Solving Structure for Network-Decomposed Problems Optimized With Augmented Lagrangian Coordination

2014 ◽  
Author(s):  
Meng Xu ◽  
Georges Fadel ◽  
Margaret M. Wiecek
Keyword(s):  
Hierarchical Structure ◽  
Augmented Lagrangian ◽  
Original Problem ◽  
Optimal Solution ◽  
Test Problems ◽  
Lagrangian Multipliers ◽  
Design And Optimization ◽  
Structure Selection ◽  
Augmented Lagrangian Coordination ◽  
Selection Of

The complexity of design and optimization tasks of modern products which cannot be carried out by a single expert or by a single design team motivated the development of the field of decomposition-based optimization. In general, the process of decomposition-based optimization consists of two procedures: (1) Partitioning the original problem into sub-problems according to the design disciplines, components or other aspects; and (2) Coordinating these sub-problems to guarantee that the aggregation of their optimal solutions results in a feasible and optimal solution for the original problem. Much current work focuses on alternative approaches for these two procedures. For a decomposed problem with a hierarchical structure, the above two procedures work very well and the Analytical Target Cascading method tailored for this type of problems can be used as the coordination method. However, for a more generally decomposed problem with a non-hierarchical structure, there are several factors that might affect the performance of the optimization by decomposition besides the traditional two procedures. In this paper, these factors are identified as: (1) the number of Lagrangian multipliers; (2) the number of decomposition levels (3) the existence and the selection of the master sub-problem. These factors further characterize the structure to solve the decomposed problem: the Solving Structure for decomposition-based optimization. Both mathematical and engineering test problems are used to explore the role of the solving structure. The results show that under the same partition and using the same coordination method, the Augmented Lagrangian Coordination, the performance of the decomposition-based optimization may be largely different in terms of efficiency, accuracy and resource cost. The results highlight the importance of choosing an optimal solving structure after deciding on the procedures of partitioning and coordination. Based on these test results, several suggestions for guidelines on the selection of an optimal solving structure selection are proposed.

scholarly journals A COMPARISON BETWEEN MILP AND MINLP APPROACHES TO OPTIMAL SOLUTION OF NONLINEAR DISCRETE TRANSPORTATION PROBLEM

Transport ◽  
2014 ◽  
Vol 30 (2) ◽  
pp. 135-144 ◽  
Author(s):  
Uroš Klanšek
Keyword(s):  
Transportation Problem ◽  
Optimal Solution ◽  
Optimization Method ◽  
Mixed Integer ◽  
Test Problems ◽  
Model Formulation ◽  
Reference Test ◽  
Adequate Model ◽  
Integer Nonlinear Programming ◽  
Selection Of

Finding an exact optimal solution of the Nonlinear Discrete Transportation Problem (NDTP) represents a challenging task in transportation science. Development of an adequate model formulation and selection of an appropriate optimization method are thus significant for attaining valuable solution of the NDTP. When nonlinearities appear within the criterion of optimization, the NDTP can be formulated directly as a Mixed-Integer Nonlinear Programming (MINLP) task or it can be linearized and converted into a Mixed-Integer Linear Programming (MILP) problem. This paper presents a comparison between MILP and MINLP approaches to exact optimal solution of the NDTP. The comparison is based on obtained results of experiments executed on a set of reference test problems. The paper discusses advantages and limitations of both optimization approaches.

Dual Residual in Augmented Lagrangian Coordination for Decomposition-Based Optimization

2014 ◽  
Author(s):  
Meng Xu ◽  
Georges Fadel ◽  
Margaret M. Wiecek
Keyword(s):  
Augmented Lagrangian ◽  
Test Problems ◽  
Initial Weight ◽  
Penalty Term ◽  
Augmented Lagrangian Relaxation ◽  
Primal And Dual ◽  
Update Strategy ◽  
Solution Accuracy ◽  
Penalty Weight ◽  
Augmented Lagrangian Coordination

As system design problems increase in complexity, researchers seek approaches to optimize such problems by coordinating the optimizations of decomposed sub-problems. Many methods for optimization by decomposition have been proposed in the literature among which, the Augmented Lagrangian Coordination (ALC) method has drawn much attention due to its efficiency and flexibility. The ALC method involves a quadratic penalty term, and the initial setting and update strategy of the penalty weight are critical to the performance of the ALC. The weight in the traditional weight update strategy always increases and previous research shows that an inappropriate initial value of the penalty weight may cause the method not to converge to optimal solutions. Inspired by the research on Augmented Lagrangian Relaxation in the convex optimization area, a new weight update strategy in which the weight can either increase or decrease is introduced into engineering optimization. The derivation of the primal and dual residuals for optimization by decomposition is conducted as a first step. It shows that the traditional weight update strategy only considers the primal residual, which may result in a duality gap and cause a relatively big solution error. A new weight update strategy considering both the primal and dual residuals is developed which drives the dual residual to zero in the optimization process, thus guaranteeing the solution accuracy of the decomposed problem. Finally, the developed strategy is applied to both mathematical and engineering test problems and the results show significant improvements in solution accuracy. Additionally, the proposed approach makes the ALC method more robust since it allows the coordination to converge with an initial weight selected from a much wider range of possible values while the selection of initial weight is a big concern in the traditional weight update strategy.

Identifying Measurement Invariant Item Sets in Cross-Cultural Settings Using an Automated Item Selection Procedure

Methodology ◽  
2018 ◽  
Vol 14 (4) ◽  
pp. 177-188 ◽  
Author(s):  
Martin Schultze ◽  
Michael Eid
Keyword(s):  
Measurement Invariance ◽  
Optimal Solution ◽  
Selection Procedure ◽  
Cross Cultural ◽  
Item Selection ◽  
Ant System ◽  
Item Quality ◽  
Ant System Algorithm ◽  
Selection For ◽  
Selection Of

Abstract. In the construction of scales intended for the use in cross-cultural studies, the selection of items needs to be guided not only by traditional criteria of item quality, but has to take information about the measurement invariance of the scale into account. We present an approach to automated item selection which depicts the process as a combinatorial optimization problem and aims at finding a scale which fulfils predefined target criteria – such as measurement invariance across cultures. The search for an optimal solution is performed using an adaptation of the [Formula: see text] Ant System algorithm. The approach is illustrated using an application to item selection for a personality scale assuming measurement invariance across multiple countries.

Generative Adversarial Networks (GANs)

2021 ◽  
Vol 54 (3) ◽  
pp. 1-42
Author(s):  
Divya Saxena ◽  
Jiannong Cao
Keyword(s):  
Optimization Technique ◽  
Generative Models ◽  
Generative Adversarial Networks ◽  
Network Architectures ◽  
Research Directions ◽  
Research Issues ◽  
Design And Optimization ◽  
Adversarial Networks ◽  
Comprehensive Survey ◽  
Selection Of

Generative Adversarial Networks (GANs) is a novel class of deep generative models that has recently gained significant attention. GANs learn complex and high-dimensional distributions implicitly over images, audio, and data. However, there exist major challenges in training of GANs, i.e., mode collapse, non-convergence, and instability, due to inappropriate design of network architectre, use of objective function, and selection of optimization algorithm. Recently, to address these challenges, several solutions for better design and optimization of GANs have been investigated based on techniques of re-engineered network architectures, new objective functions, and alternative optimization algorithms. To the best of our knowledge, there is no existing survey that has particularly focused on the broad and systematic developments of these solutions. In this study, we perform a comprehensive survey of the advancements in GANs design and optimization solutions proposed to handle GANs challenges. We first identify key research issues within each design and optimization technique and then propose a new taxonomy to structure solutions by key research issues. In accordance with the taxonomy, we provide a detailed discussion on different GANs variants proposed within each solution and their relationships. Finally, based on the insights gained, we present promising research directions in this rapidly growing field.

Mechanism of the Transition From In-Plane Buckling to Helical Buckling for a Stiff Nanowire on an Elastomeric Substrate

2016 ◽  
Vol 83 (4) ◽  
Author(s):  
Youlong Chen ◽  
Yong Zhu ◽  
Xi Chen ◽  
Yilun Liu
Keyword(s):  
High Performance ◽  
Three Dimensional ◽  
Stretchable Electronics ◽  
Buckling Mode ◽  
Design And Optimization ◽  
Out Of Plane ◽  
Plane Direction ◽  
Plane Displacement ◽  
Helical Buckling ◽  
Selection Of

In this work, the compressive buckling of a nanowire partially bonded to an elastomeric substrate is studied via finite-element method (FEM) simulations and experiments. The buckling profile of the nanowire can be divided into three regimes, i.e., the in-plane buckling, the disordered buckling in the out-of-plane direction, and the helical buckling, depending on the constraint density between the nanowire and the substrate. The selection of the buckling mode depends on the ratio d/h, where d is the distance between adjacent constraint points and h is the helical buckling spacing of a perfectly bonded nanowire. For d/h > 0.5, buckling is in-plane with wavelength λ = 2d. For 0.27 < d/h < 0.5, buckling is disordered with irregular out-of-plane displacement. While, for d/h < 0.27, buckling is helical and the buckling spacing gradually approaches to the theoretical value of a perfectly bonded nanowire. Generally, the in-plane buckling induces smaller strain in the nanowire, but consumes the largest space. Whereas the helical mode induces moderate strain in the nanowire, but takes the smallest space. The study may shed useful insights on the design and optimization of high-performance stretchable electronics and three-dimensional complex nanostructures.

scholarly journals An Interior Point Method for Solving Semidefinite Programs Using Cutting Planes and Weighted Analytic Centers

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
John Machacek ◽  
Shafiu Jibrin
Keyword(s):  
Newton’S Method ◽  
Interior Point ◽  
Newton's Method ◽  
Interior Point Method ◽  
Optimal Solution ◽  
Point Method ◽  
Feasible Region ◽  
Test Problems ◽  
Analytic Centers ◽  
Semidefinite Programs

We investigate solving semidefinite programs (SDPs) with an interior point method called SDP-CUT, which utilizes weighted analytic centers and cutting plane constraints. SDP-CUT iteratively refines the feasible region to achieve the optimal solution. The algorithm uses Newton’s method to compute the weighted analytic center. We investigate different stepsize determining techniques. We found that using Newton's method with exact line search is generally the best implementation of the algorithm. We have also compared our algorithm to the SDPT3 method and found that SDP-CUT initially gets into the neighborhood of the optimal solution in less iterations on all our test problems. SDP-CUT also took less iterations to reach optimality on many of the problems. However, SDPT3 required less iterations on most of the test problems and less time on all the problems. Some theoretical properties of the convergence of SDP-CUT are also discussed.

scholarly journals Smoothing Approximation to the Square-Root Exact Penalty Function

2016 ◽  
Vol 4 (1) ◽  
pp. 87-96
Author(s):  
Yaqiong Duan ◽  
Shujun Lian
Keyword(s):  
Penalty Function ◽  
Original Problem ◽  
Optimal Solution ◽  
Penalty Functions ◽  
Exact Penalty Functions ◽  
Exact Penalty ◽  
Square Root ◽  
Inequality Constrained Optimization ◽  
Numerical Examples ◽  
Mild Conditions

AbstractIn this paper, smoothing approximation to the square-root exact penalty functions is devised for inequality constrained optimization. It is shown that an approximately optimal solution of the smoothed penalty problem is an approximately optimal solution of the original problem. An algorithm based on the new smoothed penalty functions is proposed and shown to be convergent under mild conditions. Three numerical examples show that the algorithm is efficient.

scholarly journals A Novel Pilot Spoofing Scheme via Intelligent Reflecting Surface Based On Statistical CSI

2020 ◽  
Author(s):  
jie yang ◽  
Xinsheng Ji ◽  
Kaizhi Huang ◽  
Xiaoli Sun ◽  
Xiaoming Xu
Keyword(s):  
Original Problem ◽  
Optimal Solution ◽  
Phase Shifts ◽  
Communication Process ◽  
Secrecy Rate ◽  
Channel State ◽  
Wireless Environment ◽  
Time Division ◽  
Reflecting Surface ◽  
Secure Transmission

Pilot spoofing attack brings challenges to the physical layer secure transmission. However, since the inherent characteristics of wireless environment have not changed, active eavesdropping can be detected based on prior information. Intelligent reflecting surface (IRS), with the real-time programmable characteristics for wireless environment, provides new possibilities for effective pilot spoofing. In this paper, the IRS is deployed near the legitimate users and the control strategy is embeded into the legitimate communication process under time-division duplex (TDD) mode to assist eavesdroppers to implement pilot spoofing. By designing different phase shifts at the IRS during the uplink phase and downlink phase, the channel reciprocity between uplink and downlink disappears, and thus the secure beamforming vector is biased towards the eavesdropper. Furthermore, in order to obtain more information, the average secrecy rate based on the statistical channel state information is established by carefully designing the phase shifts. The formulated problem is non-trivial to solve. By using alternating optimization and Charnes-Cooper transformation technique, the original problem is transformed into convex form and a sub-optimal solution is achieved. Finally, simulation results show that our proposed scheme poses serious secure threat for TDD systems.

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