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Objective vectors g(yi,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{g} (\mathbf{y} ^{i}, q)$$\end{document}, i∈{1,…,8}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i \in \{ 1, \ldots , 8 \}$$\end{document}, q∈{q^,q~}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q \in \{ \hat{q}, \tilde{q} \}$$\end{document}, in the criterion space. Each solution represented by a specific color; cross- and square-markers denote the nominal (q^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{q}$$\end{document}) and worst-case (q~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{q}$$\end{document}) scenario, respectively. The sets of efficient solutions are Yeffg(q^)={y1,y3,y4}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y^\mathbf{g }_{{\mathrm{eff}}}(\hat{q}) = \{\mathbf{y }^{1},\mathbf{y }^{3},\mathbf{y }^{4}\}$$\end{document} and Yeffg(q~)={y1,y2,y3,y7,y8}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y^\mathbf{g }_{{\mathrm{eff}}}(\tilde{q}) = \{ \mathbf{y }^{1}, \mathbf{y }^{2}, \mathbf{y} ^{3}, \mathbf{y }^{7}, \mathbf{y }^{8} \}$$\end{document}

Objective vectors g(yi,q)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbf{g} (\mathbf{y} ^{i}, q)$$\end{document}, i∈{1,…,8}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$i \in \{ 1, \ldots , 8 \}$$\end{document}, q∈{q^,q~}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$q \in \{ \hat{q}, \tilde{q} \}$$\end{document}, in the criterion space. Each solution represented by a specific color; cross- and square-markers denote the nominal (q^\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hat{q}$$\end{document}) and worst-case (q~\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tilde{q}$$\end{document}) scenario, respectively. The sets of efficient solutions are Yeffg(q^)={y1,y3,y4}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y^\mathbf{g }_{{\mathrm{eff}}}(\hat{q}) = \{\mathbf{y }^{1},\mathbf{y }^{3},\mathbf{y }^{4}\}$$\end{document} and Yeffg(q~)={y1,y2,y3,y7,y8}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y^\mathbf{g }_{{\mathrm{eff}}}(\tilde{q}) = \{ \mathbf{y }^{1}, \mathbf{y }^{2}, \mathbf{y} ^{3}, \mathbf{y }^{7}, \mathbf{y }^{8} \}$$\end{document}

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In the presence of uncertainties in the parameters of a mathematical model, optimal solutions using nominal or expected parameter values can be misleading. In practice, robust solutions to an optimization problem are desired. Although robustness is a key research topic within single-objective optimization, little attention is received within mult...