress and deformation patterns under combined tension and bending are found that have not been previously reported. In addition, an experimental cord force measurement approach is included in this article.

Model Order Reduction of Transmission Line Model

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Transmission Line ◽  
Large Scale ◽  
Original System ◽  
Reduced Order Model ◽  
Benchmark Problems ◽  
Transmission Line Model ◽  
Order Model ◽  
Line Model ◽  
Reduced Order ◽  
Numerical Effort

Transmission Line model are an important role in the electrical power supply. Modeling of such system remains a challenge for simulations are necessary for designing and controlling modern power systems.In order to analyze the numerical approach for a benchmark collection Comprehensive of some needful real-world examples, which can be utilized to evaluate and compare mathematical approaches for model reduction. The approach is based on retaining the dominant modes of the system and truncation comparatively the less significant once.as the reduced order model has been derived from retaining the dominate modes of the large-scale stable system, the reduction preserves the stability. The strong demerit of the many MOR methods is that, the steady state values of the reduced order model does not match with the higher order systems. This drawback has been try to eliminated through the Different MOR method using sssMOR tools. This makes it possible for a new assessment of the error system Offered that the Observability Gramian of the original system has as soon as been thought about, an H∞ and H2 error bound can be calculated with minimal numerical effort for any minimized model attributable to The reduced order model (ROM) of a large-scale dynamical system is essential to effortlessness the study of the system utilizing approximation Algorithms. The response evaluation is considered in terms of response constraints and graphical assessments. the application of Approximation methods is offered for arising ROM of the large-scale LTI systems which consist of benchmark problems. The time response of approximated system, assessed by the proposed method, is also shown which is excellent matching of the response of original system when compared to the response of other existing approaches .

Bullying, School Violence, and Climate in Evolving Contexts

2018 ◽  
Author(s):  
Ron Avi Astor ◽  
Rami Benbenisthty
Keyword(s):  
School Violence ◽  
School Safety ◽  
Media Coverage ◽  
Large Scale ◽  
Ecological Model ◽  
Empirical Studies ◽  
Practical Applications ◽  
Teacher Student ◽  
Area Of Interest ◽  
New Research

Since 2005, the bullying, school violence, and school safety literatures have expanded dramatically in content, disciplines, and empirical studies. However, with this massive expansion of research, there is also a surprising lack of theoretical and empirical direction to guide efforts on how to advance our basic science and practical applications of this growing scientific area of interest. Parallel to this surge in interest, cultural norms, media coverage, and policies to address school safety and bullying have evolved at a remarkably quick pace over the past 13 years. For example, behaviors and populations that just a decade ago were not included in the school violence, bullying, and school safety discourse are now accepted areas of inquiry. These include, for instance, cyberbullying, sexting, social media shaming, teacher–student and student–teacher bullying, sexual harassment and assault, homicide, and suicide. Populations in schools not previously explored, such as lesbian, gay, bisexual, transgender, and queer students and educators and military- and veteran-connected students, become the foci of new research, policies, and programs. As a result, all US states and most industrialized countries now have a complex quilt of new school safety and bullying legislation and policies. Large-scale research and intervention funding programs are often linked to these policies. This book suggests an empirically driven unifying model that brings together these previously distinct literatures. This book presents an ecological model of school violence, bullying, and safety in evolving contexts that integrates all we have learned in the 13 years, and suggests ways to move forward.

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