ISE Seminar: Pareto sensitivity, most-changing sub-fronts, and optimal knee solutions

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Pareto sensitivity, most-changing sub-fronts, and optimal knee solutions

Dr. Luis Nunes Vicente
Lehigh University

When dealing with a multi-objective optimization problem with more than two objectives, obtaining a comprehensive representation of the Pareto front can be computationally expensive. Furthermore, identifying the most representative Pareto solutions can be difficult and sometimes ambiguous. In this paper, using Pareto sensitivity, we introduce a way to compute the most-changing Pareto sub-fronts around a Pareto solution, where the points are distributed along directions of maximum change. We then show how to compute Pareto knee solutions, in our case defined as Pareto solutions where the least maximal change occurs. In doing so, we hope to offer a new perspective on how to compute representative Pareto solutions, in ways that are more comprehensive than existing techniques. Our techniques are still restricted to scalarized methods, in particular to the weighted-sum or epsilon-constrained methods, and require the computation or approximations of first- and second-order derivatives. We include numerical results from synthetic problems and multi-task learning instances that illustrate the benefits of our approach. This is joint work with Tommaso Giovannelli (Univ. Cincinnati) and Marcos M. Raimundo (UNICAMP).