1. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Decision making with different combinations of the two types of uncertainties Figure Legend:

2. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Isopreference curves over two attributes Figure Legend:

3. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Pareto front over two attributes Figure Legend:

4. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Pareto front over individual value functions. Negative signs indicate a minimization problem Figure Legend:

5. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Process to select (a) the certainty equivalent curve or envelope for a given solution among all candidate utility functions and (b) the best solution from a given set of certainty equivalent envelopes for an attribute minimization decision problem Figure Legend:

6. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Inverting a utility function in a multi-attribute problem results in a CE curve Figure Legend:

7. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Performance of the solutions against all utility functions. For simplicity, only three curves in two dimensions are shown for each solution Figure Legend:

8. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Best valuations (left envelope) of the CE envelopes of Fig. 7 Figure Legend:

9. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Modified Pareto front and possible selections by the DM Figure Legend:

10. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Contour plots of the three candidate utility functions Figure Legend:

11. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 (a) Certainty equivalent curves for solution μ 1 for the three utility functions and the corresponding conservative envelope. (b) Certainty equivalent curves for solution μ 2 for the three utility functions and the corresponding conservative envelope. (c) Certainty equivalent curves for solution μ 3 for the three utility functions and the corresponding conservative envelope. Figure Legend:

12. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Left envelope (black solid line) of conservative certainty equivalent curves from Figs. 11(a)–11(c). The curves marked X_1, X_2 and X_3 indicate the conservative envelopes of the three designs, respectively. Figure Legend:

13. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Modified Pareto front and attribute realizations for the three solutions Figure Legend:

14. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Modified Pareto front and its relative position with respect to individual certainty equivalent curves Figure Legend:

15. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 Modified Pareto front defined by the right envelope of certainty equivalent surfaces Figure Legend:

16. Date of download: 9/17/2016 Copyright © ASME. All rights reserved. From: Limitations of Pareto Front in Design Under Uncertainty and Their Reconciliation J. Mech. Des. 2013;135(7):071010-071010-12. doi:10.1115/1.4024224 A simple speed reducer (adapted from Ref. [4]) Figure Legend: