Trajectory Optimization Using Analytical Target Cascading

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Xiang Li ◽  
Xiaonpeng Wang ◽  
Houjun Zhang ◽  
Yuheng Guo
Keyword(s):  
Trajectory Optimization ◽  
Large Scale ◽  
Optimization Problems ◽  
Sparse Matrix ◽  
Functional Dependence ◽  
Analytical Target Cascading ◽  
Scale Problem ◽  
Direct Collocation ◽  
Target Cascading ◽  
Direct Collocation Method

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.

Cutting Plane Methods for Analytical Target Cascading With Augmented Lagrangian Coordination

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Wenshan Wang ◽  
Vincent Y. Blouin ◽  
Melissa K. Gardenghi ◽  
Georges M. Fadel ◽  
Margaret M. Wiecek ◽  
...  
Keyword(s):  
Large Scale ◽  
Augmented Lagrangian ◽  
Optimization Problems ◽  
Cutting Plane ◽  
Analytical Target Cascading ◽  
Cutting Plane Methods ◽  
Subgradient Optimization ◽  
Decomposition Approach ◽  
Target Cascading ◽  
Augmented Lagrangian Coordination

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.

scholarly journals Multi-Disciplinary Design Optimization for Large-Scale Reverse Osmosis Systems

2014 ◽  
Author(s):  
Bo Yang Yu ◽  
Tomonori Honda ◽  
Syed Zubair ◽  
Mostafa H. Sharqawy ◽  
Maria C. Yang
Keyword(s):  
Optimal Design ◽  
Complex Systems ◽  
Design Optimization ◽  
Reverse Osmosis ◽  
Large Scale ◽  
Analytical Target Cascading ◽  
Total Water ◽  
Target Cascading ◽  
Desalination Plants ◽  
Functional Components

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.

Diagonal Quadratic Approximation for Parallelization of Analytical Target Cascading

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Yanjing Li ◽  
Zhaosong Lu ◽  
Jeremy J. Michalek
Keyword(s):  
Optimization Problems ◽  
Computational Cost ◽  
Descent Method ◽  
Quadratic Approximation ◽  
Test Problems ◽  
Analytical Target Cascading ◽  
Decomposition Approach ◽  
Diagonal Quadratic Approximation ◽  
Target Cascading ◽  
Nested Loop

Analytical target cascading (ATC) is an effective decomposition approach used for engineering design optimization problems that have hierarchical structures. With ATC, the overall system is split into subsystems, which are solved separately and coordinated via target/response consistency constraints. As parallel computing becomes more common, it is desirable to have separable subproblems in ATC so that each subproblem can be solved concurrently to increase computational throughput. In this paper, we first examine existing ATC methods, providing an alternative to existing nested coordination schemes by using the block coordinate descent method (BCD). Then we apply diagonal quadratic approximation (DQA) by linearizing the cross term of the augmented Lagrangian function to create separable subproblems. Local and global convergence proofs are described for this method. To further reduce overall computational cost, we introduce the truncated DQA (TDQA) method, which limits the number of inner loop iterations of DQA. These two new methods are empirically compared to existing methods using test problems from the literature. Results show that computational cost of nested loop methods is reduced by using BCD, and generally the computational cost of the truncated methods is superior to the nested loop methods with lower overall computational cost than the best previously reported results.

Trajectory Optimization for Spacecraft Proximity Rendezvous Using Direct Collocation Method

2012 ◽  
Vol 433-440 ◽  
pp. 6652-6656 ◽  
Author(s):  
Tao Liu ◽  
Yu Shan Zhao ◽  
Peng Shi ◽  
Bao Jun Li
Keyword(s):  
Nonlinear Programming ◽  
Control Problem ◽  
Programming Problem ◽  
Collocation Method ◽  
Trajectory Optimization ◽  
Collocation Methods ◽  
Nonlinear Programming Problem ◽  
Reference Orbit ◽  
Direct Collocation ◽  
Direct Collocation Method

Trajectory optimization problem for spacecraft proximity rendezvous with path constraints was discussed using direct collocation method. Firstly, the model of spacecraft proximity rendezvous in elliptic orbit optimization control problem was presented, with the dynamic equations established in the target local orbital frame, and the performance index was minimizing the total fuel consumption. After that the optimal control problem was transcribed into a large scale problem of Nonlinear Programming Problem (NLP) by means of Hermite-Simpson discretization, which was one of the direct collocation methods. Then the nonlinear programming problem was solved using MATLAB software package SNOPT. Finally, to verify this method, the fuel-optimal trajectory for finite thrust was planned for proximity rendezvous with elliptic reference orbit. Numerical simulation results demonstrate that the proposed method was feasible, and was not sensitive to the initial condition, having good robustness.

A Sequential Linear Programming Coordination Algorithm for Analytical Target Cascading

2010 ◽  
Vol 132 (2) ◽  
Author(s):  
Jeongwoo Han ◽  
Panos Y. Papalambros
Keyword(s):  
Design Optimization ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Test Problems ◽  
Analytical Target Cascading ◽  
Step Size ◽  
Coordination Strategy ◽  
Target Cascading ◽  
Solution Accuracy

Decomposition-based strategies, such as analytical target cascading (ATC), are often employed in design optimization of complex systems. Achieving convergence and computational efficiency in the coordination strategy that solves the partitioned problem is a key challenge. A new convergent strategy is proposed for ATC that coordinates interactions among subproblems using sequential linearizations. The linearity of subproblems is maintained using infinity norms to measure deviations between targets and responses. A subproblem suspension strategy is used to suspend temporarily inclusion of subproblems that do not need significant redesign, based on trust region and target value step size. An individual subproblem trust region method is introduced for faster convergence. The proposed strategy is intended for use in design optimization problems where sequential linearizations are typically effective, such as problems with extensive monotonicities, a large number of constraints relative to variables, and propagation of probabilities with normal distributions. Experiments with test problems show that, relative to standard ATC coordination, the number of subproblem evaluations is reduced considerably while the solution accuracy depends on the degree of monotonicity and nonlinearity.

Probabilistic optimization of engine mount to enhance vibration characteristics using first-order reliability-based target cascading

2020 ◽  
pp. 107754632093347
Author(s):  
Youngjun Kim ◽  
Jongsoo Lee
Keyword(s):  
Large Scale ◽  
Reliability Assessment ◽  
Performance Measure ◽  
Mathematical Programming Problem ◽  
Optimized Design ◽  
Analytical Target Cascading ◽  
First Order ◽  
Target Cascading ◽  
Engine Mount ◽  
Roll Axis

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.

Study of the Optimal Design for the Gliding Trajectory

2014 ◽  
Vol 568-570 ◽  
pp. 1063-1067
Author(s):  
Jian Jun Wang ◽  
Jian Qiao Yu
Keyword(s):  
Optimal Design ◽  
Trajectory Optimization ◽  
Shooting Method ◽  
Particle Trajectory ◽  
Longitudinal Plane ◽  
Direct Collocation ◽  
Direct Collocation Method ◽  
Direct Shooting ◽  
Particle Trajectory Model ◽  
Drag Ratio

The optimal design for the gliding trajectory is studied. The particle trajectory model in the longitudinal plane is established. Aiming at solving the problems in numerical solution ,the direct shooting method based on the interpolating function of Akima is put forward .In direct collocation method, the parameters of the trajectory with approximate maximum lift-drag ratio is adopted as the starting value of the optimal variables. The trajectory with approximate maximum lift-drag ratio could be obtained by the search method. The transfer approach of turning the problem of trajectory optimization to the problem of parameter optimization by the direct shooting method is illustrated. To one kind of guided vehicles in simulation, the simulation results prove the practicability of the direct shooting method.

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