A non‐dominance‐based online stopping criterion for multi‐objective evolutionary algorithms

A non‐dominance criterion‐based metric that tracks the growth of an archive of non‐dominated solutions over a few generations is proposed to generate a convergence curve for multi‐objective evolutionary algorithms (MOEAs). It was observed that, similar to single‐objective optimization problems, there were significant advances toward the Pareto optimal front in the early phase of evolution while relatively smaller improvements were obtained as the population matured. This convergence curve was used to terminate the MOEA search to obtain a good trade‐off between the computational cost and the quality of the solutions. Two analytical and two crashworthiness optimization problems were used to demonstrate the practical utility of the proposed metric. Copyright © 2010 John Wiley & Sons, Ltd.     

Robust structural damage identification based on multi‐objective optimization

Inverse analysis for structural damage identification often involves an optimization process that minimizes the discrepancies between the computed responses and the measured responses. Conventional single‐objective optimization approach defines the objective function by combining multiple error terms into a single one, which leads to a weaker constraint in solving the identification problem. A multi‐objective approach is proposed, which minimizes multiple error terms simultaneously. Its non‐domination‐based convergence provides a stronger constraint that enables robust identification of damages with lower false‐negative detection rate. Another merit of the proposed approach is quantified confidence in damage detection through processing Pareto‐optimal solutions. Numerical examples that simulate static testing are provided to compare the proposed approach with conventional formulation based on single‐objective optimization. Copyright © 2009 John Wiley & Sons, Ltd.     

Reliability‐based robust design optimization: A multi‐objective framework using hybrid quality loss function

In this globally competitive business environment, design engineers are constantly striving to establish new and effective tools and techniques to ensure a robust and reliable product design. Robust design (RD) and reliability‐based design approaches have shown the potential to deal with variability in the life cycle of a product. This paper explores the possibilities of combining both approaches into a single model and proposes a hybrid quality loss function‐based multi‐objective optimization model. The model is unique because it uses a hybrid form of quality loss‐based objective function that is defined in terms of desirable as well as undesirable deviations to obtain efficient design points with minimum quality loss. The proposed approach attempts to optimize the product design by addressing quality loss, variability, and life‐cycle issues simultaneously by combining both reliability‐based and RD approaches into a single model with various customer aspirations. The application of the approach is demonstrated using a leaf spring design example. Copyright © 2009 John Wiley & Sons, Ltd.     

A multi‐objective optimization using distribution characteristics of reference data for reverse engineering

As different industries produce similar products, engineers tend to analyze the products of competitors and adopt the excellent merits in their current products. This process is called reverse engineering. There can be multiple target characteristics in reverse engineering. In many cases, the improved design from reverse engineering usually keeps the data distribution characteristics of the competitors unless the developed product is a fully new creative design. The distribution should be considered in reverse engineering. Therefore, the reverse engineering process can be modeled as multi‐objective optimization considering data distribution. Recently, Taguchi developed the Mahalanobis Taguchi system (MTS) technique to minimize the Mahalanobis distance (MD), which is defined by a multi‐objective function with data distribution. However, the MTS technique has the limit that the new design is not better than the mean values of the competitors. In this research, a function named as the skewed Mahalanobis distance (SMD) is proposed to overcome the drawbacks of the MTS technique. SMD is a new distance scale defined by multiplying the skewed value of a design point to MD. SMD is used instead of MD and the method is named the SMD method. The SMD method can always give a unique Pareto optimum solution. To verify the efficiency of the SMD method, a non‐convex mathematical example, a cantilever beam, and a practical automobile suspension system are optimized. Copyright © 2010 John Wiley & Sons, Ltd.     

A multi‐start threshold accepting algorithm for multiple objective continuous optimization problems

A multi‐start threshold accepting algorithm with an adaptive memory (MS‐TA) is proposed to solve multiple objective continuous optimization problems. The aim of this paper is to find efficiently multiple Pareto‐optimal solutions. Comparisons are carried out with multiple objective taboo search algorithm and genetic algorithm. Experiments on literature problems show that the proposed algorithm is more effective. The presented multi‐start adaptive algorithm improves the best‐known results by a significant margin. Copyright © 2010 John Wiley & Sons, Ltd.     

Large strain phase‐field‐based multi‐material topology optimization

A multi‐material topology optimization scheme is presented. The formulation includes an arbitrary number of phases with different mechanical properties. To ensure that the sum of the volume fractions is unity and in order to avoid negative phase fractions, an obstacle potential function, which introduces infinity penalty for negative densities, is utilized. The problem is formulated for nonlinear deformations, and the objective of the optimization is the end displacement. The boundary value problems associated with the optimization problem and the equilibrium equation are solved using the finite element method. To illustrate the possibilities of the method, it is applied to a simple boundary value problem where optimal designs using multiple phases are considered. Copyright © 2015 John Wiley & Sons, Ltd.     

Studies of multi‐start clustering for global optimization

Global/multi‐modal optimization problems arise in many engineering applications. Owing to the existence of multiple minima, it is a challenge to solve the multi‐modal optimization problem and to identify the global minimum especially if efficiency is a concern. In this paper, variants of the multi‐start with clustering strategy are developed and studied for identifying multiple local minima in nonlinear global optimization problems. The study considers the sampling procedure, the use of Hessian information in forming clusters, the technique for cluster analysis and the local search procedure. Variations of multi‐start with clustering are applied to 15 multi‐modal problems. A comparative study focuses on the overall search effectiveness in terms of the number of local searches performed, local minima found and required function evaluations. The performance of these multi‐start clustering algorithms ranges from very efficient to very robust. Copyright © 2002 John Wiley & Sons, Ltd.     

Exploiting semantics of temporal multi‐scale methods to optimize multi‐level mesh partitioning

Multi‐scale problems are often solved by decomposing the problem domain into multiple subdomains, solving them independently using different levels of spatial and temporal refinement, and coupling the subdomain solutions back to obtain the global solution. Most commonly, finite elements are used for spatial discretization, and finite difference time stepping is used for time integration. Given a finite element mesh for the global problem domain, the number of possible decompositions into subdomains and the possible choices for associated time steps is exponentially large, and the computational costs associated with different decompositions can vary by orders of magnitude. The problem of finding an optimal decomposition and the associated time discretization that minimizes computational costs while maintaining accuracy is nontrivial. Existing mesh partitioning tools, such as METIS, overlook the constraints posed by multi‐scale methods and lead to suboptimal partitions with a high performance penalty. We present a multi‐level mesh partitioning approach that exploits domain‐specific knowledge of multi‐scale methods to produce nearly optimal mesh partitions and associated time steps automatically. Results show that for multi‐scale problems, our approach produces decompositions that outperform those produced by state‐of‐the‐art partitioners like METIS and even those that are manually constructed by domain experts. Copyright © 2017 John Wiley & Sons, Ltd.     

Improved multi‐level Newton solvers for fully coupled multi‐physics problems

An algorithm is suggested to improve the efficiency of the multi‐level Newton method that is used to solve multi‐physics problems. It accounts for full coupling between the subsystems by using the direct differentiation method rather than error prone finite difference calculations and retains the advantage of greater flexibility over the tightly coupled approaches. Performance of the algorithm is demonstrated by solving a fluid–structure interaction problem. Copyright © 2003 John Wiley & Sons, Ltd.     

A computational framework for scale‐bridging in multi‐scale simulations

A computational framework for scale‐bridging in multi‐scale simulations is presented. The framework enables seamless combination of at‐scale models into highly dynamic hierarchies to build a multi‐scale model. Its centerpiece is formulated as a standalone module capable of fully asynchronous operation. We assess its feasibility and performance for a two‐scale model applied to two challenging test problems from impact physics. We find that the computational cost associated with using the framework may, as expected, become substantial. However, the framework has the ability of effortlessly combining at‐scale models to render complex multi‐scale models. The main source of the computational inefficiency of the framework is related to poor load balancing of the lower‐scale model evaluation We demonstrate that the load balancing can be efficiently addressed by recourse to conventional load‐balancing strategies. Copyright © 2016 John Wiley & Sons, Ltd.     

Sustainable product‐package design in a food supply chain: A multi‐criteria life cycle approach

This paper presents a multi‐criteria decision‐making approach for the selection of a sustainable product‐package design, accounting for the different actors within a food supply chain. The study extends the focus of sustainable packaging design to the collective of all supply chain actors. Decision criteria are identified via a literature review, and current product‐package alternatives are collected via interviews. With the inputs of these criteria and the alternative designs, a multi‐criteria decision‐making problem is formulated and solved using Best Worst Method (BWM). BWM finds the weights of the criteria. Using these weights, the ranking of the alternatives is found. The implementation of the analysis took place for three selected products of the Kraft Heinz Company. Data on the preferences of the supply chain members of these selected products were collected, and the optimal package designs were selected. It is shown through sensitivity analysis that modifying the weights that decision makers assign to the preferences of the supply chain members and the importance of the dimensions of sustainability have an effect on the selection of the optimal design.     

Opportunistic maintenance of multi‐equipment system: a case study

A case study on preventive maintenance (PM) of a multi‐equipment system is presented in this paper. Each equipment of the system consists of many components/subsystems connected in series. Because of the series structure, opportunistic maintenance (OM) policies are more effective for the components of the equipment. A new OM policy based on the classification of opportunities has been proposed. Various OM policies have been evaluated using simulation modeling, and the new policy has been found to be more effective than the existing OM policies. The impact of this policy on the overall system has also been simulated. Copyright © 2000 John Wiley & Sons, Ltd.     

Efficient generation of pareto‐optimal topologies for compliance optimization

In multi‐objective optimization, a design is defined to beit pareto‐optimal if no other design exists that is better with respect to one objective, and as good with respect to other objectives. In this paper, we first show that if a topology is pareto‐optimal, then it must satisfy certain properties associated with the topological sensitivity field, i.e. no further comparison is necessary. This, in turn, leads to a deterministic, i.e. non‐stochastic, method for efficiently generating pareto‐optimal topologies using the classic fixed‐point iteration scheme. The proposed method is illustrated, and compared against SIMP‐based methods, through numerical examples. In this paper, the proposed method of generating pareto‐optimal topologies is limited to bi‐objective optimization, namely compliance–volume and compliance–compliance. The future work will focus on extending the method to non‐compliance and higher dimensional pareto optimization. Copyright © 2011 John Wiley & Sons, Ltd.     

An approach to multi‐start clustering for global optimization with non‐linear constraints

This paper describes a multi‐start with clustering strategy for use on constrained optimization problems. It is based on the characteristics of non‐linear constrained global optimization problems and extends a strategy previously tested on unconstrained problems. Earlier studies of multi‐start with clustering found in the literature have focused on unconstrained problems with little attention to non‐linear constrained problems. In this study, variations of multi‐start with clustering are considered including a simulated annealing or random search procedure for sampling the design domain and a quadratic programming (QP) sub‐problem used in cluster formation. The strategies are evaluated by solving 18 non‐linear mathematical problems and six engineering design problems. Numerical results show that the solution of a one‐step QP sub‐problem helps predict possible regions of attraction of local minima and can enhance robustness and effectiveness in identifying local minima without sacrificing efficiency. In comparison to other multi‐start techniques found in the literature, the strategies of this study can be attractive in terms of the number of local searches performed, the number of minima found, whether the global minimum is located, and the number of the function evaluations required. Copyright © 2002 John Wiley & Sons, Ltd.     

A literature review on selective maintenance for multi‐unit systems

Selective maintenance is regarded as a type of profit‐generating maintenance policy, playing an important role in balancing limited maintenance resources with system performance. Since 1988, increasing interest has been focused on this research area. Nevertheless, to the best of our knowledge, there is a lack of critical reviews of selective maintenance. This paper is the first systematic review focusing on this relevant topic. In this work, a definition and some specific features of selective maintenance are elaborated. Based on these features, a set of criteria that have been considered in selective maintenance optimization are summarized into 3 categories: system characteristics, maintenance characteristics, and mission profile characteristics. Based on these criteria, a comprehensive literature review on selective maintenance is undertaken. The solution approaches, as well as a general procedure for selective maintenance optimization, are discussed. Finally, some possible directions for further research are provided.     

Integrated layout design of multi‐component system

A new integrated layout optimization method is proposed here for the design of multi‐component systems. By introducing movable components into the design domain, the components layout and the supporting structural topology are optimized simultaneously. The developed design procedure mainly consists of three parts: (i) Introduction of non‐overlap constraints between components. The finite circle method (FCM) is used to avoid the components overlaps and also overlaps between components and the design domain boundaries. (ii) Layout optimization of the components and supporting structure. Locations and orientations of the components are assumed as geometrical design variables for the optimal placement while topology design variables of the supporting structure are defined by the density points. Meanwhile, embedded meshing techniques are developed to take into account the finite element mesh change caused by the component movements. (iii) Consistent material interpolation scheme between element stiffness and inertial load. The commonly used solid isotropic material with penalization model is improved to avoid the singularity of localized deformation in the presence of design dependent loading when the element stiffness and the involved inertial load are weakened by the element material removal. Finally, to validate the proposed design procedure, a variety of multi‐component system layout design problems are tested and solved on account of inertia loads and gravity center position constraint. Solutions are compared with traditional topology designs without component. Copyright © 2008 John Wiley & Sons, Ltd.     

An implicit multi‐material Eulerian formulation

Multi‐material Eulerian methods were originally developed to solve problems in hypervelocity impact. They have proven to be useful for many other problems involving high‐strain rates such as the dynamic compaction of a powder and high‐speed machining. An implicit formulation has been developed to extend the range of applicability to quasi‐static problems such as hot isostatic pressing (HIP) and other material processing operations. Copyright © 2000 John Wiley & Sons, Ltd.     

Nonhierarchical multi‐model fusion using spatial random processes

New model fusion techniques based on spatial‐random‐process modeling are developed in this work for combining multi‐fidelity data from simulations and experiments. Existing works in multi‐fidelity modeling generally assume a hierarchical structure in which the levels of fidelity of the simulation models can be clearly ranked. In contrast, we consider the nonhierarchical situation in which one wishes to incorporate multiple models whose levels of fidelity are unknown or cannot be differentiated (e.g., if the fidelity of the models changes over the input domain). We propose three new nonhierarchical multi‐model fusion approaches with different assumptions or structures regarding the relationships between the simulation models and physical observations. One approach models the true response as a weighted sum of the multiple simulation models and a single discrepancy function. The other two approaches model the true response as the sum of one simulation model and a corresponding discrepancy function, and differ in their assumptions regarding the statistical behavior of the discrepancy functions, such as independence with the true response or a common spatial correlation function. The proposed approaches are compared via numerical examples and a real engineering application. Furthermore, the effectiveness and relative merits of the different approaches are discussed. Copyright © 2015 John Wiley & Sons, Ltd.     

A new approach to solving problems of multi‐state system reliability optimization

Usually engineers try to achieve the required reliability level with minimal cost. The problem of total investment cost minimization, subject to reliability constraints, is well known as the reliability optimization problem. When applied to multi‐state systems (MSS), the system has many performance levels, and reliability is considered as a measure of the ability of the system to meet the demand (required performance). In this case, the outage effect will be essentially different for units with different performance rate. Therefore, the performance of system components, as well as the demand, should be taken into account. In this paper, we present a technique for solving a family of MSS reliability optimization problems, such as structure optimization, optimal expansion, maintenance optimization and optimal multistage modernization. This technique combines a universal generating function (UGF) method used for fast reliability estimation of MSS and a genetic algorithm (GA) used as an optimization engine. The UGF method provides the ability to estimate relatively quickly different MSS reliability indices for series‐parallel and bridge structures. It can be applied to MSS with different physical nature of system performance measure. The GA is a robust, universal optimization tool that uses only estimates of solution quality to determine the direction of search. Copyright © 2001 John Wiley & Sons, Ltd.