在現代化物流倉庫中，代理人在地圖上移動以完成無窮無盡、即時分配的任務，這被規範為一個終身多智能體路徑規劃（lifelong MAPF）問題。解決此問題的目標是在有限的時間內找到每個代理人的理想路徑，同時最大化完成任務的吞吐量。然而，隨著地圖大小或代理人密度的增加，現有方法除了遇到了計算時間的指數級增長外，還會產生死結和繞道等負面現象。為了應對終身 MAPF 中的這些挑戰，我們調查了主要用於一次性多智能體路徑規劃（one-shot MAPF）的高速公路概念，也就是通過鼓勵代理人朝著同一方向移動以降低路徑規劃問題的複雜度。在本文中，我們提出兩種方法將高速公路的概念融入到終身 MAPF 框架中，並討論可以最小化現有死結和繞道問題的特性。實驗結果顯示，隨著地圖的增大，加入高速公路的概念能使計算時間顯著減少，並且幾乎不會對吞吐量造成影響。此外，當代理人密度增加時，利用高速公路也能顯著減少了死結和繞道的現象。

In modern fulfillment warehouses, agents traverse the map to complete endless tasks that arrive on the fly, which is formulated as a lifelong Multi-Agent Path Finding (lifelong MAPF) problem. The goal of tackling this challenging problem is to find the path for each agent in a finite runtime while maximizing the throughput. However, existing methods encounter exponential growth of runtime and undesirable phenomena of deadlocks and rerouting as the map size or agent density grows. To address these challenges in lifelong MAPF, we explore the idea of highways mainly studied for one-shot MAPF (i.e., finding paths at once beforehand), which reduces the complexity of the problem by encouraging agents to move in the same direction. We utilize two methods to incorporate the highway idea into the lifelong MAPF framework and discuss the properties that minimize the existing problems of deadlocks and rerouting. The experimental results demonstrate that the runtime is considerably reduced and the decay of throughput is gradually insignificant as the map size enlarges under the settings of the highway. Furthermore, when the density of agents increases, the phenomena of deadlocks and rerouting are significantly reduced by leveraging the highway.

摘要 --- i
Abstract --- ii
1 Introduction --- 1
2 Related Work --- 3
2.1 One-shot MAPF --- 3
2.2 Lifelong MAPF --- 4
2.3 Lifelong Solutions --- 4
2.4 Highway --- 5
3 Problem Definition --- 7
4 Lifelong MAPF with Highways --- 9
4.1 Highway Definition --- 9
4.2 Lifelong MAPF Framework --- 9
4.3 Strict-limit Highway and Soft-limit Highway --- 10
4.3.1 Strict-limit Highway --- 11
4.3.2 Soft-limit Highway --- 11
4.4 Highway Behaviors --- 12
4.5 Property of Avoiding Deadlocks --- 13
4.6 Property of Avoiding Rerouting --- 15
5 Experiments --- 17
5.1 Environment --- 17
5.2 Fulfillment Warehouse --- 19
5.3 From No Highway to Highway --- 19
5.4 Scaling up --- 21
5.4.1 Map Size --- 21
5.4.2 Number of Agents --- 22
6 Conclusion --- 25
References --- 27

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