ITA-ECBS: A Bounded-Suboptimal Algorithm for the Combined Target-Assignment and Path-Finding Problem

TL;DR

This paper tackles Combined Target-Assignment and Path-Finding (TAPF), a TAPF variant of MAPF where targets are assigned to agents while planning collision-free paths to minimize flowtime. It introduces ITA-ECBS, the first bounded-suboptimal TAPF solver derived from the single-CT ITA-CBS framework, by deriving target assignments from a new Lower-Bound (LB) matrix $M_L$ and using focal search to maintain efficiency. The approach avoids the unboundedness observed when naively applying ECBS to ITA-CBS, and it leverages shortest-path costs as LB values to accelerate search. Empirical results show ITA-ECBS outperforms the prior bound-suboptimal method ECBS-TA in 87.42% of 54,033 solvable cases across eight MAPF maps, indicating substantial practical gains for TAPF problems in large-scale, constrained environments.

Abstract

Multi-Agent Path Finding (MAPF), i.e., finding collision-free paths for multiple robots, plays a critical role in many applications. Sometimes, assigning a target to each agent also presents a challenge. The Combined Target-Assignment and Path-Finding (TAPF) problem, a variant of MAPF, requires one to simultaneously assign targets to agents and plan collision-free paths for agents. Several algorithms, including CBM, CBS-TA, and ITA-CBS, optimally solve the TAPF problem, with ITA-CBS being the leading algorithm for minimizing flowtime. However, the only existing bounded-suboptimal algorithm ECBS-TA is derived from CBS-TA rather than ITA-CBS. So, it faces the same issues as CBS-TA, such as searching through multiple constraint trees and spending too much time on finding the next-best target assignment. We introduce ITA-ECBS, the first bounded-suboptimal variant of ITA-CBS. Transforming ITA-CBS to its bounded-suboptimal variant is challenging because different constraint tree nodes can have different assignments of targets to agents. ITA-ECBS uses focal search to achieve efficiency and determines target assignments based on a new lower bound matrix. We show that it runs faster than ECBS-TA in 87.42% of 54,033 test cases.

Figures (5)

• Figure 1: This figure shows the unbounded problem if we directly use ECBS in ITA-CBS. We have 2 agents $\{X,Y\}$ and target sets $X$:$\{A, B\}$ and $Y$:$\{A,B,C\}$. Red numbers represent the matrix's optimal TA solution. Orange cells represent the row update since the new constraint is related to only one agent. The suboptimality factor $w$ is $2$. ITA-CBS utilizes $M_c$ to obtain the optimal TA solution. Here, $\pi_{ta}$ is the TA solution of $M_c$. $c$ represents the flowtime based on $\pi_{ta}$. $c_L$ is the sum of LB values selected from $M_L$ based on $\pi_{ta}$. Real $c_L$ is the cost of the optimal TA solution of $M_L$. $d(H)$ represents the user-defined heuristic function used in FOCAL.
• Figure 2: Each subfigure contains 9,600 $(8\cdot 15\cdot 4\cdot 20)$ distinct test cases. We have chosen three suboptimality factors $w$ {1.00, 1.02, 1.20} to find optimal and bounded-suboptimal valid solutions with small and large suboptimality factors.
• Figure 3: ITA-ECBS overview: There are two CT nodes {$H_0, H_1$} in OPEN. (1) Although $H_0$ has a lower $c_L$ value and precedes $H_1$ in OPEN, the heuristic function $d(H)$ may result in $H_1$ being selected for expansion. (2) We verify whether $H_1.\pi$ is collision-free. If not, we generate two child CT nodes with new constraint sets $\Omega_2$ and $\Omega_3$ and then use focal search to obtain new $M_L$ and $M_c$ for each node. A new $M_L$ leads to a new $\pi_{ta}$ and $c_L$. The updated $\pi_{ta}$ and $M_c$ give us a bounded-suboptimal solution $\pi$ and the cost $c$. We then calculate $d(H)$. (3) We insert these two nodes into OPEN, indicated by the red values. (4) All CT nodes in OPEN with cost $c \leq w \cdot H_0.c_L$ are added to FOCAL. $H_2$ could be positioned ahead of $H_0$ in FOCAL by the heuristic function $d$.
• Figure 4: The success rates of different algorithms as a function of the suboptimality factor.
• Figure 6: Runtime breakdown (seconds) for target assignment (\ref{['alg:ITA-ECBS1']} Line 28), low-level search (Line 27), heuristic calculation for CT nodes (Line 32), CT node creation (Line 21), which requires copying variables and other tasks.