Designing a production process normally is involved with some important constraints such as uncertainty, trade-off between production costs and quality, customer’s expectations and production tolerances. In this paper, a novel multi-objective robust optimization model is introduced to investigate the best levels of design variables. The primary objective is to minimize the production cost while increasing robustness and performance. The response surface methodology is utilized as a common approximation model to fit the relationship between responses and design variables in the worst-case scenario of uncertainties. The target mean ratio α is applied to ensure the quality of the process by providing the robustness for all types of quality characteristics and with a trade-off between variability and deviance from the ideal point. The Lp metric method is used to integrate all objectives in one overall function. In order to estimate target value of the quality loss by considering production tolerances, the process capability ratio (Cpm) is applied. At the end, a numerical chemical mixture problem is served to show the applicability of the proposed method.

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, multi-responses, 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.

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.