Effective Integration of Weighted Cost-to-go and Conflict Heuristic within Suboptimal CBS

TL;DR

The paper challenges the conventional view that weighting the cost-to-go in CBS is detrimental by introducing two variants, WO-EECBS and WF-EECBS, that integrate a weighted cost-to-go with the conflict heuristic in bounded-suboptimal MAPF solvers. It uncovers that the relative weight of the conflict heuristic, captured by the parameter $r$, largely governs performance, while the cost-to-go weight $w_h$ has a secondary effect; the authors also establish a formal link between Prioritized Planning and bounded-suboptimal CBS, showing PP as a root-step case in CBS with infinite suboptimality and that W-EECBS generalizes this relationship. Empirical results show substantial speedups (up to 50–100× in some maps) and broad applicability across ECBS and EECBS, though an update indicates that these gains can drop to roughly 1.2–10× depending on the conflict heuristic. The work provides practical guidance for balancing low-level and high-level work in MAPF, offering a generalizable approach to leverage conflicts more effectively within CBS-based solvers.

Abstract

Conflict-Based Search (CBS) is a popular multi-agent path finding (MAPF) solver that employs a low-level single agent planner and a high-level constraint tree to resolve conflicts. The vast majority of modern MAPF solvers focus on improving CBS by reducing the size of this tree through various strategies with few methods modifying the low level planner. Typically low level planners in existing CBS methods use an unweighted cost-to-go heuristic, with suboptimal CBS methods also using a conflict heuristic to help the high level search. In this paper, we show that, contrary to prevailing CBS beliefs, a weighted cost-to-go heuristic can be used effectively alongside the conflict heuristic in two possible variants. In particular, one of these variants can obtain large speedups, 2-100x, across several scenarios and suboptimal CBS methods. Importantly, we discover that performance is related not to the weighted cost-to-go heuristic but rather to the relative conflict heuristic weight's ability to effectively balance low-level and high-level work. Additionally, to the best of our knowledge, we show the first theoretical relation of prioritized planning and bounded suboptimal CBS and demonstrate that our methods are their natural generalization. Update March 2024: We found that the relative speedup decreases to around 1.2-10x depending on how the conflict heuristic is computed (see appendix for more details).

Figures (10)

• Figure 1: CBS's original low-level planner finds shortest paths ignoring additional conflicts created, resulting in a large amount of CT nodes for the high-level search to resolve the conflicts. Suboptimal CBS (ECBS, EECBS) utilize a low-level focal search that minimizes future conflicts alongside path length, resulting in a slower low level planner but substantially reducing the high level work and boosting performance. Our Weighted Focal method improves performance by finding a sweet spot in the middle. We introduce a hyper-parameter $r$ in the low-level focal search which controls trading off low level work (finding paths) and high level work (resolving conflicts), allowing us to find low-level plans faster with a little more high level work than current suboptimal CBS methods.
• Figure 2: Viewing the effect of improving the lowerbound on the WO-EECBS | The "+" label denotes using an improved lowerbound; improving the lowerbound leads to a significant higher usage of CBS improvements with the y-axis denoting the average number (across 5 seeds) of cardinal conflicts and symmetry reasoning applied for each problem instance. Without the improved lower bound, WO-EECBS is usually unable to use these CBS improvements. Methods terminate on a map once they fail all 5 seeds on a certain number of agents or they reach the maximum number of agents in a scene, fractional values are due to the averaging over 5 seeds.
• Figure 3: WO-EECBS full results | The "+" label denotes using an improved lowerbound. A medium weighted value of w=1.5 performs the best on both maps. However, the maximum speed up peaks at around 35 in the Paris scenario and it struggles in all the harder scenarios (e.g. both random maps, empty-32-32, den312d). Additionally the improved lowerbound actually decreases performance contrary to our expectations.
• Figure 4: WF-EECBS $w_h, r$ Analysis | Left half: Lines with the same color have the same $w_h$ values, each $w_h$ color had 6 different line/marker styles corresponding to different $r$ values. We expect performance to be primarily driven by $w_h$, with methods with same $w_h$ values performing similarly and larger $w_h$ resulting in larger speed ups. However we see that methods with the same $w_h$ value (e.g. all the blue lines) are wildly scattered. Right half: Lines with the same color have the same $r$ values. We see a striking grouping effect across runs with same $r$ values but different $w_h$ values, showing how performance is tightly linked to $r$ and not$w_h$ across different $r$ and $w_h$ values across all the maps. Additionally, values too low $r=1,2$ (red, yellow) and too high $r=16,100$ (blue, purple) perform worse than $r=4,8$ (lime green, turquoise), implying some optimal region of $r \in [2,16]$.
• Figure 5: PP, CBS, W-EECBS equivalence | We see that running "CBSPP" (WO-EECBS with a very large suboptimality factor simulating $w_{so} \gets \infty, w_h=w$, or equivalently WF-EECBS with $w_{so}, r \gets \infty, w_h = w$) is equivalent to running $w$ weighted prioritized planning with CBS's conflict resolution capability. This is highlighted by the number of high level nodes sticking to one with low numbers of agents (identical to PP) as opposed to the baseline with several high level nodes, and then increasing only after conflicts are forced. Observe how the larger maps (top row) are able to be solved in only one high level node (i.e. no conflict resolution required), but smaller maps require reasoning over conflicts. Note the differing log y-axis values across different graphs. Fractional values due to averaging across 5 seeds.

Theorems & Definitions (2)

• Lemma 1
• proof