![]() In other words, a Pareto reference set is only optimal within the bounds of the model it was generated from. The global optimal design…depends on the…(objective) functions and constraints…however, these functions alwaysrepresent models and/or approximations of the real world. For the purposes of this blog post, we shall use the definition of optimality as laid out by Beyer and Sendoff in their 2007 paper: From a purely technical perspective, a Pareto optimal set is a set of decision variables or solutions that maps to a Pareto front, or a set of performance objectives where improving one objective cannot be improved without causing performance degradation in another. The formal term for this method, Deeply Uncertain (DU) Re-evaluation was coined in a 2019 paper by Trindade et al. To demonstrate the differences better, we will also reevaluate the Pareto optimal set of solutions under a more challenging set of states of the world (SOWs), a method first used in Herman et al (2013, 2014) and Zeff et al (2014). In this post, we will explain the differences between optimality and robustness, and justify the importance of robust optimization instead of sole reliance on a set of optimal solutions (aka an optimal portfolio). ![]() ![]() Using these metrics, we found that Pareto-optimality does not guarantee satisfactory robustness, a statement that is justified by showing that not all portfolios within the reference set satisfied the robustness criteria. In the previous MORDM post, we visualized the reference set of performance objectives for the North Carolina Research Triangle and conducted a preliminary multi-criterion robustness analysis using two criteria: (1) regional reliability should be at least 98%, and (2) regional restriction frequency should be not more than 20%. ![]()
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