We present a deterministic non-gradient based approach that uses robustness measures in multi-objective optimization problems where uncontrollable parameter variations cause variation in the objective and constraint values. The approach is applicable for cases that have discontinuous objective and constraint functions with respect to uncontrollable parameters, and can be used for objective or feasibility robust optimization, or both together. In our approach, the known parameter tolerance region maps into sensitivity regions in the objective and constraint spaces. The robustness measures are indices calculated, using an optimizer, from the sizes of the acceptable objective and constraint variation regions and from worst-case estimates of the sensitivity regions’ sizes, resulting in an outer-inner structure. Two examples provide comparisons of the new approach with a similar published approach that is applicable only with continuous functions. Both approaches work well with continuous functions. For discontinuous functions the new approach gives solutions near the nominal Pareto front; the earlier approach does not.
A New Deterministic Approach Using Sensitivity Region Measures for Multi-Objective Robust and Feasibility Robust Design Optimization
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Li, M., Azarm, S., and Boyars, A. (December 20, 2005). "A New Deterministic Approach Using Sensitivity Region Measures for Multi-Objective Robust and Feasibility Robust Design Optimization." ASME. J. Mech. Des. July 2006; 128(4): 874–883. https://doi.org/10.1115/1.2202884
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