Fast approximate bi-objective Pareto sets with quality bounds

William Bailey, Judy Goldsmith, Brent Harrison, Siyao Xu

Abstract: We present and empirically characterize a general, parallel, heuristic algorithm for computing small \(\epsilon \)-Pareto sets. A primary feature of the algorithm is that it maintains and improves an upper bound on the \(\epsilon \) value throughout the algorithm. The algorithm can be used as part of a decision support tool for settings in which computing points in objective space is computationally expensive. We use the bi-objective TSP and graph clearing problems as benchmark examples. We characterize the performance of the algorithm through \(\epsilon \)-Pareto set size, upper bound on \(\epsilon \) value provided, true \(\epsilon \) value provided, and parallel speedup achieved. Our results show that the algorithm’s combination of small \(\epsilon \)-Pareto sets and parallel speedup is sufficient to be appealing in settings requiring manual review (i.e., those that have a human in the loop) or real-time solutions.