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An optimization framework for design space reduction in early-stage design under uncertainty
Published in Pentti Kujala, Liangliang Lu, Marine Design XIII, 2018
Robust optimisation is characterised by the goal of finding an optimal solution such that the feasibility of the design is minimally affected by parameter uncertainty (Bertsimas, et al., 2011). Many different objective functions have been suggested in the literature such as minimising the worst-case regret and minimising the worst case objective function, known as min-max robustness (Ehrgott, et al., 2014). Another approach is to formulate the problem as a multi-objective optimisation problem with the mean and standard deviation of the objective function as the two objectives (Wang & Shan, 2004). One of the major limitations of robust optimisation is that the solutions are often suboptimal for many of the possible realised values of the uncertain parameters (Ehrgott, et al., 2014). Another limitation of robust optimisation is the lack of established methods for multi-objective problems (Ehrgott, et al., 2014).
Robust design of hybrid steel fiber reinforced concrete tunnel lining segments
Published in Günther Meschke, Bernhard Pichler, Jan G. Rots, Computational Modelling of Concrete Structures, 2018
G.E. Neu, V.E. Gall, S. Freitag, G. Meschke
Robust optimization is strongly related to uncertainty modeling. A conventional, deterministic optimal design may not always lead to an optimal product, if uncertainties in design and a priori parameters are considered. There are multiple sources of uncertainties, which result in a variance or at least ranges of the assumed geometrical and material parameters. In this work, uncertain parameters are modeled as stochastic numbers. Robust optimization incorporates the variances for finding an optimal design, which provides a sufficient performance under all considered conditions and not only for a specific parameter combination. Figure 3 illustrates exemplary the methodology of robust optimization.
The integrated lot-sizing and cutting stock problem under demand uncertainty
Published in International Journal of Production Research, 2023
Eduardo Curcio, Vinícius L. de Lima, Flávio K. Miyazawa, Elsa Silva, Pedro Amorim
The differences between stochastic programming and robust optimisation are well known in the literature. Usually, stochastic programming is used to optimise the expected value of the objective function, while maintaining the feasibility for all scenarios considered. Stochastic programming also requires assuming a probabilistic distribution function to generate scenarios, which can be highly intractable depending on the number of scenarios generated (Shapiro and Philpott 2007). On the other hand, robust optimisation is used to find an optimal solution that is feasible for any realisation of the uncertain parameter over a given set. By using a budget-uncertainty set, it can have a similar computational tractability as its deterministic counterpart, but its solutions can be rather conservative since it optimises for the worst-case values of the uncertainty set.
A fuzzy mixed-integer robust design optimization model to obtain optimum settings of both qualitative and quantitative input variables under uncertainty
Published in Engineering Optimization, 2023
Figure 1 shows graphs of the predicted response values versus the actual response values for the mean, standard deviation and variance response. The experimental data points in Figure 1 are generally split evenly by the 45° line, so most of the observations are well predicted by the model. A large prediction error may exist in a local region for the multi-fidelity metamodel (Zhou et al. 2018) and the prediction uncertainty from the model may result in non-optimal robustness (Zhou et al. 2018). In this article, the prediction accuracy is good enough for the regression models when performing robust optimization. As shown in Table 7, the optimal operating conditions are obtained for qualitative and quantitative input variables. If prediction uncertainty was observed for the regression models in Equations (12)–(14), the optimization models could result in infeasible solutions. Moreover, the validation study shows that the robust optimization and the experimental results are in good agreement.
Optimal operation scheduling of a microgrid using a novel scenario-based robust approach
Published in Engineering Optimization, 2023
Zhangyi Shen, Linli Wu, Seyed Amin Sedgh, Fereydun Radmehr
Robust optimization has a wide application in dealing with problems having uncertain parameters. This article proposes scenario-based robust scheduling for MG energy management optimization under uncertainty. The scenario-based robust model introduced by Mulvey, Vanderbei, and Zenios (1995) to optimize large-scale problems has been developed by extending the bi-level stochastic model. Stochastic scheduling only minimizes the expected value of scenarios in the objective function, while the scenario-based robust model optimizes the acceptable distance of scenarios from the expected value. Thus, the new model allows for simultaneous control of optimality and feasibility. By using the penalty in control constraints, feasibility violations under some scenarios can be controlled. However, the feasibility penalty approach is not addressed in this article.