Many problems in robotics seek to simultaneously optimize several competing objectives under constraints. A conventional approach to solving such multi-objective optimization problems is to create a single cost function comprised of the weighted sum of the individual objectives. Solutions to this scalarized optimization problem are Pareto optimal solutions to the original multi-objective problem. However, finding an accurate representation of a Pareto front remains an important challenge. Using uniformly spaced weight vectors is often inefficient and does not provide error bounds. Thus, we address the problem of computing a finite set of weight vectors such that for any other weight vector, there exists an element in the set whose error compared to optimal is minimized. To this end, we prove fundamental properties of the optimal cost as a function of the weight vector, including its continuity and concavity. Using these, we propose an algorithm that greedily adds the weight vector least-represented by the current set, and provide bounds on the error. Finally, we illustrate that the proposed approach significantly outperforms uniformly distributed weights for different robot planning problems with varying numbers of objective functions.
|Title of host publication||Algorithmic Foundations of Robotics XV|
|Subtitle of host publication||Proceedings of the Fifteenth Workshop on the Algorithmic Foundations of Robotics|
|Editors||Steven M. LaValle, Jason M. O’Kane, Michael Otte, Dorsa Sadigh, Pratap Tokekar|
|Publication status||Published - 2023|
|Event||15th Workshop on the Algorithmic Foundations of Robotics, WAFR 2022 - College Park, United States|
Duration: 22 Jun 2022 → 24 Jun 2022
|Name||Springer Proceedings in Advanced Robotics|
|Conference||15th Workshop on the Algorithmic Foundations of Robotics, WAFR 2022|
|Period||22/06/22 → 24/06/22|
Bibliographical noteGreen Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-care
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
- Human-robot interaction
- Multi-objective optimization