Multi-objective design optimization of variable stiffness composite cylinders

The bending-induced buckling improvement in a variable stiffness (VS) composite cylinder (made by fiber steering) is studied. For such a cylinder, the effect of the variation of the direction of the load on its buckling performance of the cylinder is also examined. Compromise programming, as a multi-objective optimization method, is used to design for buckling of the VS cylinder subjected to bending load in either of the two opposite directions. Different combinations of weight factors for the structural performance in the two opposite directions were also applied to obtain the Pareto frontier as the main decision making tool for the designers in a multi-objective design problem.     

Surrogate-based multi-objective optimization of a composite laminate with curvilinear fibers

A variable stiffness design can increase the structural performance of a composite plate and provides flexibility for trade-offs between structural properties. In this paper, we examine the simultaneous optimization of stiffness and buckling load of a composite laminate plate with curvilinear fiber paths. The problem, which falls in the area of multi-objective optimization, is formulated and solved through a surrogate-based optimization algorithm capable of finding the set of optimum Pareto solutions. We integrate surrogate modeling into an evolutionary algorithm to reduce the high computational cost required to solve the optimization process. The results show that a curvilinear fiber path can increase both buckling load and stiffness simultaneously over the quasi-isotropic laminate. Furthermore, the optimum direction for varying the fiber angle is dependent on the loading direction and boundary conditions. The results for a plate under uniform compression with free transverse edges shows that varying the fiber orientation perpendicular to the loading direction can increase the buckling load by 116% with respect to that of a quasi-isotropic laminate.     

Topology optimization of structures under multiple loading cases with a new compliance–volume product

This article proposes a new topology optimization method for the design of structures under multiple loading cases. The design is formulated as a multi-objective optimization problem by minimizing a new compliance–volume product, which optimizes the overall stiffness and volume simultaneously to avoid the empirical decision on design constraints and obtain an even lower structural volume. A normalized exponential weighted criterion (NEWC) method is included in the multi-objective optimization problem for the capture of the entire Pareto frontier. A weight evaluation method, in terms of the fuzzy multiple-attribute group decision-making (FMAGDM) theory, is incorporated in the problem to evaluate the weights of the objectives and guarantee the optimal design in an acceptable level. The solid isotropic material with penalty (SIMP) method is used to represent the dependence of elemental densities on material properties. Three typical numerical examples are employed to show the effectiveness of the proposed method.     

Efficient Pareto Frontier Exploration using Surrogate Approximations

In this paper we present an efficient and effective method of using surrogate approximations to explore the design space and capture the Pareto frontier during multiobjective optimization. The method employs design of experiments and metamodeling techniques (e.g., response surfaces and kriging models) to sample the design space, construct global approximations from the sample data, and quickly explore the design space to obtain the Pareto frontier without specifying weights for the objectives or using any optimization. To demonstrate the method, two mathematical example problems are presented. The results indicate that the proposed method is effective at capturing convex and concave Pareto frontiers even when discontinuities are present. After validating the method on the two mathematical examples, a design application involving the multiobjective optimization of a piezoelectric bimorph grasper is presented. The method facilitates multiobjective optimization by enabling us to efficiently and effectively obtain the Pareto frontier and identify candidate designs for the given design requirements.     

基于统计提升准则的注塑工艺参数优化

为了同时改善生产平板型注塑制品时的总体收缩度和收缩均匀度,提出基于统计提升准则的注塑成型工艺参数的多目标优化方法,寻找平衡两个质量指标的优化设计.首先利用小规模的实验设计方法获得建模数据集,针对应用中存在的建模数据奇异点问题提出一种数据预处理方法,并依此分别建立两个指标的初始替代模型,用于代替优化过程中代价高昂的计算分析;随后依据Pareto统计提升准则寻找新的采样点加入建模数据集来重新建模,使寻优结果不断趋近真实的Pareto前沿.仿真结果表明,较常规的建模优化方法,本文提出的方法能使用较少的采样数据,显著地改善平板制品的收缩质量.对于HDPE材质的矩形制品,保压曲线先恒定后线性递减可以获得好的收缩均匀度,使用压力上限值恒定保压可以获得好的平均收缩度.     

Pareto optimization using the struggle genetic crowding algorithm

Many real-world engineering design problems involve the simultaneous optimization of several conflicting objectives. In this paper, a method combining the struggle genetic crowding algorithm with Pareto-based population ranking is proposed to elicit trade-off frontiers. The new method has been tested on a variety of published problems, reliably locating both discontinuous Pareto frontiers as well as multiple Pareto frontiers in multi-modal search spaces. Other published multi-objective genetic algorithms are less robust in locating both global and local Pareto frontiers in a single optimization. For example, in a multi-modal test problem a previously published non-dominated sorting GA (NSGA) located the global Pareto frontier in 41% of the optimizations, while the proposed method located both global and local frontiers in all test runs. Additionally, the algorithm requires little problem specific tuning of parameters.     

基于密度分布曲线法的复合材料变刚度铺层优化

基于梯度的优化方法对复合材料层合板进行了变刚度铺层优化设计。在优化过程中需确定铺层中各单元的密度以及角度。为了使优化结果具有可制造性,优化结果需满足制造工艺约束并且铺层角度需从预定角度中选取。为了避免在优化问题中引入过多的约束并减少设计变量的数目,提出密度分布曲线法(DDCM)对层合板中各单元的密度进行参数化。根据各单元的密度以及角度设计变量并基于Bi-value Coding Parameterization(BCP)方法中的插值公式确定各单元的弹性矩阵。优化过程中以结构柔顺度作为优化目标,结构体积作为约束,优化算法采用凸规划对偶算法。对碳纤维复合材料的算例结果表明:采用DDCM可得到较理想的优化结果,并且收敛速率较快。     

Usage scenarios for design space exploration with a dynamic multiobjective optimization formulation

In a recent publication, we presented a new strategy for engineering design and optimization, which we termed formulation space exploration. The formulation space for an optimization problem is the union of all variable and design objective spaces identified by the designer as being valid and pragmatic problem formulations. By extending a computational search into this new space, the solution to any optimization problem is no longer predefined by the optimization problem formulation. This method allows a designer to both diverge the design space during conceptual design and converge onto a solution as more information about the design objectives and constraints becomes available. Additionally, we introduced a new way to formulate multiobjective optimization problems, allowing the designer to change and update design objectives, constraints, and variables in a simple, fluid manner that promotes exploration. In this paper, we investigate three usage scenarios where formulation space exploration can be utilized in the early stages of design when it is possible to make the greatest contributions to development projects. Specifically, we look at formulation space boundary exploration, Pareto frontier generation for multiple concepts in the formulation space, and a new way to perform targeted boundary expansion. The benefits of these methods are illustrated with the conceptual design of an impact driver.     

Minimum cost and weight design of fuselage frames: Part B: cost considerations,optimization, and results

An approach is presented to design fuselage frames for minimum weight, minimum cost, or a combination of the two. The approach combines structural requirements and manufacturing constraints into an optimization scheme that alters the geometry of the individual frame components until the objective function is minimized. In addition to the lowest weight and cost points, a near-optimal Pareto set of designs is found, out of which the design that minimizes both cost and weight is determined through a penalty function approach. Four different fabrication processes are considered: conventional sheet metal, high speed machined metal, hand laid-up composite, and resin transfer molded composite. For lightly loaded frames, an automated resin transfer molding process gives the lowest cost and weight designs. For highly loaded frames, high speed machining gives the lowest cost design but automated resin transfer molding gives the lowest weight design. The effects of fabrication process and some of the design and manufacturing constraints on cost and weight are examined.     

Multi-objective genetic algorithm for solving N-version program design problem

N-version programming (NVP) is a programming approach for constructing fault tolerant software systems. Generally, an optimization model utilized in NVP selects the optimal set of versions for each module to maximize the system reliability and to constrain the total cost to remain within a given budget. In such a model, while the number of versions included in the obtained solution is generally reduced, the budget restriction may be so rigid that it may fail to find the optimal solution. In order to ameliorate this problem, this paper proposes a novel bi-objective optimization model that maximizes the system reliability and minimizes the system total cost for designing N-version software systems. When solving multi-objective optimization problem, it is crucial to find Pareto solutions. It is, however, not easy to obtain them. In this paper, we propose a novel bi-objective optimization model that obtains many Pareto solutions efficiently.We formulate the optimal design problem of NVP as a bi-objective 0–1 nonlinear integer programming problem. In order to overcome this problem, we propose a Multi-objective genetic algorithm (MOGA), which is a powerful, though time-consuming, method to solve multi-objective optimization problems. When implementing genetic algorithm (GA), the use of an appropriate genetic representation scheme is one of the most important issues to obtain good performance. We employ random-key representation in our MOGA to find many Pareto solutions spaced as evenly as possible along the Pareto frontier. To pursue improve further performance, we introduce elitism, the Pareto-insertion and the Pareto-deletion operations based on distance between Pareto solutions in the selection process.The proposed MOGA obtains many Pareto solutions along the Pareto frontier evenly. The user of the MOGA can select the best compromise solution among the candidates by controlling the balance between the system reliability and the total cost.     

Particle swarm-based structural optimization of laminated composite hydrokinetic turbine blades

Composite blade manufacturing for hydrokinetic turbine application is quite complex and requires extensive optimization studies in terms of material selection, number of layers, stacking sequence, ply thickness and orientation. To avoid a repetitive trial-and-error method process, hydrokinetic turbine blade structural optimization using particle swarm optimization was proposed to perform detailed composite lay-up optimization. Layer numbers, ply thickness and ply orientations were optimized using standard particle swarm optimization to minimize the weight of the composite blade while satisfying failure evaluation. To address the discrete combinatorial optimization problem of blade stacking sequence, a novel permutation discrete particle swarm optimization model was also developed to maximize the out-of-plane load-carrying capability of the composite blade. A composite blade design with significant material saving and satisfactory performance was presented. The proposed methodology offers an alternative and efficient design solution to composite structural optimization which involves complex loading and multiple discrete and combinatorial design parameters.     

Multi-objective scheduling problems: Determination of pruned Pareto sets

There are often multiple competing objectives for industrial scheduling and production planning problems. Two practical methods are presented to efficiently identify promising solutions from among a Pareto optimal set for multi-objective scheduling problems. Generally, multi-objective optimization problems can be solved by combining the objectives into a single objective using equivalent cost conversions, utility theory, etc., or by determination of a Pareto optimal set. Pareto optimal sets or representative subsets can be found by using a multi-objective genetic algorithm or by other means. Then, in practice, the decision maker ultimately has to select one solution from this set for system implementation. However, the Pareto optimal set is often large and cumbersome, making the post-Pareto analysis phase potentially difficult, especially as the number of objectives increase. Our research involves the post Pareto analysis phase, and two methods are presented to filter the Pareto optimal set to determine a subset of promising or desirable solutions. The first method is pruning using non-numerical objective function ranking preferences. The second approach involves pruning by using data clustering. The k-means algorithm is used to find clusters of similar solutions in the Pareto optimal set. The clustered data allows the decision maker to have just k general solutions from which to choose. These methods are general, and they are demonstrated using two multi-objective problems involving the scheduling of the bottleneck operation of a printed wiring board manufacturing line and a more general scheduling problem.     

Pareto Frontier Based Concept Selection Under Uncertainty,with Visualization

In a recent publication, we presented a new multiobjective decision-making tool for use in conceptual engineering design. In the present paper, we provide important developments that support the next phase in the evolution of the tool. These developments, together with those of our previous work, provide a concept selection approach that capitalizes on the benefits of computational optimization. Specifically, the new approach uses the efficiency and effectiveness of optimization to rapidly compare numerous designs, and characterize the tradeoff properties within the multiobjective design space. As such, the new approach differs significantly from traditional (non-optimization based) concept selection approaches where, comparatively speaking, significant time is often spent evaluating only a few points in the design space. Under the new approach, design concepts are evaluated using a so-calleds-Pareto frontier; this frontier originates from the Pareto frontiers of various concepts, and is the Pareto frontier for thesetof design concepts. An important characteristic of the s-Pareto frontier is that it provides a foundation for analyzing tradeoffs between design objectives and the tradeoffs between design concepts. The new developments presented in this paper include; (i) the notion ofminimally representingthe s-Pareto frontier, (ii) the quantification of concept goodness using s-Pareto frontiers, (iii) the development of an interactive design space exploration approach that can be used to visualizen-dimensional s-Pareto frontiers, and (iv) s-Pareto frontier-based approaches for considering uncertainty in concept selection. Simple structural examples are presented that illustrate representative applications of the proposed method.     

Integrated optimization of machine product design and process design

In order to attain the true integration of computer-aided design and computer-aided manufacturing not only is a smooth flow of information required, but also decision making for both product design and process design must be synthesized. In this paper an integrated design process is proposed in which decisions concerning both product design and process design are simultaneously made. According to the proposed design procedures, an integrated optimization problem is formulated. This optimization is expressed as a multiobjective optimization problem which produces many Pareto optimum solution sets corresponding to combinations of materials used for parts. The algorithm for solving the problem is also presented. The proposed method is applied to designing a cylindrical co-ordinate robot, thereby demonstrating the effectiveness of conducting a simultaneous process through product design and process design.     

Computational strategy for multiobjective optimization of composite stiffened panels

This paper presents a multiobjective optimization methodology for composite stiffened panels. The purpose is to improve the performances of an existing design of stiffened composite panels in terms of both its first buckling load and ultimate collapse or failure loads. The design variables are the stacking sequences of the skin and of the stiffeners of the panel. The optimization is performed using a multiobjective evolutionary algorithm specifically developed for the design of laminated parts. The algorithm takes into account the industrial design guidelines for stacking sequence design. An original method is proposed for the initialization of the optimization that significantly accelerates the search for the Pareto front. In order to reduce the calculation time, Radial Basis Functions under Tension are used to approximate the objective functions. Special attention is paid to generalization errors around the optimum. The multiobjective optimization results in a wide set of trade-offs, offering important improvements for both considered objectives, among which the designer can make a choice.     

层合板频率响应与声功率双目标优化设计

利用遗传算法对复合材料层合板结构的固有频率间隔和辐射声功率进行双目标优化设计。利用分层理论结合有限元模型求解层合板的固有频率和振速分布。通过声辐射模态理论,计算层合板结构辐射声功率。以铺设角度作为设计变量,第一阶与第二阶固有频率间隔和辐射声功率作为双目标优化目标函数,以某4层的层合板结构为例,采用目标加权法优化目标函数。研究了不同权重系数、不同频率时固有频率间隔最大化和声功率最小化对应的优化铺设角度。由数值分析结果可知:不同的权重系数比下获得的Pareto最优解不同;在同一权重系数下,两个优化目标所起的作用不尽相同;随着频率的增加,选择相对较大的权重系数可使Pareto最优解较好地兼顾两个优化目标。     

Ultra-efficient wound composite truss structures

This paper presents the design, analysis, manufacturing, experimental testing, and multiobjective optimization of a new family of ultra-efficient composite truss structures. The continuously wound truss concept introduced here is a versatile, low cost and scalable method of manufacturing truss structures based on a simple winding process. A prototype truss configuration is shown and experimentally characterized under torsion and three point bending loads. A large deformation implementation of the direct stiffness method is shown to provide good prediction of the stiffness properties of the prototype truss. This model is extended to include strength prediction with multiple failure modes. The design space achievable with these truss structures is then explored through multiobjective optimization using the NSGA II genetic algorithm. These continuously wound truss structures have the potential to provide between one and two orders of magnitude increase in structural efficiency compared to existing carbon fiber composite tubes.     

A Multi‐Objective Design Approach for the c Chart Considering Taguchi Loss Function

The present paper proposes a multi‐objective design approach for the c chart, considering in the optimization process of the chart parameters both the statistical and the economic objectives. In particular, the minimization of the hourly total quality related costs is the considered objective to carry out the economic goal, whereas the statistical objective is reached by the minimization the out‐of‐control average run length of the chart. A mixed integer non‐linear constrained mathematical model is formulated to solve the treated multi‐objective optimization problem, whereas the Pareto optimal frontier is described by the ε‐constraint method. In order to show the employment of the proposed approach, an illustrative example is developed and the related considerations are given. Finally, some sensitivity analysis is also performed to investigate the effects of operative and costs parameters on the chart performance. Copyright © 2013 John Wiley & Sons, Ltd.