ロボット計画問題におけるパレートフロントの誤差有界近似
Error-Bounded Approximation of Pareto Fronts in Robot Planning Problems
多目的最適化において、重みベクトルを適応的に選択することでパレートフロントを誤差保証付きで近似する手法を提案し、ロボット計画問題で有効性を示した。
著者: Alexander Botros, Armin Sadeghi, Nils Wilde, Javier Alonso-Mora, Stephen L. Smith
分類: cs.RO
原文アブストラクト
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.
