392. On the Pareto-efficient points of Simple Constrained Multiobjective Problems
Invited abstract in session MD-1: Derivative-Free Optimization Methods for challenging applications: Handling Nonsmoothness and Constraints, stream Zeroth and first-order optimization methods.
Monday, 16:30-18:30Room: B100/1001
Authors (first author is the speaker)
| 1. | Dimo Brockhoff
|
| Inria and IP Paris |
Abstract
Numerical benchmarking is a crucial aspect of designing and recommending practically relevant multiobjective optimization algorithms. It helps in terms of the interpretation of benchmarking experiments if we fundamentally understand the used benchmark problems and their properties---in particular with respect to their Pareto-efficient points (also known as the Pareto set). There is no fundamental difference when we move towards more realistic *constrained* multiobjective problems.
In this talk, I will discuss, as a first step towards better understanding of multiobjective *constrained* problems, our recent results on the Pareto sets of some of the simplest multiobjective constrained problems. The focus of my talk will be on problems where each single objective function is convex quadratic and the constraints are linear. Building on classical results from convex analysis, our main result proves that the Pareto set of the constrained problem equals the projection of the unconstrained Pareto set into the feasible (convex) set. Besides discussing the theory, I will visually show the Pareto sets and fronts of some problems and compare them to the performance of the well-established NSGA-II algorithm.
This is joint work with Anne Auger (Inria and IP Paris, France), Jordan N. Cork and Tea Tušar (both Jožef Stefan Institute and Jožef Stefan International Postgraduate School, Slovenia).
Keywords
- Multi-objective optimization
Status: accepted
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