Concurrent optimization of assembly tolerances for quality with position control using scatter search approach

Tolerance allocation to individual parts in any assembly should be a vital design function with which both the design and manufacturing engineers are concerned. Generally design engineers prefer to have tighter tolerances to ensure the quality of their design, whereas manufacturing engineers prefer loose tolerances for ease of production and the need to be economical. This paper introduces a concurrent tolerance approach, which determines optimal product tolerances and minimizes combined manufacturing and quality related costs in the early stages of design. A non-linear multivariable optimization model is formulated here for assembly. A combinatorial optimization problem by treating cost minimization as the objective function and stack-up conditions as the constraints are solved using scatter search algorithm. In order to further explore the influence of geometric tolerances in quality as well as in the manufacturing cost, position control is included in the model. The results show how position control enhances quality and reduces cost.     

Optimization of laminate stacking sequence for failure load maximization using Tabu search

In this paper, design of a laminate is treated as a combinatorial optimization problem. Optimization of the stacking sequence of a laminate for buckling response, matrix cracking, and strength requirements is conducted. Optimum designs are generated using a heuristic search technique known as Tabu search. Preliminary studies used to examine the effect of different aspects of Tabu search are presented. Three load cases, which have been used in previous studies with Genetic Algorithm, were utilized in this work. The relative performance of Tabu search compared to Genetic Algorithm was found to depend on the load case. For the first two cases, and for average of all the three load cases, Tabu search was found to reduce the computing cost of generating equivalent results by 26, 55 and 1%, respectively. For the third load case, the computing cost with Tabu search was higher by 302%.     

A multi-objective scatter search for the ladle scheduling problem

We consider the ladle scheduling problem, which can be regarded as a vehicle routing problem with semi-soft time windows and adjustment times. The problem concerns allocating ladles to serve molten steel based on a given steelmaking scheduling plan, and determining the modification operations for the empty ladles after the service process. In addition, combining the controllable processing time of molten steel, the other aspect of the problem is to determine the service start times taking into consideration the technological constraints imposed in practice. We present a non-linear mathematical programming model with the conflicting objectives of minimising the occupation ratio of the ladles and maximising the degree of satisfaction with meeting the soft windows. To solve the multi-objective model, we develop a new scatter search (SS) approach by re-designing the common components of SS and incorporating a diversification generator, a combination method and a diversification criterion to conduct a wide exploration of the search space. We analyse and compare the performance of the proposed approach with a multi-objective genetic algorithm and with manual scheduling adopted in practical production using three real-life instances from a well-known iron–steel production plant in China. The computational results demonstrate the effectiveness of the proposed SS approach for solving the ladle scheduling problem.     

Automated synthesis of modular fixture designs using an evolutionary search algorithm

Fixture design is a complex problem that requires a designer to ensure that a workpiece is located deterministically, totally restrained and sufficiently supported during a manufacturing process. The use of modular fixtures, while presenting an opportunity to improve the responsiveness of a manufacturing system, adds to the complexity of the fixture design problem. The complexity is a result of the large number of fixture elements in a modular fixture system and the constraints of specified locations in which fixture elements can be placed in a grid-based modular system. This paper presents an evolutionary search algorithm that aids a fixture designer by exploring the large number of possible fixture designs and suggesting an appropriate one. The algorithm can explore the large solution space using a flexible and generic representation and it considers fixture layout and fixture configuration constraints concurrently in arriving at appropriate solutions. The initial results of the algorithm are promising.     

An effective hybrid cuckoo search and genetic algorithm for constrained engineering design optimization

This article presents an effective hybrid cuckoo search and genetic algorithm (HCSGA) for solving engineering design optimization problems involving problem-specific constraints and mixed variables such as integer, discrete and continuous variables. The proposed algorithm, HCSGA, is first applied to 13 standard benchmark constrained optimization functions and subsequently used to solve three well-known design problems reported in the literature. The numerical results obtained by HCSGA show competitive performance with respect to recent algorithms for constrained design optimization problems.     

A multi-objective scatter search for a bi-criteria no-wait flow shop scheduling problem

The flow shop problem as a typical manufacturing challenge has gained wide attention in academic fields. This article considers a bi-criteria no-wait flow shop scheduling problem (FSSP) in which weighted mean completion time and weighted mean tardiness are to be minimized simultaneously. Since a FSSP has been proved to be NP-hard in a strong sense, a new multi-objective scatter search (MOSS) is designed for finding the locally Pareto-optimal frontier of the problem. To prove the efficiency of the proposed algorithm, various test problems are solved and the reliability of the proposed algorithm, based on some comparison metrics, is compared with a distinguished multi-objective genetic algorithm (GA), i.e. SPEA-II. The computational results show that the proposed MOSS performs better than the above GA, especially for the large-sized problems.     

A scatter search for the extended resource renting problem

In this paper, the extended Resource Renting Problem (RRP/extended) is presented. The RRP/extended is a time-constrained project scheduling problem, in which the total project cost is minimised. In the RRP/extended, this total project cost is determined by a number of extra costs, which are defined in this paper. These costs are based on the costs that are used in the traditional Resource Renting Problem and the Total Adjustment Cost Problem. Therefore, the RRP/extended represents a union of these two problems. To solve the RRP/extended, a scatter search is developed. The building blocks of this scatter search are specifically designed for the RRP/extended. We introduce two crossovers and an improvement method. The efficiency of these building blocks will be shown in the paper. Furthermore, a sensitivity analysis is presented in which the five costs have diverse values.     

基于连续函数优化的禁忌搜索算法

提出了一种连续禁忌搜索算法,用于求解连续函数优化问题.邻域规则及禁忌规则是禁忌搜索算法的核心,针对连续函数解空间的连续性,提出了一种邻域分割法来进行邻域搜索,并对禁忌规则进行了设计.通过经典函数测试可以看出,禁忌搜索算法在连续函数优化问题中显示出很强的"爬山"能力,优化结果与实际最优值非常接近,是一种有效的全局优化算法.     

Scatter search heuristic for least-cost design of water distribution networks

The optimization problems of water distribution networks are complex, multi-modal and discrete-variable problems that cannot be easily solved with conventional optimization algorithms. Heuristic algorithms such as genetic algorithms, simulated annealing, tabu search and ant colony optimization have been extensively employed over the last decade. This article proposed an optimization procedure based on the scatter search (SS) framework, which is also a heuristic algorithm, to obtain the least-cost designs of three well-known looped water distribution networks (two-loop, Hanoi and New York networks). The computational results obtained with the three benchmark instances indicate that SS is able to find solutions comparable to those provided by some of the most competitive algorithms published in the literature.     

Damage in NCF composites under tension: Effect of layer stacking sequence

Non-crimp fabric (NCF) cross-ply composites response to tensile loading is investigated showing large effect of the fabric layer stacking sequence: much larger elastic modulus reduction was observed in [0/90/0/90]_S than in [90/0/90/0]_S case. Since transverse cracks in 90°-bundles may give modulus decrease about 5%, the observed 40% stiffness reduction is attributed to failure and delamination of bundles oriented in the direction of the applied load. Analysis of micrographs shows extensive delaminations and 0°-bundle breaks. FE calculations showed that failure of 0°-bundles at the surface is energetically more favorable. However, the fracture resistance of surface bundles is higher due to smaller bundle waviness and the density of bundle cracks on the surface was not larger than inside.Two possible reasons for the higher stiffness reduction in the [0/90/0/90]_S NCF composite were suggested: (a) If two imperfect 0°-bundle layers are separated by a 90°-bundle layer their resistance to failure is lower than when they are situated next to each other; (b) the effect of each surface 0°-bundle break on the composite stiffness is larger (due to less constraint from the surrounding material the opening of surface bundle breaks is much larger).     

A constrained optimization algorithm based on the simplex search method

In this article, a robust method is presented for handling constraints with the Nelder and Mead simplex search method, which is a direct search algorithm for multidimensional unconstrained optimization. The proposed method is free from the limitations of previous attempts that demand the initial simplex to be feasible or a projection of infeasible points to the nonlinear constraint boundaries. The method is tested on several benchmark problems and the results are compared with various evolutionary algorithms available in the literature. The proposed method is found to be competitive with respect to the existing algorithms in terms of effectiveness and efficiency.     

Optimization of hybrid laminated composites using the multi-objective gravitational search algorithm (MOGSA)

The multi-objective gravitational search algorithm (MOGSA) technique is applied to hybrid laminates to achieve minimum weight and cost. The investigated laminate is made of glass–epoxy and carbon–epoxy plies to combine the economical attributes of the first with the light weight and high-stiffness properties of the second in order to make the trade-off between the cost and weight as the objective functions. The first natural flexural frequency was considered as a constraint. The results obtained using the MOGSA, including the Pareto set, optimum stacking sequences and number of plies made of either glass or carbon fibres, were compared with those using the genetic algorithm (GA) and ant colony optimization (ACO) reported in the literature. The comparisons confirmed the advantages of hybridization and showed that the MOGSA outperformed the GA and ACO in terms of the functions’ value and constraint accuracy.     

A search game model of the scatter hoarder's problem

Scatter hoarders are animals (e.g. squirrels) who cache food (nuts) over a number of sites for later collection. A certain minimum amount of food must be recovered, possibly after pilfering by another animal, in order to survive the winter. An optimal caching strategy is one that maximizes the survival probability, given worst case behaviour of the pilferer. We modify certain ‘accumulation games’ studied by Kikuta & Ruckle (2000 J. Optim. Theory Appl.) and Kikuta & Ruckle (2001 Naval Res. Logist.), which modelled the problem of optimal diversification of resources against catastrophic loss, to include the depth at which the food is hidden at each caching site. Optimal caching strategies can then be determined as equilibria in a new ‘caching game’. We show how the distribution of food over sites and the site-depths of the optimal caching varies with the animal''s survival requirements and the amount of pilfering. We show that in some cases, ‘decoy nuts’ are required to be placed above other nuts that are buried further down at the same site. Methods from the field of search games are used. Some empirically observed behaviour can be shown to be optimal in our model.     

A level set model for simulating fatigue-driven delamination in composites

This paper proposes a level set model for simulating delamination propagation in composites under high-cycle fatigue loading. For quasi-static loading conditions, interface elements with a cohesive law are widely used for the simulation of delamination. However, basic concepts from fatigue analysis such as the notion that the crack growth rate is a function of energy release rate cannot be embedded in existing cohesive laws. Therefore, we propose a model in which the cohesive zone is eliminated from the computation while maintaining the flexibility that the crack shape is not bound to element edges. The model is able to predict the delamination growth rate and its front shape accurately. To demonstrate the validity of the model, several tests under different fracture modes are conducted and the results are compared with experimental data, analytical solutions and results from cohesive zone analysis.     

A surrogate assisted parallel multiobjective evolutionary algorithm for robust engineering design

A number of multi-objective evolutionary algorithms have been proposed in recent years and many of them have been used to solve engineering design optimization problems. However, designs need to be robust for real-life implementation, i.e. performance should not degrade substantially under expected variations in the variable values or operating conditions. Solutions of constrained robust design optimization problems should not be too close to the constraint boundaries so that they remain feasible under expected variations. A robust design optimization problem is far more computationally expensive than a design optimization problem as neighbourhood assessments of every solution are required to compute the performance variance and to ensure neighbourhood feasibility. A framework for robust design optimization using a surrogate model for neighbourhood assessments is introduced in this article. The robust design optimization problem is modelled as a multi-objective optimization problem with the aim of simultaneously maximizing performance and minimizing performance variance. A modified constraint-handling scheme is implemented to deal with neighbourhood feasibility. A radial basis function (RBF) network is used as a surrogate model and the accuracy of this model is maintained via periodic retraining. In addition to using surrogates to reduce computational time, the algorithm has been implemented on multiple processors using a master–slave topology. The preliminary results of two constrained robust design optimization problems indicate that substantial savings in the actual number of function evaluations are possible while maintaining an acceptable level of solution quality.     

A three-dimensional micromechanical model to predict the viscoelastic behavior of woven composites

Polymer matrix based cloth composites are increasingly used in engineering applications. For such composites, significant viscoelastic behavior can be observed for dynamic load conditions. The viscoelastic effect is primarily due to the polymeric matrix used as most of the fibers used in structural applications are elastic. Matrix does not show a major contribution in the axial properties of composites, thus in the traditional modeling its viscoelastic nature is often ignored. However, the effective out of plane properties are influenced by the matrix material and exhibit significant damping characteristics. Therefore, a complete three-dimensional (3-D) model considering the viscoelastic nature of matrix is needed for better understanding of cloth composites. An analytical 3-D micromechanical model based on classical laminate theory (CLT) is verified, in this paper for the prediction of effective elastic and viscoelastic properties of a cloth composite. The method is shown to be accurate. This model is extended to the viscoelastic regime with the use of Laplace transform and correspondence principle. Prony series coefficients for composite cloth are obtained for different volume fractions of fibers in yarn. It is observed from the hysteresis plots that dissipation in out of plane normal and shear modes is significantly higher than the normal directions.     

Design of experiments for stacking sequence optimizations with genetic algorithm using response surface approximation

This study describes a new method of experimental design to obtain a response surface of buckling load of laminated composites. Many evaluations for genetic algorithms for stacking sequence optimizations require high computational cost. That evaluation cost can be reduced by an approximation using a response surface. For a response surface for stacking sequence optimizations, lamination parameters are adopted as variables of the approximation function of the entire design space instead of ply angles for each ply. This study presents, proposes and investigates a new method of experimental design in detail. For most analytical tools, stacking sequences is demand as input data and lamination parameters cannot be applied directly to the tools. Therefore, the present study proposes and applies a new D-optimal set of laminates to the stacking sequence optimizations of the problem of maximization of buckling load of a composite cylinder. The new experimental design is a set of stacking sequences selected from candidate stacks using D-optimality. Consequently, the D-optimal set of laminates is shown to be effective for design of experiments of response surfaces for maximization of the buckling load of composite structures.     

The harmony search heuristic algorithm for discrete structural optimization

Many methods have been developed and are in use for structural size optimization problems, in which the cross-sectional areas or sizing variables are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes an efficient optimization method for structures with discrete-sized variables based on the harmony search (HS) heuristic algorithm. The recently developed HS algorithm was conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. In this article, a discrete search strategy using the HS algorithm is presented in detail and its effectiveness and robustness, as compared to current discrete optimization methods, are demonstrated through several standard truss examples. The numerical results reveal that the proposed method is a powerful search and design optimization tool for structures with discrete-sized members, and may yield better solutions than those obtained using current methods.     

Optimization of cardinality constrained portfolios with a hybrid local search algorithm

One of the main advantages of portfolios over single assets is that risk can be diversified without necessarily reducing the expected return - provided "proper" assets are selected and they are assigned the "proper" weights. Since in practice investors tend to restrict themselves to a rather small number of different assets, the decision which securities to include is a crucial one that turns out to be NP-hard. In this paper we suggest a hybrid local search algorithm which combines principles of Simulated Annealing and evolutionary strategies and which proved to highly efficiently approach this problem. Correspondence to: Dietmar MaringerThe authors would like to thank participants of the 4^th Metaheuristics International Conference and the Econometrics Research Seminar at the University of Geneva, U. Derigs, M. Gilli, H.-O. Günther, and two anonymous referees for valuable comments on earlier versions of this paper.     

基于遗传算法的复合材料层合板削层结构铺层优化

针对应力变化较大的碳纤维增强复合材料层合板,提出削层结构铺层分级优化模式。通过将结构分解为若干子铺层并对各子铺层的位置、尺寸、铺层数以及铺层顺序进行优化,得到了满足强度和可制造性要求且质量最小的结构设计方案。该模式的第1、2级优化利用参考层对各子铺层位置及尺寸进行优化,第3级优化通过引入3次样条插值参数化方法对各子铺层层数和铺层顺序进行优化。参考层的引入可减少设计变量的数量,3次样条插值参数化方法可解决以铺层角为设计变量时设计变量数目不确定的问题。利用有限元方法对结构进行力学分析计算,并依据Tsai-Wu准则确定结构强度。在第2、3级优化中利用遗传算法对优化问题进行求解。算例计算表明:削层结构铺层分级优化模式结果合理可信。与均匀铺层方法结果比较可知:削层结构可有效减少结构质量。