In the real world of engineering problems, in order to reduce optimization costs in physical processes, running simulation experiments in the format of computer codes have been conducted. It is desired to improve the validity of simulation-optimization results by attending the source of variability in the model's output(s). Uncertainty can increase complexity and computational costs in Designing and Analyzing of Computer Experiments (DACE). In this state-of the art review paper, a systematic qualitative and quantitative review is implemented among Metamodel Based Robust Simulation Optimization (MBRSO) for black-box and expensive simulation models under uncertainty. This context is focused on the management of uncertainty, particularly based on the Taguchi worldview on robust design and robust optimization methods in the class of dual response methodology when simulation optimization can be handled by surrogates. At the end, while both trends and gaps in the research field are highlighted, some suggestions for future research are directed.

Nowadays, process optimization has been an interest in engineering design for improving the performance and reducing cost. In practice, in addition to uncertainty or noise parameters, a comprehensive optimization model must be able to attend other circumstances which might be imposed in problems under real operational conditions such as dynamic objectives, multiresponses, various probabilistic distribution, discrete and continuous data, physical constraints to design parameters, performance cost, computational complexity and multi-process environment. The main goal of this paper is to give a general overview on topics with brief systematic review and concise discussions about the recent development on comprehensive robust design optimization methods under hybrid aforesaid circumstances. Both optimization methods of mathematical programming based on Taguchi approach and robust optimization based on scenario sets are briefly described. Metamodels hybrid robust design is discussed as an appropriate methodology to decrease computational complexity in problems under uncertainty. In this context, the authors' policy is to choose important topics for giving a systematic picture to those who wish to be more familiar with recent studies about robust design optimization hybrid metamodels, also by attending real circumstances in practice. In particular, production and project management are considered as two important methodologies that could be improved by applications of advanced robust design combining with metamodel methods.

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Classical proportional-integral-derivative (PID) tuning methods such as Ziegler-Nichols simply increase robustness against disturbances that may arise from the load. Thus, uncertainty in the load parameters has generally not been considered in previous methods, and tuning has been done only in fixed and under certain conditions. Moreover, when one or more load parameters are changed, the best previous results for the PID controller lose their validity and need to be adjusted according to the change in those load parameters. In such case, finding an optimal design for a PID controller might be too inefficient in terms of computational time and cost. This paper aims at proposing a new less time-consuming method for tuning of a multiloop PID controller for robustness when the output of the model is varying due to the changeability of load parameters in multiple subsystems as a source of variability. Kriging and radial basis function (RBF) metamodels as two common global approximation models together with the Latin hypercube sampling (LHS) method are used to fit input-output models with the least number of running computer experiments. Robust design terminology in the class of dual response is applied to design a multi-input multi-output (MIMO) mathematical programming model under disturbance factors. A MIMO numerical case in tuning a multiloop PID controller, proportional-integral (PI) controller, and fractional-order PID (FOPID) controller for speed control of a DC motor is provided as an example to show the flexibility and applicability of the proposed method.

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In spite of the wide improvements in computer simulation packages, many complex simulation models, particularly under uncertainty, may be inefficient to run in terms of time, computation, and resources. To address such a challenge, integrating metamodels and robust design optimization has been applied. In the current paper, a systematic comparative study is implemented to evaluate the performance of three common metamodels, namely polynomial regression, kriging, and radial basis function. The required experiments are designed by different space-filling methods including the orthogonal array design and three forms of Latin hypercube sampling such as randomized, maximin, and correlation approaches. Although, the impact of sample size on the performance of metamodels in robust optimization results are investigated. All methods are analyzed using five two-dimensional test problems and one engineering problem while all of them are considered in two forms that are expensive (with a small sample size) and semi-expensive (with a large sample size). Uncertainty is assumed in all problems as a source of variability, so all test problems are conducted in the format of robust optimization in the class of dual response surface in order to estimate robust Pareto frontier. The performances of methods are studied in two terms of accuracy and robustness. Finally, the results of comparison, an applicable guideline is provided to aid the practitioners in selecting the appropriate combination of metamodels and sampling design methods for investigating set of robust optimal points (estimated Pareto frontier) in simulation–optimization problems under uncertainty.

This paper aims to further increase the reliability of optimal results by setting the simulation conditions to be as close as possible to the real or actual operation to create a Cyber-Physical System (CPS) view for the installation of the Fractional-Order PID (FOPID) controller. For this purpose, we consider two different sources of variability in such a CPS control model. The first source refers to the changeability of a target of the control model (multiple setpoints) because of environmental noise factors and the second source refers to an anomaly in sensors that is raised in a feedback loop. We develop a new approach to optimize two objective functions under uncertainty including signal energy control and response error control while obtaining the robustness among the source of variability with the lowest computational cost. A new hybrid surrogate-metaheuristic approach is developed using Particle Swarm Optimization (PSO) to update the Gaussian Process (GP) surrogate for a sequential improvement of the robust optimal result. The application of efficient global optimization is extended to estimate surrogate prediction error with less computational cost using a jackknife leave-one-out estimator. This paper examines the challenges of such a robust multi-objective optimization for FOPID control of a five-bar linkage robot manipulator. The results show the applicability and effectiveness of our proposed method in obtaining robustness and reliability in a CPS control system by tackling required computational efforts.

This paper aims to make a trade‐off between performance and robustness in stochastic control systems with probabilistic uncertainties. For this purpose, we develop a surrogate‐based robust simulation‐optimization approach for robust tuning and analyzing the sensitivity of stochastic controllers. Kriging surrogate is combined with robust design optimization to construct a robust simulation‐optimization model in the class of dual response surfaces. Randomness in simulation experiments due to uncertainty is analyzed through bootstrapping technique by computing confidence regions for the estimation of Pareto frontier. Results confirmed a proper trade‐off between the model's performance with the measure of expected Integral Squared Error (ISE) and robustness against uncertainty in the plant's physical parameters. Finally, the proposed method is evaluated in terms of accuracy, computational cost, and simplicity particularly in comparison with some common existed techniques in the tuning of the Proportional‐Integral‐Derivative (PID) and Fractional‐Order PID (FOPID) controllers.