Cost-based, integrated design optimization

Prompted by a shift in design philosophy from product performance to cost-effectiveness, the present work addresses issues pertaining to the evaluation of cost during design and its subsequent incorporation in the design optimization process. Various cost modeling methodologies as applicable to engineering design are studied. Following a comparison of the performance-oriented and cost-driven approaches to design optimization, a novel, unified approach termed design-for-integrated-cost-and-performance is developed. Moreover, focusing mainly on structural design, implications of the simultaneous design paradigm, which extends the design process beyond its conventional boundaries, are highlighted by considering manufacturing and fabrication constraints alongside the typical structural requirements such as mass, stiffness, or strength.     

Imparting desired attributes in structural design by means of multi-objective optimization

Commonly available optimization methods typically produce a single optimal design as a constrained minimum of a particular objective function. However, in engineering design practice it is quite often important to explore as much of the design space as possible, with respect to many attributes, to discover what behaviors are possible and not possible within the initially adopted design concept. This paper shows that the very simple method of the sum of weighted objectives is useful for such exploration. By geometrical argument it is demonstrated that if every weighting coefficient is allowed to change its magnitude and its sign then the method returns a set of designs that are all feasible, diverse in their attributes, and include the Pareto and non-Pareto solutions, at least for convex cases. Numerical examples in the paper include the case of an aircraft wing structural box with thousands of degrees of freedom and constraints, and over 100 design variables, whose attributes are structural mass, volume, displacement, and frequency. The weighted coefficients method is inherently suitable for parallel, coarse-grained implementation that enables exploration of the design space in the elapsed time of a single structural optimization.     

Structural optimization based on topology optimization techniques using frame elements considering cross-sectional properties

This paper discusses a new structural optimization method, based on topology optimization techniques, using frame elements where the cross-sectional properties can be treated as design variables. For each of the frame elements, the rotational angle denoting the principal direction of the second moment of inertia is included as a design variable, and a procedure to obtain the optimal angle is derived from Karush–Kuhn–Tucker (KKT) conditions and a complementary strain energy-based approach. Based on the above, the optimal rotational angle of each frame element is obtained as a function of the balance of the internal moments. The above methodologies are applied to problems of minimizing the mean compliance and maximizing the eigen frequencies. Several examples are provided to show the utility of the presented methodology.     

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.     

A multi-objective optimization for green supply chain network design

In this paper, we study a supply chain network design problem with environmental concerns. We are interested in the environmental investments decisions in the design phase and propose a multi-objective optimization model that captures the trade-off between the total cost and the environment influence. We conduct a comprehensive set of numerical experiments. The results show that our model can be applied as an effective tool in the strategic planning for green supply chain. Meanwhile, the sensitivity analysis provides some interesting managerial insights for firms.     

An open platform of shape design optimization for shell structure

A general platform built on a computer-aided design (CAD) system is developed for parameterized shape design optimization of shell structure. Within the platform, parameterized surface modeling and computer-aided engineering (CAE) applications are embedded and seamlessly integrated with the CAD system through its application programming interface (API). Firstly, instead of the CAD system inherent surface modeling, a parameterized surface modeling for shell structure is fulfilled through integrating with parametric solid modeling of the CAD system. Thus, any dimensions for parametric solid modeling can be used to control shape modification of shell structure and serve as design variables for shape design optimization. Secondly, seamless integration of geometry modeling and finite-element modeling for shell structure is implemented. Finally, with integrated procedures of finite-element analysis and optimization algorithms, a general platform for parameterized shape optimization of shell structure is realized. Numerical examples are presented, and the results validate the effectiveness and efficiency of the platform. A shorten version of this paper was presented to the 7th World Congress of Computation Mechanics (WCCM 2006), July 16–22, 2006, Los Angeles, CA, USA.     

基于改进PSO算法的嵌套环式微陀螺结构优化设计

摘要：改变嵌套环陀螺的结构设计会引起陀螺性能发生很大的改变,但由于其结构复杂,参数众多,导致陀螺在仿真过程中计算量过大,难以探索陀螺多参数变量对陀螺性能的影响规律,针对这一问题提出了一种基于改进PSO算法的嵌套环陀螺结构优化设计方法。该方法在传统PSO算法寻优的基础上,引入极值扰动来避免算法陷入局部极值,并针对嵌套环陀螺进行了一定的条件约束,解决了多参数在总和固定情况下的优化问题。改进后的优化算法以机械热噪声为目标函数,在波音设计的陀螺模型基础上对其间隙分布进行了优化实验,并与未优化前进行了性能对比,结果表明,改进后的优化算法使嵌套环陀螺性能显著提高,结构优化设计更加高效简洁,适用于嵌套环陀螺进行各种多参数的优化问题。     

Improved hybrid method as a robust tool for reliability-based design optimization

In the engineering problems, the randomness and the uncertainties of the distribution of the structural parameters are a crucial problem. In the case of reliability-based design optimization (RBDO), it is the objective to play a dominant role in the structural optimization problem introducing the reliability concept. The RBDO problem is often formulated as a minimization of the initial structural cost under constraints imposed on the values of elemental reliability indices corresponding to various limit states. The classical RBDO leads to high computing time and weak convergence, but a Hybrid Method (HM) has been proposed to overcome these two drawbacks. As the hybrid method successfully reduces the computing time, we can increase the number of variables by introducing the standard deviations as optimization variables to minimize the error values in the probabilistic model. The efficiency of the hybrid method has been demonstrated on static and dynamic cases with extension to the variability of the probabilistic model. In this paper, we propose a modification on the formulation of the hybrid method to improve the optimal solutions. The proposed method is called, Improved Hybrid Method (IHM). The main benefit of this method is to improve the structure performance by much more minimizing the objective function than the hybrid method. It is also shown to demonstrate the optimality conditions. The improved hybrid method is next applied to two numerical examples, with consideration of the standard deviations as optimization variables (for linear and nonlinear distributions). When integrating the improved hybrid method within the probabilistic model variability, we minimize the objective function more and more.     

On some applications of ant colony optimization metaheuristic to plane truss optimization

Ant colony optimization metaheuristic (ACO) represents a new class of algorithms particularly suited to solve real-world combinatorial optimization problems. ACO algorithms, published for the first time in 1991 by M. Dorigo [Optimization, learning and natural algorithms (in Italian). Ph.D. Thesis, Dipartimento di Elettronica, Politecnico di Milano, Milan, 1992] and his coworkers, have been applied, particularly starting from 1999 (Bonabeau et al., Swarm intelligence: from natural to artificial systems, Oxford University Press, New York, 1999; Dorigo et al., Artificial life 5(2):137–172, 1999; Dorigo and Di Caro, Ant colony optimization: a new metaheuristic, IEEE Press, Piscataway, NJ, 1999; Dorigo et al., Ant colony optimization and swarm intelligence, Springer, Berlin Heidelberg New York, 2004; Dorigo and Stutzle, Ant colony optimization, MIT Press, Cambridge, MA, 2004), to several kinds of optimization problems such as the traveling salesman problem, quadratic assignment problem, vehicle routing, sequential ordering, scheduling, graph coloring, management of communications networks, and so on. The ant colony optimization metaheuristic takes inspiration from the studies of real ant colonies’ foraging behavior. The main characteristic of such colonies is that individuals have no global knowledge of problem solving but communicate indirectly among themselves, depositing on the ground a chemical substance called pheromone, which influences probabilistically the choice of subsequent ants, which tend to follow paths where the pheromone concentration is higher. Such behavior, called stigmergy, is the basic mechanism that controls ant activity and permits them to take the shortest path connecting their nest to a food source. In this paper, it is shown how to convert natural ant behavior to algorithms able to escape from local minima and find global minimum solutions to constrained combinatorial problems. Some examples on plane trusses are also presented.     

Design process and data models to support the design of sustainable remanufactured products

The need for increased levels of reuse and remanufacturing is driving the need for sustainable design of remanufactured products. It is acknowledged that design for remanufacturing benefits the environment. However, it seldom integrates eco-design approaches as it requires ‘life cycle thinking’ with closed-loop life cycles. The objective of this paper is to support eco-design of remanufactured products with design process and data models structuring the activities to be performed and providing the support required. We consider the development of two activities in particular: definition of the target, and environmental analysis. The first activity exploits the concept of RPP (Remanufacturable Product Profile), building on the criteria that are crucial for a successful remanufactured product. The second one exploits the life cycle brick concept that associates each product component with a specific life cycle and related environmental impacts. The models proposed are exploited in a case study concerning the design of remanufactured truck gearboxes.     

Economic performance analysis in the design of on-line batch optimization systems

In this paper, the on-line optimization of batch reactors under parametric uncertainty is considered. A method is presented that estimates the likely economic performance of the on-line optimizer. The method of orthogonal collocation is employed to convert the differential algebraic optimization problem (DAOP) of the dynamic optimization into a nonlinear program (NLP) and determine the nominal optimum. Based on the resulting NLP, the optimization steps are approximated by neighbouring extremal problems and the average deviation from the true process optimum is estimated dependent on the measurement error and the parametric uncertainty. The true process optimum is assumed to be represented by the optimum of the process model with the true parameter values. A back off from the active path and endpoint inequality constraints is determined at each optimization step which ensures the feasible operation of the process. Based on the analysis results the optimal structure of the optimizer in terms of measured variables and estimated parameters can be determined. The method of the average deviation from optimum is developed for the fixed terminal time case and for time optimal problems. In both cases, the theory is demonstrated on an example.     

An elitist self-adaptive step-size search for structural design optimization

This paper presents a method for optimal sizing of truss structures based on a refined self-adaptive step-size search (SASS) algorithm. An elitist self-adaptive step-size search (ESASS) algorithm is proposed wherein two approaches are considered for improving (i) convergence accuracy, and (ii) computational efficiency. In the first approach an additional randomness is incorporated into the sampling step of the technique to preserve exploration capability of the algorithm during the optimization. Furthermore, an adaptive sampling scheme is introduced to enhance quality of the final solutions. In the second approach computational efficiency of the technique is accelerated through avoiding unnecessary analyses throughout the optimization process using the so-called upper bound strategy (UBS). The numerical results indicate the efficiency of the proposed ESASS algorithm.     

A level-set based variational method for design and optimization of heterogeneous objects

A heterogeneous object is referred to as a solid object made of different constituent materials. The object is of a finite collection of regions of a set of prescribed material classes of continuously varying material properties. These properties have a discontinuous change across the interface of the material regions. In this paper, we propose a level-set based variational approach for the design of this class of heterogeneous objects. Central to the approach is a variational framework for a well-posed formulation of the design problem. In particular, we adapt the Mumford-Shah model which specifies that any point of the object belongs to either of two types: inside a material region of a well-defined gradient or on the boundary edges and surfaces of discontinuities. Furthermore, the set of discontinuities is represented implicitly, using a multi-phase level set model. This level-set based variational approach yields a computational system of coupled geometric evolution and diffusion partial differential equations. Promising features of the proposed method include strong regularity in the problem formulation and inherent capabilities of geometric and material modeling, yielding a common framework for optimization of the heterogeneous objects that incorporates dimension, shape, topology, and material properties. The proposed method is illustrated with several 2D examples of optimal design of multi-material structures and materials.     

A novel optimization approach for minimum cost design of trusses

This paper describes new optimization strategies that offer significant improvements in performance over existing methods for bridge-truss design. In this study, a real-world cost function that consists of costs on the weight of the truss and the number of products in the design is considered. We propose a new sizing approach that involves two algorithms applied in sequence – (1) a novel approach to generate a “good” initial solution and (2) a local search that attempts to generate the optimal solution by starting with the final solution from the previous algorithm. A clustering technique, which identifies members that are likely to have the same product type, is used with cost functions that consider a cost on the number of products. The proposed approach gives solutions that are much lower in cost compared to those generated in a comprehensive study of the same problem using genetic algorithms (GA). Also, the number of evaluations needed to arrive at the optimal solution is an order of magnitude lower than that needed in GAs. Since existing optimization techniques use cost functions like those of minimum-weight truss problems to illustrate their performance, the proposed approach is also applied to the same examples in order to compare its relative performance. The proposed approach is shown to generate solutions of not only better quality but also much more efficiently. To highlight the use of this sizing approach in a broader optimization framework, a simple geometry optimization algorithm that uses the sizing approach is presented. This algorithm is also shown to provide solutions better than the existing results in literature.     

Structural optimization of as-built parts using reverse engineering and evolution strategies

In industry, some parts are prone to failures or their design is simply sub-optimal. In those critical situations, one would like to be able to make changes to the part, making it lighter or improving its mechanical resistance. The problem of as-built parts is that the original computer-aided design (CAD) model is not available or is lost. To optimize them, a reverse engineering process is necessary to capture the shape and topology of the original design. This paper describes how to capture the original design geometry using a semi-automated reverse engineering process based on measurement provided by an optical 3D sensor. Following this reverse engineering process, a Fixed Grid Finite Element method and evolutionary algorithms are used to find the optimum shape that will minimize stress and weight. Several examples of industrial parts are presented. These examples show the advantages and disadvantages of the proposed method in an industrial scenario. Presented at the 7th World Congress on Computational Mechanics, Los Angeles 2006.     

Hybrid evolutionary algorithm and application to structural optimization

This paper introduces a new evolutionary algorithm with a globally stochastic but locally heuristic search strategy. It is implemented by incorporating a modified micro-genetic algorithm with two local optimization operators. Performance tests using two benchmarking functions demonstrate that the new algorithm has excellent convergence performance when applied to multimodal optimization problems. The number of objective function evaluations required to obtain global optima is only 3.5–3.7% of that of using the conventional micro-genetic algorithm. The new algorithm is used to optimize the design of an 18-bar truss, with the aim of minimizing its weight while meeting the stress, section area, and geometry constraints. The corresponding optimal design is obtained with considerably fewer computational operations than required for the existing algorithms.