Sequential linearization in analytical target cascading for optimization of complex multilevel systems

Author(s):  
K-Y Chan

Large-scale design problems are high dimensional and deeply coupled in nature. The complexity of such large-scale systems prevents designers from solving them as a whole. Analytical target cascading (ATC) provides a systematic approach in solving decomposed large-scale systems that has solvable subsystems. By coordinating between subsystems, ATC can obtain the same optima as they were undecomposed. However, a convergent coordination requires series of ATC iterations that may hinder the efficiency of ATC. In this research, a sequential linearization technique is proposed to improve the efficiency of ATC. The proposed linearization technique is applied to each ATC iteration, and therefore each iteration has all linear subsystems that can be solved with high efficiency. The global convergence of this approach is ensured by a filter to determine the acceptance of the optima at each iteration and the corresponding trust region. One further motivation of the proposed strategy is its perceived potential in handling multilevel problems with random design variables. As previously studied, the sequential linear programming (SLP) algorithm provides a good balance between efficiency, accuracy, and convergence for single-level design optimization under random design variables. The proposed linearization technique can integrate with the SLP algorithm for multilevel systems. In this work, a geometric programming example is used to demonstrate the efficiency of the proposed method over standard ATC solution process without loss of accuracy.

Author(s):  
Kuei-Yuan Chan

Large-scale design problems are high dimensional and deeply-coupled in nature. The complexity of such large-scale systems prevents designers from solving them as a whole. Analytical target cascading (ATC) provides a systematic approach in solving decomposed large-scale systems that has solvable subsystems. By coordinating between subsystems, ATC can obtain the same optima as they were undecomposed. However, a convergent coordination requires series of ATC iterations that may hinder the efficiency of ATC. In this research, a sequential linearization technique is proposed to improve the efficiency of ATC. The proposed linearization technique is applied to each ATC iteration, therefore each iteration has all linear subsystems that can be solved with high efficiency. One further motivation of the proposed strategy is its perceived potential in handling multilevel problems with random design variables. As previously studied, the sequential linear programming (SLP) algorithm in [1] provides a good balances between efficiency, accuracy and convergence for single-level design optimization under random design variables. The proposed linearization technique can integrate with the SLP algorithm for multilevel systems. The global convergence of this approach is ensured by a filter to determine the acceptance of the optima at each iteration and the corresponding trust region. A geometric programming example and a structure design example demonstrate the efficiency of the proposed method over standard ATC solution process without loss of accuracy.


Author(s):  
Bo Yang Yu ◽  
Tomonori Honda ◽  
Syed Zubair ◽  
Mostafa H. Sharqawy ◽  
Maria C. Yang

Large-scale desalination plants are complex systems with many inter-disciplinary interactions and different levels of sub-system hierarchy. Advanced complex systems design tools have been shown to have a positive impact on design in aerospace and automotive, but have generally not been used in the design of water systems. This work presents a multi-disciplinary design optimization approach to desalination system design to minimize the total water production cost of a 30,000m3/day capacity reverse osmosis plant situated in the Middle East, with a focus on comparing monolithic with distributed optimization architectures. A hierarchical multi-disciplinary model is constructed to capture the entire system’s functional components and subsystem interactions. Three different multi-disciplinary design optimization (MDO) architectures are then compared to find the optimal plant design that minimizes total water cost. The architectures include the monolithic architecture multidisciplinary feasible (MDF), individual disciplinary feasible (IDF) and the distributed architecture analytical target cascading (ATC). The results demonstrate that an MDF architecture was the most efficient for finding the optimal design, while a distributed MDO approach such as analytical target cascading is also a suitable approach for optimal design of desalination plants, but optimization performance may depend on initial conditions.


Author(s):  
Liunan Yang ◽  
Federico Ballo ◽  
Giorgio Previati ◽  
Massimiliano Gobbi ◽  
Gianpiero Mastinu

Abstract Two widely used decomposition-based multi-disciplinary optimisation (MDO) methods, namely analytical target cascading (ATC) and collaborative optimisation (CO), are applied to the design of the suspension system of a road vehicle. Instead of directly optimising the spring stiffness and the damping coefficient, three parameters of the spring and three parameters of the damper are selected as design variables. Discomfort, road holding, and the total mass of the spring-damper system, are considered as objective functions. An investigation is completed to analyse the performance of the two decomposition methods compared with the conventional all-in-one (AiO) formulation in terms of efficiency and applicability.


2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Wenshan Wang ◽  
Vincent Y. Blouin ◽  
Melissa K. Gardenghi ◽  
Georges M. Fadel ◽  
Margaret M. Wiecek ◽  
...  

Analytical target cascading (ATC), a hierarchical, multilevel, multidisciplinary coordination method, has proven to be an effective decomposition approach for large-scale engineering optimization problems. In recent years, augmented Lagrangian relaxation methods have received renewed interest as dual update methods for solving ATC decomposed problems. These problems can be solved using the subgradient optimization algorithm, the application of which includes three schemes for updating dual variables. To address the convergence efficiency disadvantages of the existing dual update schemes, this paper investigates two new schemes, the linear and the proximal cutting plane methods, which are implemented in conjunction with augmented Lagrangian coordination for ATC-decomposed problems. Three nonconvex nonlinear example problems are used to show that these two cutting plane methods can significantly reduce the number of iterations and the number of function evaluations when compared to the traditional subgradient update methods. In addition, these methods are also compared to the method of multipliers and its variants, showing similar performance.


2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Debiao Meng ◽  
Xiaoling Zhang ◽  
Hong-Zhong Huang ◽  
Zhonglai Wang ◽  
Huanwei Xu

The distributed strategy of Collaborative Optimization (CO) is suitable for large-scale engineering systems. However, it is hard for CO to converge when there is a high level coupled dimension. Furthermore, the discipline objectives cannot be considered in each discipline optimization problem. In this paper, one large-scale systems control strategy, the interaction prediction method (IPM), is introduced to enhance CO. IPM is utilized for controlling subsystems and coordinating the produce process in large-scale systems originally. We combine the strategy of IPM with CO and propose the Interaction Prediction Optimization (IPO) method to solve MDO problems. As a hierarchical strategy, there are a system level and a subsystem level in IPO. The interaction design variables (including shared design variables and linking design variables) are operated at the system level and assigned to the subsystem level as design parameters. Each discipline objective is considered and optimized at the subsystem level simultaneously. The values of design variables are transported between system level and subsystem level. The compatibility constraints are replaced with the enhanced compatibility constraints to reduce the dimension of design variables in compatibility constraints. Two examples are presented to show the potential application of IPO for MDO.


2020 ◽  
pp. 107754632093347
Author(s):  
Youngjun Kim ◽  
Jongsoo Lee

Uncertainties cause tremendous failures, especially in large-scale system design, because they are accumulated from each of the subsystems. Analytical target cascading is a multidisciplinary design optimization method that enables the achievement of a concurrent and consistent design for large-scale systems. To address the uncertainties in analytical target cascading efficiently, we propose reliability-based target cascading combined with first-order reliability assessment algorithms, such as mean-value first-order second moment, performance measure analysis, and reliability index analysis. The effectiveness of the implemented algorithms was first demonstrated via a mathematical programming problem and then a practical engineering problem, involving automotive engine mount optimization, for minimizing both the difference between torque roll axis and elastic roll axis and the vibration transmissibility under mode purity requirements. The optimized design solutions are compared among three reliability assessment algorithms of reliability-based target cascading, and the uncertainty propagation with Gaussian distributions was quantified and verified. The probabilistic design results indicate that the first-order reliability-based target cascading methods successfully identify more reliable and conservative optimized solutions than analytical target cascading.


2020 ◽  
Author(s):  
Παναγιώτης Παπαδόπουλος

Η νέα εποχή με κάμερες και τηλεοράσεις υψηλής, 4K και 8K (UHD), ανάλυσης προέκυψε από τις ολοένα αυξανόμενες απαιτήσεις για υψηλότερης ανάλυσης βίντεο. Το βίντεο είναι μακράν το "μεγαλύτερο" Big Data, οδηγώντας σε εκτεταμένη χρήση του δικτύου και σε σημαντικά μεγάλη δέσμευση της χωρητικότητας αποθήκευσης. Για την αντιμετώπιση αυτής της κατάστασης, η συμπίεση βίντεο αποτελεί ενεργό πεδίο μελέτης εδώ και πολλά χρόνια και παράγοντας τεράστιου εμπορικού ενδιαφέροντος. Ένα από τα πιο επιτυχημένα και ευρέως χρησιμοποιούμενα πρότυπα κωδικοποίησης βίντεο είναι το H.264/AVC. Ενώ το H.264/AVC είναι αρκετά επιτυχημένο, οι αδυναμίες και οι περιορισμοί του στην αντιμετώπιση των αναλύσεων UHD έγιναν εμφανείς σχετικά νωρίς. Για αυτόν τον λόγο, ξεκίνησαν νέα πρότυπα κωδικοποίησης βίντεο ως διάδοχοι του H.264/AVC. Τα πιο επιφανή παραδείγματα των προτύπων κωδικοποίησης βίντεο νέας γενιάς είναι το High Efficiency Video Coding (HEVC), το AV1 που ολοκληρώθηκε πρόσφατα και το τώρα αναπτυσσόμενο Versatile Video Coding (VVC). Κάθε ένα από τα νέα πρότυπα κωδικοποίησης βίντεο σχεδιάστηκε με πρωταρχικό στόχο να ξεπεράσει τα προηγούμενα πρότυπα καλύπτοντας τις υπάρχουσες ανάγκες που έχουν προκύψει. Επομένως, κάθε νέο πρότυπο εισήγαγε νέα εργαλεία κωδικοποίησης που αυξάνουν την υπολογιστική πολυπλοκότητα τόσο στην πλευρά του κωδικοποιητή όσο και σε αυτήν του αποκωδικοποιητή. Επίσης υπήρξε συμβιβασμός μεταξύ πολυπλοκότητας και αποτελεσματικότητας συμπίεσης στα στάδια σχεδιασμού του κάθε προτύπου. Τόσο οι απαιτήσεις υψηλής ανάλυσης όσο και η αυξημένη υπολογιστική πολυπλοκότητα των προτύπων κωδικοποίησης βίντεο, οδηγούν σε χρονοβόρες εργασίες και απαιτούν σημαντικούς πόρους ενός υπολογιστικού συστήματος. Η αξιοποίηση των υψηλών υπολογιστικών απαιτήσεων γίνεται με την εκμετάλλευση του παραλληλισμού σε διάφορα επίπεδα. Σε αυτήν τη διατριβή αντιμετωπίζουμε και τις δύο από τις προαναφερθείσες πτυχές, δηλαδή την αξιοποίηση των υπολογιστικών πόρων μέσω του παραλληλισμού και την πιθανή μείωση της κατανάλωσης πόρων σε συστήματα μεγάλης κλίμακας. Όσον αφορά την πρώτη πτυχή (παραλληλισμός), εστιάζουμε σε επίπεδο μπλοκ, coarse grain παράλληλες προσεγγίσεις, οι οποίες χωρίζουν μια εικόνα σε ομάδες από μπλοκ και θεωρούν κάθε ομάδα ως ανεξάρτητη εργασία. Συγκεκριμένα στη μέθοδο τμηματοποίησης που ονομάζεται tile partitioning, θεωρείται ότι μία εικόνα χωρίζεται σε οριζόντιες και κατακόρυφες ζώνες τα σημεία τομής των οποίων σχηματίζουν τα επωνομαζόμενα tiles. Προτείνουμε και αξιολογούμε αλγόριθμους που ορίζουν την τμηματοποίηση των tiles χρησιμοποιώντας διάφορα σενάρια με σκοπό την εξισορρόπηση του φόρτου που προκύπτει στους επεξεργαστές. Όσον αφορά τη μείωση της κατανάλωσης των πόρων σε υψηλής κλίμακας συστήματα, η μεγαλύτερη συμπίεση που επιτυγχάνεται από το HEVC σε σύγκριση με το H.264/AVC είναι ο βασικός παράγοντας που επιλέχθηκε η χρήση του. Επίσης αντιμετωπίζουμε ζητήματα που σχετίζονται με τη διακωδικοποίηση (transcoding) μεταξύ του H.264/AVC και του HEVC. Ως προς αυτή την κατεύθυνση εξετάζονται δύο μονοπάτια. Στο πρώτο προτείνουμε μια μέθοδο για την εκτίμηση περιοχών υψηλής πολυπλοκότητας μέσα σε μία εικόνα, βάσει των πληροφοριών που μπορούν να εξαχθούν από το προηγούμενο πρότυπο (H.264/AVC). Αυτές οι πληροφορίες είναι σημαντικές στην περίπτωση ενός παράλληλου transcoder, καθώς μπορούν να χρησιμοποιηθούν για την αποτελεσματική εξισορρόπηση του φόρτου εργασίας των επεξεργαστών. Στο δεύτερο μονοπάτι αντιμετωπίζουμε το πρόβλημα του προγραμματισμού διεργασιών διακωδικοποίησης σε μαζική κλίμακα, ώστε να μεγιστοποιήσουμε τα οφέλη των δεσμευμένων υπολογιστικών πόρων, ελαχιστοποιώντας ταυτόχρονα το λειτουργικό τους κόστος.


2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Xiang Li ◽  
Xiaonpeng Wang ◽  
Houjun Zhang ◽  
Yuheng Guo

In the previous reports, analytical target cascading (ATC) is generally applied to product optimization. In this paper, the application area of ATC is expanded to trajectory optimization. Direct collocation method is utilized to convert a trajectory optimization into a nonlinear programing (NLP) problem. The converted NLP is a large-scale problem with sparse matrix of functional dependence table (FDT) suitable for the application of ATC. Three numerical case studies are provided to show the effects of ATC in solving trajectory optimization problems.


Author(s):  
Saima Naz ◽  
Christophe Tribes ◽  
J.-Y. Trépanier ◽  
Jason Nichols ◽  
Eddy Petro

Analytical Target Cascading (ATC), a multilayer multidisciplinary design optimization (MDO) formulation employed on a transonic fan design problem. This paper demonstrates the ATC solution process including the specific way of initializing the problem and handling system level and discipline level targets. High-fidelity analysis tools for aerodynamics, structure and dynamics disciplines have been used. A multi-level parameterization of the fan blade is considered for reducing the number of design variables. The overall objective is the transonic fan efficiency improvement under structure and dynamics constraints. This design approach is applied to the redesign of the NASA Rotor 67. The overall study explores the key points of implementation of ATC on transonic fan design practical problem.


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