scholarly journals Multi-Agent Path Finding with Deadlines

2018 ◽  
Author(s):  
Hang Ma ◽  
Glenn Wagner ◽  
Ariel Felner ◽  
Jiaoyang Li ◽  
T. K. Satish Kumar ◽  
...  
Keyword(s):  
Flow Problem ◽  
Search Algorithms ◽  
The Other ◽  
Path Finding ◽  
Combinatorial Search ◽  
Programming Formulation ◽  
Commodity Flow ◽  
Linear Programming Formulation ◽  
Multi Agent ◽  
Integer Linear Programming Formulation

We formalize Multi-Agent Path Finding with Deadlines (MAPF-DL). The objective is to maximize the number of agents that can reach their given goal vertices from their given start vertices within the deadline, without colliding with each other. We first show that MAPF-DL is NP-hard to solve optimally. We then present two classes of optimal algorithms, one based on a reduction of MAPF-DL to a flow problem and a subsequent compact integer linear programming formulation of the resulting reduced abstracted multi-commodity flow network and the other one based on novel combinatorial search algorithms. Our empirical results demonstrate that these MAPF-DL solvers scale well and each one dominates the other ones in different scenarios.

scholarly journals Tournaments as Feedback Arc Sets

10.37236/1214 ◽  
1995 ◽  
Vol 2 (1) ◽  
Author(s):  
Garth Isaak
Keyword(s):  
Linear Programming ◽  
Lower Bounds ◽  
Integer Linear Programming ◽  
Minimum Size ◽  
Programming Formulation ◽  
Binary Expansion ◽  
Feedback Arc Set ◽  
Disjoint Cycles ◽  
Linear Programming Formulation ◽  
Integer Linear Programming Formulation

We examine the size $s(n)$ of a smallest tournament having the arcs of an acyclic tournament on $n$ vertices as a minimum feedback arc set. Using an integer linear programming formulation we obtain lower bounds $s(n) \geq 3n - 2 - \lfloor \log_2 n \rfloor$ or $s(n) \geq 3n - 1 - \lfloor \log_2 n \rfloor$, depending on the binary expansion of $n$. When $n = 2^k - 2^t$ we show that the bounds are tight with $s(n) = 3n - 2 - \lfloor \log_2 n \rfloor$. One view of this problem is that if the 'teams' in a tournament are ranked to minimize inconsistencies there is some tournament with $s(n)$ 'teams' in which $n$ are ranked wrong. We will also pose some questions about conditions on feedback arc sets, motivated by our proofs, which ensure equality between the maximum number of arc disjoint cycles and the minimum size of a feedback arc set in a tournament.

The Cloud Inside the Network

2015 ◽  
pp. 2198-2224
Author(s):  
João Soares ◽  
Romeu Monteiro ◽  
Márcio Melo ◽  
Susana Sargento ◽  
Jorge Carapinha
Keyword(s):  
Cloud Service ◽  
Integrated Approach ◽  
Cloud Services ◽  
Programming Formulation ◽  
Network Resources ◽  
Major Drawback ◽  
Linear Programming Formulation ◽  
Different Levels ◽  
Integer Linear Programming Formulation ◽  
Cloud Resources

The access infrastructure to the cloud is usually a major drawback that limits the uptake of cloud services. Attention has turned to rethinking a new architectural deployment of the overall cloud service delivery. In this chapter, the authors argue that it is not sufficient to integrate the cloud domain with the operator's network domain based on the current models. They envision a full integration of cloud and network, where cloud resources are no longer confined to a data center but are spread throughout the network and owned by the network operator. In such an environment, challenges arise at different levels, such as in resource management, where both cloud and network resources need to be managed in an integrated approach. The authors particularly address the resource allocation problem through joint virtualization of network and cloud resources by studying and comparing an Integer Linear Programming formulation and a heuristic algorithm.

scholarly journals Explanation Generation for Multi-Modal Multi-Agent Path Finding with Optimal Resource Utilization using Answer Set Programming

2020 ◽  
Vol 20 (6) ◽  
pp. 974-989
Author(s):  
AYSU BOGATARKAN ◽  
ESRA ERDEM
Keyword(s):  
Answer Set Programming ◽  
Search Problem ◽  
Path Finding ◽  
Combinatorial Search ◽  
Transportation Modes ◽  
Optimal Resource ◽  
Multi Agent ◽  
Nonexistence Of Solutions ◽  
Velocity Constraints ◽  
Answer Set

AbstractThe multi-agent path finding (MAPF) problem is a combinatorial search problem that aims at finding paths for multiple agents (e.g., robots) in an environment (e.g., an autonomous warehouse) such that no two agents collide with each other, and subject to some constraints on the lengths of paths. We consider a general version of MAPF, called mMAPF, that involves multi-modal transportation modes (e.g., due to velocity constraints) and consumption of different types of resources (e.g., batteries). The real-world applications of mMAPF require flexibility (e.g., solving variations of mMAPF) as well as explainability. Our earlier studies on mMAPF have focused on the former challenge of flexibility. In this study, we focus on the latter challenge of explainability, and introduce a method for generating explanations for queries regarding the feasibility and optimality of solutions, the nonexistence of solutions, and the observations about solutions. Our method is based on answer set programming.

Sign in / Sign up

Export Citation Format

Share Document