Multiple parameter optimization methodology by integrating a game theory principle into priority-based decision making

In the present paper, we explore issues in handling equality constraints in multiobjective robust design optimization (RDO) problems. Satisfying an equality constraint exactly under uncertainty can be a challenging task. The challenge of handling equality constraints is compounded in multiobjective RDO problems. Modeling the tradeoffs between the mean of the performance and the variation of the performance for each design objective in a multiobjective RDO problem is a complex task by itself. Equality constraints add to this complexity because of the additional tradeoffs that are introduced between constraint satisfaction under uncertainty and multiobjective performance. Satisfying equality constraints at their mean values, an approach typically followed, could lead to undesirable results. In this paper, we study the implications of equality constraint satisfaction in a multiobjective RDO problem, and provide a new problem formulation approach to resolve the above discussed tradeoffs. We illustrate that the proposed formulation can be used as an effective multiobjective design space exploration tool, with emphasis on equality constraint satisfaction under uncertainty. We present numerical examples to illustrate our theoretical developments.

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.

Swarm intelligence hybridized with genetic search in multi-objective design optimization under constrained-Pareto dominance

<p>The primary objective of this study is to develop new computational methods for robust design optimization (RDO) and reliability-based design optimization (RBDO) of high-dimensional, complex engineering systems. Four major research directions, all anchored in polynomial dimensional decomposition (PDD), have been defined to meet the objective. They involve: (1) development of new sensitivity analysis methods for RDO and RBDO; (2) development of novel optimization methods for solving RDO problems; (3) development of novel optimization methods for solving RBDO problems; and (4) development of a novel scheme and formulation to solve stochastic design optimization problems with both distributional and structural design parameters.</p> <p>The major achievements are as follows. Firstly, three new computational methods were developed for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to random inputs. The first method represents a novel integration of PDD of a multivariate stochastic response function and score functions, leading to analytical expressions of design sensitivities of the first two moments. The second and third methods, relevant to probability distribution or reliability analysis, exploit two distinct combinations built on PDD: the PDD-SPA method, entailing the saddlepoint approximation (SPA) and score functions; and the PDD-MCS method, utilizing the embedded Monte Carlo simulation (MCS) of the PDD approximation and score functions. For all three methods developed, both the statistical moments or failure probabilities and their design sensitivities are both determined concurrently from a single stochastic analysis or simulation. Secondly, four new methods were developed for RDO of complex engineering systems. The methods involve PDD of a high-dimensional stochastic response for statistical moment analysis, a novel integration of PDD and score functions for calculating the second-moment sensitivities with respect to the design variables, and standard gradient-based optimization algorithms. The methods, depending on how statistical moment and sensitivity analyses are dovetailed with an optimization algorithm, encompass direct, single-step, sequential, and multi-point single-step design processes. Thirdly, two new methods were developed for RBDO of complex engineering systems. The methods involve an adaptive-sparse polynomial dimensional decomposition (AS-PDD) of a high-dimensional stochastic response for reliability analysis, a novel integration of AS-PDD and score functions for calculating the sensitivities of the failure probability with respect to design variables, and standard gradient-based optimization algorithms, resulting in a multi-point, single-step design process. The two methods, depending on how the failure probability and its design sensitivities are evaluated, exploit two distinct combinations built on AS-PDD: the AS-PDD-SPA method, entailing SPA and score functions; and the AS-PDD-MCS method, utilizing the embedded MCS of the AS-PDD approximation and score functions. In addition, a new method, named as the augmented PDD method, was developed for RDO and RBDO subject to mixed design variables, comprising both distributional and structural design variables. The method comprises a new augmented PDD of a high-dimensional stochastic response for statistical moment and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms, leading to a multi-point, single-step design process.</p> <p>The innovative formulations of statistical moment and reliability analysis, design sensitivity analysis, and optimization algorithms have achieved not only highly accurate but also computationally efficient design solutions. Therefore, these new methods are capable of performing industrial-scale design optimization with numerous design variables.</p>

Powder metallurgy offers several advantages over traditional manufacturing methods, such as improved material utilization and waste reduction. The powder metallurgy process involves four primary steps, metal powder preparation, mixing, compaction, and sintering, followed by secondary operations such as forging, rolling, and extrusion. However, existing studies have predominantly focused on refining the primary processes, neglecting secondary processes that could further enhance mechanical properties. A systematic literature review following the Preferred Reporting Items for Systematic Review and Meta-Analysis method identified twenty-three relevant articles over a ten-year period, highlighting three main optimization methods, that are, the Taguchi method, Taguchi-based Grey Relational Analysis, and Response Surface Methodology. These methods effectively reduce experimental trials and optimize key parameters like compaction pressure and weight percentage, which significantly influence mechanical properties. The review emphasizes the key powder metallurgy process parameters that have a significant impact on mechanical properties, becoming the primary targets for optimization. It offers a focused examination of which process parameters require thorough investigation for optimization and the suitable optimization method to achieve optimal outcomes, whether for single or multiple responses, thereby enhancing the manufacturing process. However, inconsistencies in parameter significance across studies indicate the material-dependent nature of powder metallurgy materials. The review also identifies a gap in the literature regarding secondary process optimization and comparative analyses of optimization methods. Future research should explore optimizing secondary processes in powder metallurgy, conduct comparative studies of different optimization methods, and develop novel approaches for optimization to further enhance mechanical properties and process efficiency.

A multistage and multiple response optimization approach for serial manufacturing system

The paper is devoted to model uncertainties (or model form uncertainties) induced by modeling errors in computational sciences and engineering (such as in computational structural dynamics, fluid-structure interaction, and vibroacoustics, etc.) for which a parametric high-fidelity computational model (HFM) is used for addressing optimization problems (such as a robust design optimization problem), which are solved by introducing a parametric reduced-order model (ROM) constructed using an adapted reduced-order basis (ROB) derived from the parametric HFM. Two main methodologies are available to take into account such modeling errors. The first one is the usual output-predictive error method that has been introduced for many years. This approach can induce some difficulties because the parametric HFM and ROM do not learn from data. The second one is the nonparametric probabilistic approach of model uncertainties introduced in the framework of structural dynamics fifteen years ago. This approach is adapted, but is mainly limited to linear operators of the parametric HFM. The present paper deals with this challenging problem and proposes a novel nonparametric probabilistic approach of the modeling errors for any parametric nonlinear HFM for which a parametric nonlinear ROM can be constructed from the HFM. The methodology proposed consists in substituting the deterministic ROB with a stochastic ROB for which the probability measure in constructed on a subset of a compact Stiefel manifold. The stochastic model depends on a small number of hyperparameters for which the identification is performed by solving a statistical inverse problem. An application is presented in nonlinear computational structural dynamics.

Aiming at the problem of supply chain robust optimization with multiple performance responses, a robust optimization method was proposed by combining principal component analysis with double response surface method based on Kriging meta-model. Firstly, through principal component analysis, the location characteristics and divergence characteristics of multiple related performance responses were transformed into the principal component comprehensive score of supply chain performance; secondly, the Kriging metamodels of location characteristics and divergence characteristics of multiple performance responses were constructed respectively, and the principal component comprehensive score model of comprehensive performance based on Kriging meta-model was constructed. Thus the optimal operating conditions by optimizing the constructed robust optimization strategy were obtained in order to realize the robust optimization of supply chain system with correlated multiple responses. Finally, a supply chain simulation case was given to illustrate the effectiveness of our proposed optimization method, and the robustness of different methods was also discussed. The comparison results showed that our proposed was more robust.

Many Industrial processes have multiple quality characteristics to be optimized. However, among them some are conflicting with each other and optimizing one response causes loss in the other response. Such a problem is called Multiresponse optimization (MRO) problem which involves optimizing conflicting multiple responses simultaneously. Unifying approaches are the most common approaches to solve MRO problem, theses approaches convert a MRO problem into a single response optimization problem by combining the multiple responses into one index, which is used for optimization. Principal Component Analysis (PCA) is one of the tool used to unify the responses. The major advantage of PCA is it takes consideration of correlation among responses. However, there are certain shortcomings as well, this paper address those shortcomings and proposes an Weighted PCA- Artificial Neural Network- Genetic Algorithm (WPCA-ANN-GA ) approach to perform multi response optimization. A case study using data from published literature is presented at the end to demonstrate the WPCA-ANN-GA approach.

Purpose: For more than 30 years, robust parameter design (RPD), which attempts to minimize the process bias (i.e., deviation between the mean and the target) and its variability simultaneously, has received consistent attention from researchers in academia and industry. Based on Taguchi’s philosophy, a number of RPD methodologies have been developed to improve the quality of products and processes. The primary purpose of this paper is to review and discuss existing RPD methodologies in terms of the three sequential RPD procedures of experimental design, parameter estimation, and optimization.Methods: This literature study composes three review aspects including experimental design, estimation modeling, and optimization methods.Results: To analyze the benefits and weaknesses of conventional RPD methods and investigate the requirements of future research, we first analyze a variety of experimental formats associated with input control and noise factors, output responses and replication, and estimation approaches. Secondly, existing estimation methods are categorized according to their implementation of least-squares, maximum likelihood estimation, generalized linear models, Bayesian techniques, or the response surface methodology. Thirdly, optimization models for single and multiple responses problems are analyzed within their historical and functional framework.Conclusion: This study identifies the current RPD foundations and unresolved problems, including ample discussion of further directions of study.

An ellipsoidal distance-based search strategy of ants for nonlinear single and multiple response optimization problems

Robust design optimization (RDO) has been eminent, ascertaining optimal configuration of engineering systems in presence of uncertainties. However, computational aspect of conventional RDO can often get computationally intensive as neighborhood assessments of every solution are required to compute the performance variance and ensure feasibility. Surrogate assisted optimization is one of the efficient approaches in order to mitigate this issue of computational expense. However, the performance of a surrogate model plays a key factor in determining the optima in multi-modal and highly non-linear landscapes, in presence of uncertainties. In other words, the approximation accuracy of the model is principal in yielding the actual optima and thus, avoiding any misguide to the decision maker on the basis of false or, local optimum points. Therefore, an extensive survey has been carried out by employing most of the well-known surrogate models in the framework of RDO. It is worth mentioning that the numerical study has revealed consistent performance of a model out of all the surrogates utilized. Finally, the best performing model has been utilized in solving a large-scale practical RDO problem. All the results have been compared with that of Monte Carlo simulation results.

This study implements robust design optimization (RDO) of a self-centering viscous damper in the presence of seismic uncertainty. The RDO minimizes the effect of random input parameters on the output response, thus providing a robust solution. The optimal phenomenological parameters of the self-centering viscous damper are evaluated to ensure its robustness. The objective function of the RDO is cast as a sum of the mean and standard deviation of maximum floor acceleration and a constraint function of the inter-storey drift ratio of the floors. The mean component of the objective function minimizes the structural responses due to external loads, whereas the other component reduces the propagation of uncertainty from the input parameters. To reduce the computational cost of the RDO, a wavelet-based neural network is used as a surrogate model. The proposed optimization method is implemented in a 16-storey steel moment resisting frame with consideration of two ensembles of ground motions, i.e. far-field and near-field records, which are taken from FEMA P695 (ATC-63). To highlight the effectiveness of the proposed self-centering damper in mitigating maximum and residual drift ratios, two additional optimizations are undertaken using viscous and self-centering dampers. The numerical study shows that the neural network with a Gaussian wavelet function produces better accuracy compared to other wavelet functions. Also, the numerical analysis clearly elucidates the advantages of the proposed damper in reducing the residual drift of the floors over a viscous damper and a self-centering damper, which may lead to minimizing the post-earthquake economic losses.

Purpose – The purpose of this paper is to study the consideration of uncertainty from analysis modules for aircraft conceptual design by implementing uncertainty-based design optimization methods. Reliability-Based Design Optimization (RBDO), Possibility-Based Design Optimization (PBDO) and Robust Design Optimization (RDO) methods were developed to handle uncertainties of design optimization. The RBDO method is found suitable for uncertain parameters when sufficient information is available. On the other hand, the PBDO method is proposed when uncertain parameters have insufficient information. The RDO method can apply to both cases. The RBDO, PBDO and RDO methods were considered with the Multidisciplinary Design Optimization (MDO) method to generate conservative design results when low fidelity analysis tools are used. Design/methodology/approach – Methods combining MDO with RBDO, PBDO and RDO were developed and have been applied to a numerical analysis and an aircraft conceptual design. This research eva...

The optimization of parameters to achieve desired performance outcomes presents significant challenges due to high dimensionality, collinearity among variables, and data noise. Traditional optimization methods, such as Response Surface Methodology (RSM), often face limitations when tackling these complexities. Additionally, the lack of efficient techniques for identifying and prioritizing influential parameters further exacerbates the difficulties in the optimization process. To address these intertwined issues, we propose an enhanced optimization methodology that integrates Principal Component Analysis (PCA) with Multi- Response Surface Methodology (MRSM). This integration aims to reduce dimensionality and highlight the most significant parameters, facilitating a more effective optimization process. We evaluated the effectiveness of the PCA-MRSM approach using a simulated dataset. Our findings indicate that the PCA-MRSM technique significantly outperforms traditional MRSM, leading to improved optimization outcomes and reduced variability. The analysis of response surface plots reveals a curved relationship between the principal components and the response variable, suggesting intricate interactions among the components. The results highlight the potential of the PCA-MRSM approach for optimizing complex systems characterized by multiple responses and correlated input variables. By effectively addressing the challenges of high dimensionality and collinearity, this methodology paves the way for more robust and insightful optimization techniques in intricate contexts.