Dealing with redundancy and inconsistency in constructive geometric constraint solving

General constructive geometric constraint solvers are pre-processed by a degree-of-freedom analysis, which enables efficient graph decomposition and recombination. However, all these methods are based on the assumption that structural rigidity automatically assures solvability. In this paper, we show that this assumption fails in numerous, even the most basic, configurations. We introduce several simple but efficient rules aimed to additionally analyse solvability in such cases. Another novelty addresses conditional constraints between three or more geometric parts, rules for their simplification and a redundancy check. All these functionalities are built into our original 2D geometric constraint solver, based on concepts of rigid clusters and constrained-angle (CA) sets.     

自由曲线在参数化设计中的应用

对与自由曲线有关的几何约束种类进行比较全面地研究,讨论了自由曲线应用到参数化设计系统中后几何约束的求解问题,提出可以用基于图的自由度分析方法对几何约束问题进行分解,介绍了简单凝聚模式下有关自由曲线几何约束的凝聚计算问题.     

Formulating global integrity constraints during derivation of global schema

In a heterogeneous distributed database environment, each component database is characterized by its own logical schema and its own set of integrity constraints. The task of generating a global schema from a constituent local schemata has been addressed by many researchers. The complementary problem of using multiple sets of integrity constraints to create a new set of global integrity constraints is examined in this paper. These global integrity constraints facilitate both query optimization and update validation tasks.     

The challenge of equality constraints in robust design optimization: examination and new approach

In recent years, robust design optimization (RDO) has emerged as a significant area of research. The focus of RDO is to obtain a design that minimizes the effects of uncertainty on product reliability and performance. The effectiveness of the resulting solution in RDO highly depends on how the objective function and the constraints are formulated to account for uncertainties. Inequality constraint and objective function formulations under uncertainty have been studied extensively in the literature. However, the approaches for formulating equality constraints in the RDO literature are in a state of disharmony. Moreover, we observe that these approaches are generally applicable only to certain special cases of equality constraints. There is a need for a systematic approach for handling equality constraints in RDO, which is the motivation for this research. In this paper, we examine critical issues pertinent to formulating equality constraints in RDO. Equality constraints in RDO can be classified as belonging to two classes: (1) those that cannot be satisfied, because of the uncertainty inherently present in the RDO problem, and (2) those that must be satisfied, regardless of the uncertainty present in the problem. In this paper, we propose a linearization- based approach to classify equality constraints into the above two classes, and propose respective formulation methods. The theoretical developments presented in this paper are illustrated with the help of two numerical examples.     

Topology optimization for minimum mass design considering local failure constraints and contact boundary conditions

This paper studies the optimum design of a 1×2 mechanical optical switch. First, a novel switch configuration is designed with an included antithermal mechanism. Then, parametric programs are developed to automatically generate the solid model and to analyze thermal behavior of the switch. From the analysis of the initial design, it revealed that the amount of transverse offset between fiber tips failed in satisfying the Bellcore specifications. Finally, an integrated program combining CAD software, genetic algorithms, and finite element software was developed for optimum design of optical switches. With the capability of continuously changing critical design parameters of the switch in the integrated design program, the final optimum design satisfying the design constraints and specifications can be found.     

Interactive design of 3D models with geometric constraints

In this paper, an interactive graphical approach for the design of parameterized part-hierarchies is presented. Primitive solids can be grouped into compound objects, and multiple instances of a compound object can be used in further designs. Geometric relations between primitives and instances are specified by geometric constraints between their local coordinate systems. The user can specify and edit a model by direct manipulation on a perspective or parallel projection with a mouse, whereas a procedural model representations is automatically generated via visual programming. The obtained twoview approach offers two concurrent interface styles to the end-user and enables the combination of an intuitive direct manipulation interface with the expressiveness of a procedural modeling language.     

Tolerances in computer-aided geometric design

In the design of discrete part shapes, the specification of tolerance constraints can have major consequences for product quality and cost. Traditional methods for tolerance analysis and synthesis are timeconsuming, and have limited applicability. This paper presents the results of research into the use of solid modeling technology for the automated solution of tolerancing problems. A linear programming method is presented for the solution of tolerance analysis problems on a worst-case basis. A Monte Carlo method is presented for both worst-case and statistical tolerance analysis. Both methods automatically derive all necessary geometric relationships from a solid model of the assembly. Example problems are solved using the experimental GEOTOL geometric design system.     

Optimal truss design including plastic collapse constraints

A new algorithm is presented for size optimization of truss structures with any kind of smooth objectives and constraints, together with constraints on the collapse loading obtained by limit analysis, for several loading conditions. The main difficulty of this problem is the fact that the collapse loading is a nonsmooth function of the design variables. In this paper we avoid nonsmooth optimization techniques based on the fact that limit analysis constraints are linear by parts. Our approach is based on a feasible directions interior point algorithm for nonlinear constrained optimization. Three illustrative examples are discussed. The numerical results show that the calculation effort when limit analysis constraints are included is only slightly increased with respect to classic constraints.     

Real-time optimization under parametric uncertainty: a probability constrained approach

Uncertainty is an inherent characteristic in most industrial processes, and a variety of approaches including sensitivity analysis, robust optimization and stochastic programming have been proposed to deal with such uncertainty. Uncertainty in a steady state nonlinear real-time optimization (RTO) system and particularly making robust decisions under uncertainty in real-time has received little attention. This paper discusses various sources of uncertainty within such closed loop RTO systems and a method, based on stochastic programming, that explicitly incorporates uncertainty into the RTO problem is presented. The proposed method is limited to situations where uncertain parameters enter the constraints nonlinearly and uncertain economics enter the objective function linearly. Our approach is shown to significantly improve the probability of a feasible solution in comparison to more conventional RTO techniques. A gasoline blending example is used to demonstrate the proposed robust RTO approach.     

An intelligent moving object optimization algorithm for design problems with mixed variables, mixed constraints and multiple objectives

This paper presents an optimization algorithm for engineering design problems having a mix of continuous, discrete and integer variables; a mix of linear, non-linear, differentiable, non-differential, equality, inequality and even discontinuous design constraints; and conflicting multiple design objectives. The intelligent movement of objects (vertices and compounds) is simulated in the algorithm based on a Nelder–Mead simplex with added features to handle variable types, bound and design constraints, local optima, search initiation from an infeasible region and numerical instability, which are the common requirements for large-scale, complex optimization problems in various engineering and business disciplines. The algorithm is called an INTElligent Moving Object algorithm and tested for a wide range of benchmark problems. Validation results for several examples, which are manageable within the scope of this paper, are presented herein. Satisfactory results have been obtained for all the test problems, hence, highlighting the benefits of the proposed method.     

A novel evolutionary root system growth algorithm for solving multi-objective optimization problems

This paper proposes a novel multi-objective root system growth optimizer (MORSGO) for the copper strip burdening optimization. The MORSGO aims to handle multi-objective problems with satisfactory convergence and diversity via implementing adaptive root growth operators with a pool of multi-objective search rules and strategies. Specifically, the single-objective root growth operators including branching, regrowing and auxin-based tropisms are deliberately designed. They have merits of appropriately balancing exploring & exploiting and self-adaptively varying population size to reduce redundant computation. The effective multi-objective strategies including the fast non-dominated sorting and the farthest-candidate selection are developed for saving and retrieving the Pareto optimal solutions with remarkable approximation as well as uniform spread of Pareto-optimal solutions. With comprehensive evaluation against a suit of benchmark functions, the MORSGO is verified experimentally to be superior or at least comparable to its competitors in terms of the IGD and HV metrics. The MORSGO is then validated to solve the real-world copper strip burdening optimization with different elements. Computation results verifies the potential and effectiveness of the MORSGO to resolve complex industrial process optimization.     

The design and implementation of parametric types in Pascal

Parametric types offer an attractive solution to the problems of dealing with arrays in Pascal. These problems arise from the use of strong, static type checking, especially of array-type procedure arguments. Parametric types provide solutions both for the array procedure argument problem and allow the consistent inclusion of arrays with dynamic bounds. A parametric type mechanism is proposed and design issues are discussed. The inclusion of parametric types has major effects on the implementation of a language like Pascal. The implementation issues and implementation versus design tradeoffs are examined. The implementation strategy used can be extended to accommodate the standard and generic types in Ada.     

基于参数方程处理等式约束优化的粒子群算法

针对目前已有的粒子群优化算法求解有等式约束优化问题时对收敛速度和解的精度的影响,提出了一种新的基于参数方程的粒子群优化算法.它是粒子群在初始化和选代进化过程中使用求解参数方程的方法处理等式约束设计出的粒子群优化算法.数值实验结果表明,新算法是有效的.它不仅提高了收敛速度和解的精度,而且是一种通用的智能算法.     

UXDs-driven conceptual design process model for contradiction solving using CAIs

Design is situational, which means the explicit consideration of the state of the environment, the knowledge and experience of the designer, and the interaction between the designer and the environment during designing interact. When computer-aided innovation systems (CAIs) are applied to the design, the environment and the situation are different from the traditional design process and environment. The basic principles of some CAIs available in the world market are directly related to theory of inventive problem solving (TRIZ). Special TRIZ solutions, which have a few inventive principles and the related cases for contradiction problem solving, are medium-solutions to domain problems. The second stage analogy process is used to generate domain solutions and in this process, the TRIZ solutions are used as source designs of analogy-based process. Unexpected discoveries (UXDs) are the key factors to trigger designers to generate new ideas for domain solutions. The type of UXDs for the specific TRIZ solutions is studied and a UXDs-driven contradiction solving for conceptual design is formed. A case study shows the application of the process step by step.     

A new algorithm for solving convex parametric quadratic programs based on graphical derivatives of solution mappings

In this paper we derive formulas for computing graphical derivatives of the (possibly multivalued) solution mapping for convex parametric quadratic programs. Parametric programming has recently received much attention in the control community, however most algorithms are based on the restrictive assumption that the so called critical regions of the solution form a polyhedral subdivision, i.e. the intersection of two critical regions is either empty or a face of both regions. Based on the theoretical results of this paper, we relax this assumption and show how we can efficiently compute all adjacent full dimensional critical regions along a facet of an already discovered critical region. Coupling the proposed approach with the graph traversal paradigm, we obtain very efficient algorithms for the solution of parametric convex quadratic programs.     

Optimizing reliability-based robust design model using multi-objective genetic algorithm

Reliability-based robust design optimization (RBRDO) is one of the most important tools developed in recent years to improve both quality and reliability of the products at an early design stage. This paper presents a comparative study of different formulation approaches of RBRDO models and their performances. The paper also proposes an evolutionary multi-objective genetic algorithm (MOGA) to one of the promising hybrid quality loss functions (HQLF)-based RBRDO model. The enhanced effectiveness of the HQLF-based RBRDO model is demonstrated by optimizing suitable examples.     

An interactive method for the selection of design criteria and the formulation of optimization problems in computer aided optimal design

This paper presents an interactive method for the selection of design criteria and the formulation of optimization problems within a computer aided optimization process of engineering systems. The key component of the proposed method is the formulation of an inverse optimization problem for the purpose of determining the design preferences of the engineer. These preferences are identified based on an interactive modification of a preliminary optimization result that is the solution of an initial problem statement. A formulation of the inverse optimization problem is presented, which is based on a weighted-sum multi-objective approach and leads to an explicit optimization problem that is computationally inexpensive to solve. Numerical studies on structural shape optimization problems show that the proposed method is able to identify the optimization criteria and the formulation of the optimization problem which drive the interactive user modifications.