A local convergence analysis of bilevel decomposition algorithms

Multidisciplinary design optimization (MDO) problems are engineering design problems that require the consideration of the interaction between several design disciplines. Due to the organizational aspects of MDO problems, decomposition algorithms are often the only feasible solution approach. Decomposition algorithms reformulate the MDO problem as a set of independent subproblems, one per discipline, and a coordinating master problem. A popular approach to MDO problems is bilevel decomposition algorithms. These algorithms use nonlinear optimization techniques to solve both the master problem and the subproblems. In this paper, we propose two new bilevel decomposition algorithms and analyze their properties. In particular, we show that the proposed problem formulations are mathematically equivalent to the original problem and that the proposed algorithms converge locally at a superlinear rate. Our computational experiments illustrate the numerical performance of the algorithms.     

A single-loop optimization method for reliability analysis with second order uncertainty

Reliability analysis may involve random variables and interval variables. In addition, some of the random variables may have interval distribution parameters owing to limited information. This kind of uncertainty is called second order uncertainty. This article develops an efficient reliability method for problems involving the three aforementioned types of uncertain input variables. The analysis produces the maximum and minimum reliability and is computationally demanding because two loops are needed: a reliability analysis loop with respect to random variables and an interval analysis loop for extreme responses with respect to interval variables. The first order reliability method and nonlinear optimization are used for the two loops, respectively. For computational efficiency, the two loops are combined into a single loop by treating the Karush–Kuhn–Tucker (KKT) optimal conditions of the interval analysis as constraints. Three examples are presented to demonstrate the proposed method.     

多学科设计优化的数值算法及其组合算法比较的研究

针对多学科设计优化的数值算法比较研究上存在的不足,提出了算法在进行优化时所需的时间、解决问题个数及选用目标函数的相对精度等三项评估标准相结合的三维算法比较方法,首次将精度作为算法比较的一个重要指标,由此得到的算法比较三维模型,为算法选择提供了更加合理的理论依据.在理论研究的基础上,对组合算法和数值算法进行了比较,突破了传统算法比较局限在数值算法的不足.结果表明,在时间变化不大的情况下,组合算法的精度比单纯的数值算法有大幅度的提高,为工程应用提供了更全面的支持.在此基础上给出了数值算法及其组合的算法选择流程.最后,通过手机的多学科设计优化实例,验证了所提出的算法选择流程的合理性和可行性.     

An improvement of Kriging based sequential approximate optimization method via extended use of design of experiments

When Kriging is used as a meta-model for an inequality constrained function, approximate optimal solutions are sometimes infeasible in the case where they are active at the constraint boundary. This article explores the development of a Kriging-based meta-model that enhances the constraint feasibility of an approximate optimal solution. The trust region management scheme is used to ensure the convergence of the approximate optimal solution. The present study proposes a method of enhancing the constraint feasibility in which the currently infeasible design is replaced by the most feasible-usable design during the sequential approximate optimization process. An additional convergence condition is also included to reinforce the design accuracy and feasibility. Latin hypercube design and (2n+1) design are used as tools for design of experiments. The proposed approach is verified through a constrained mathematical function problem and a number of engineering optimization problems to support the proposed strategies.     

一般约束最优化超线性与二次收敛的SQP拟可行方法

讨论一般约束最优化问题,利用序列二次规划(SQP)技术和强收敛方法思想建立问题的一个新的拟可行下降算法,算法每次迭代只需解一个要求较弱的二次规划或用广义投影技术产生搜索方向。分析和论证了算法的全局收敛件、强收敛性、超线性收敛性和二次收敛率。     

Multidisciplinary grammars supporting design optimization of buildings

Optimization often focuses only on the variation of parameters while neglecting the consideration of alternative systems. However, the rearrangement of the components of a design offers important scope for improvement. To deal with such variations concerning the system structure of models for multidisciplinary design optimization (MDO), this paper proposes a framework for generating models dynamically using a design grammar with an underlying component-oriented analysis. Decomposition and modification rules support the derivation of alternative optimization model and the formalization of system changes. By linking qualitative characteristics with quantitative analyses, the components serve to assign architectural qualities to economic and environmental resources such as costs and energy consumption and thus to include non-numerical, qualitative characteristics within numerical optimization. The approach is developed with the help of a frame-based hall design and demonstrates system modifications of the optimization model by a specific rule set. The rule set focuses on the structural design but considers the effects for the other essential disciplines involved in the design case. The setup and the prototypical implementation of an optimization model for this design illustrate a way of including grammar-based system variations in MDO.

ENHANCED MULTIOBJECTIVE OPTIMIZATION TECHNIQUE FOR MULTIDISCIPLINARY DESIGN

An enhanced multiobjective formulation technique, capable of emphasizing specific objective functions during the optimization process, has been demonstrated on a complex multidisciplinary design application. The Kreisselmeier - Steinhauser (K-S) function approach, which has been used successfully in a variety of multiobjective optimization problems, has been modified using weight factors which enables the designer to emphasize specific design objectives during the optimization process. The technique has been implemented in two distinctively different problems. The first is a classical three bar truss problem and the second is a high-speed aircraft (a doubly swept wing-body configuration) application in which the multiobjective optimization procedure simultaneously minimizes the sonic boom and the drag-to-lift ratio (C_D/C_L) of the aircraft while maintaining the lift coefficient within prescribed limits. The results are compared with those of an equally weighted K-S multiobjective optimization. Results demonstrate the effectiveness of the enhanced multiobjective optimization procedure.     

An asymmetric suboptimization approach to aerostructural optimization

An asymmetric suboptimization method for performing multidisciplinary design optimization is introduced. The objective of the proposed method is to improve the overall efficiency of aerostructural optimization, by simplifying the system-level problem, and thereby reducing the number of calls to a potentially costly aerodynamics solver. To guide a gradient-based optimization algorithm, an extension of the coupled sensitivity equations is developed to include post-optimality information from the structural suboptimization. The optimization of an aircraft wing is performed using linear aerodynamic and structural analyses, and a thorough performance comparison is made between the new approach and the conventional multidisciplinary feasible method. The asymmetric suboptimization method is found to be the more efficient approach when it adequately simplifies the system-level problem, or when there is a large enough discrepancy between disciplinary solution times. I.R. Chittick is graduate student. J.R.R.A. Martins is assistant Professor.     

Fast parallel algorithms for the Maximum Empty Rectangle problem

We present efficient parallel algorithms for the maximum empty rectangle problem in this paper. On crew pram, we solve the area version of this problem inO(log ² n) time usingO(nlogn) processors. The perimeter version of this problem is solved inO(logn) time usingO(nlog ² n) processors. On erew pram, we solve both the problems inO(logn) time usingO(n ²/logn) processors. We also present anO(logn) time algorithm on a mesh-of-trees architecture.     

Collaborative Reliability Analysis under the Framework of Multidisciplinary Systems Design

Traditional Multidisciplinary Design Optimization (MDO) generates deterministic optimal designs, which are frequently pushed to the limits of design constraint boundaries, leaving little or no room to accommodate uncertainties in system input, modeling, and simulation. As a result, the design solution obtained may be highly sensitive to the variations of system input which will lead to performance loss and the solution is often risky (high likelihood of undesired events). Reliability-based design is one of the alternative techniques for design under uncertainty. The natural method to perform reliability analysis in multidisciplinary systems is the all-in-one approach where the existing reliability analysis techniques are applied directly to the system-level multidisciplinary analysis. However, the all-in-one reliability analysis method requires a double loop procedure and therefore is generally very time consuming. To improve the efficiency of reliability analysis under the MDO framework, a collaborative reliability analysis method is proposed in this paper. The procedure of the traditional Most Probable Point (MPP) based reliability analysis method is combined with the collaborative disciplinary analyses to automatically satisfy the interdisciplinary consistency when conducting reliability analysis. As a result, only a single loop procedure is required and all the computations are conducted concurrently at the individual discipline-level. Compared with the existing reliability analysis methods in MDO, the proposed method is efficient and therefore provides a cheaper tool to evaluate design feasibility in MDO under uncertainty. Two examples are used for the purpose of verification.     

线性约束LC1凸优化问题的内点信赖域算法

本文提出一种解线性约束凸规划的数值方法。通过将问题的KKT系统转化成一个约束方程,算法在每步迭代只需解一个线性方程组即可得到搜索方向。算法运用了信赖域方法利内点技术。在较弱的条件下,我们证明了算法的全局收敛性。     

某型飞机风挡及舱盖系统减重多学科设计优化方法研究

研究了某型飞机风挡及舱盖减重多学科设计优化的方法,优化过程中考虑风挡舱盖相关的传热、结构强度、屈曲和模态各学科之间的影响,建立了包括4个学科在内的风挡及舱盖系统多学科优化模型,通过改变透明件厚度达到减重的目的.采用本文提出的优化方法,使得风挡舱盖在满足约束条件的情况下,总重量减少了15.73%,各个设计变量收敛到最优值.本文提供了一种解决风挡及舱盖设计中学科耦合问题的方法,并为进一步研究飞机整机减重优化提供了一定的技术支持.     

An uncertain multidisciplinary design optimization method using interval convex models

This article proposes an uncertain multi-objective multidisciplinary design optimization methodology, which employs the interval model to represent the uncertainties of uncertain-but-bounded parameters. The interval number programming method is applied to transform each uncertain objective function into two deterministic objective functions, and a satisfaction degree of intervals is used to convert both the uncertain inequality and equality constraints to deterministic inequality constraints. In doing so, an unconstrained deterministic optimization problem will be constructed in association with the penalty function method. The design will be finally formulated as a nested three-loop optimization, a class of highly challenging problems in the area of engineering design optimization. An advanced hierarchical optimization scheme is developed to solve the proposed optimization problem based on the multidisciplinary feasible strategy, which is a well-studied method able to reduce the dimensions of multidisciplinary design optimization problems by using the design variables as independent optimization variables. In the hierarchical optimization system, the non-dominated sorting genetic algorithm II, sequential quadratic programming method and Gauss–Seidel iterative approach are applied to the outer, middle and inner loops of the optimization problem, respectively. Typical numerical examples are used to demonstrate the effectiveness of the proposed methodology.     

一般约束最优化超线性与二次收敛的序列线性方程组算法

讨论了一般等式和不等式约束优化问题,利用序列线性方程组技术和广义投影技巧,建立问题的一个“可行下降”算法,每次迭代只需解一个线性方程组和计算一次广义投影。在适当条件下,证明算法超线性和二次收敛于原问题的K—T点。     

博弈分析法在建筑设计方案优化中的应用

  建筑设计是开发商投资的关键阶段。根据我国建筑设计规范与法规体系的要求,借助博弈理论,分析建筑设计质量在设计方不同态度情况下的设计方案优化问题,采用博弈中的图解分析法,说明委托方与设计方之间的博弈,提出优化建筑设计方案的对策,从而使建筑设计方案达到最优。