scholarly journals Branch-and-Cut-and-Price for Multi-Agent Pathfinding

2019 ◽  
Author(s):  
Edward Lam ◽  
Pierre Le Bodic ◽  
Daniel D. Harabor ◽  
Peter J. Stuckey
Keyword(s):  
State Of The Art ◽  
Optimal Algorithm ◽  
Mathematical Optimization ◽  
Combinatorial Problems ◽  
The State ◽  
Branch And Cut ◽  
Multi Agent

There are currently two broad strategies for optimal Multi-agent Pathfinding (MAPF): (1) search-based methods, which model and solve MAPF directly, and (2) compilation-based solvers, which reduce MAPF to instances of well-known combinatorial problems, and thus, can benefit from advances in solver techniques. In this work, we present an optimal algorithm, BCP, that hybridizes both approaches using Branch-and-Cut-and-Price, a decomposition framework developed for mathematical optimization. We formalize BCP and compare it empirically against CBSH and CBSH-RM, two leading search-based solvers. Conclusive results on standard benchmarks indicate that its performance exceeds the state-of-the-art: solving more instances on smaller grids and scaling reliably to 100 or more agents on larger game maps.

scholarly journals Multifeature Extreme Ordinal Ranking Machine for Facial Age Estimation

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Wei Zhao ◽  
Han Wang ◽  
Guang-Bin Huang
Keyword(s):  
Age Estimation ◽  
Optimization Problems ◽  
State Of The Art ◽  
Mathematical Optimization ◽  
The State ◽  
Estimation Methods ◽  
Estimation Accuracy ◽  
Training Process ◽  
Ordinal Ranking ◽  
Facial Age

Recently the state-of-the-art facial age estimation methods are almost originated from solving complicated mathematical optimization problems and thus consume huge quantities of time in the training process. To refrain from such algorithm complexity while maintaining a high estimation accuracy, we propose a multifeature extreme ordinal ranking machine (MFEORM) for facial age estimation. Experimental results clearly demonstrate that the proposed approach can sharply reduce the runtime (even up to nearly one hundred times faster) while achieving comparable or better estimation performances than the state-of-the-art approaches. The inner properties of MFEORM are further explored with more advantages.

scholarly journals Integer Programming, Constraint Programming, and Hybrid Decomposition Approaches to Discretizable Distance Geometry Problems

2021 ◽  
Author(s):  
Moira MacNeil ◽  
Merve Bodur
Keyword(s):  
Integer Programming ◽  
Constraint Programming ◽  
State Of The Art ◽  
Valid Inequalities ◽  
Distance Geometry ◽  
The State ◽  
Bp Algorithm ◽  
Branch And Cut ◽  
Vertex Order ◽  
Hybrid Decomposition

Given an integer dimension K and a simple, undirected graph G with positive edge weights, the Distance Geometry Problem (DGP) aims to find a realization function mapping each vertex to a coordinate in [Formula: see text] such that the distance between pairs of vertex coordinates is equal to the corresponding edge weights in G. The so-called discretization assumptions reduce the search space of the realization to a finite discrete one, which can be explored via the branch-and-prune (BP) algorithm. Given a discretization vertex order in G, the BP algorithm constructs a binary tree where the nodes at a layer provide all possible coordinates of the vertex corresponding to that layer. The focus of this paper is on finding optimal BP trees for a class of discretizable DGPs. More specifically, we aim to find a discretization vertex order in G that yields a BP tree with the least number of branches. We propose an integer programming formulation and three constraint programming formulations that all significantly outperform the state-of-the-art cutting-plane algorithm for this problem. Moreover, motivated by the difficulty in solving instances with a large and low-density input graph, we develop two hybrid decomposition algorithms, strengthened by a set of valid inequalities, which further improve the solvability of the problem. Summary of Contribution: We present a new model to solve a combinatorial optimization problem on graphs, MIN DOUBLE, which comes from the highly active area of distance geometry and has applications in a wide variety of fields. We use integer programming (IP) and present the first constraint programming (CP) models and hybrid decomposition methods, implemented as a branch-and-cut procedure, for MIN DOUBLE. Through an extensive computational study, we show that our approaches advance the state of the art for MIN DOUBLE. We accomplish this by not only combining generic techniques from IP and CP but also exploring the structure of the problem in developing valid inequalities and variable fixing rules. Our methods significantly improve the solvability of MIN DOUBLE, which we believe can also provide insights for tackling other problem classes and applications.

scholarly journals Automated Algorithm Selection: Survey and Perspectives

2019 ◽  
Vol 27 (1) ◽  
pp. 3-45 ◽  
Author(s):  
Pascal Kerschke ◽  
Holger H. Hoos ◽  
Frank Neumann ◽  
Heike Trautmann
Keyword(s):  
State Of The Art ◽  
Combinatorial Problems ◽  
The State ◽  
Problem Instance ◽  
Ai Planning ◽  
Algorithm Selection ◽  
Automated Algorithm ◽  
Continuous Problems ◽  
Algorithm Configuration ◽  
The One

It has long been observed that for practically any computational problem that has been intensely studied, different instances are best solved using different algorithms. This is particularly pronounced for computationally hard problems, where in most cases, no single algorithm defines the state of the art; instead, there is a set of algorithms with complementary strengths. This performance complementarity can be exploited in various ways, one of which is based on the idea of selecting, from a set of given algorithms, for each problem instance to be solved the one expected to perform best. The task of automatically selecting an algorithm from a given set is known as the per-instance algorithm selection problem and has been intensely studied over the past 15 years, leading to major improvements in the state of the art in solving a growing number of discrete combinatorial problems, including propositional satisfiability and AI planning. Per-instance algorithm selection also shows much promise for boosting performance in solving continuous and mixed discrete/continuous optimisation problems. This survey provides an overview of research in automated algorithm selection, ranging from early and seminal works to recent and promising application areas. Different from earlier work, it covers applications to discrete and continuous problems, and discusses algorithm selection in context with conceptually related approaches, such as algorithm configuration, scheduling, or portfolio selection. Since informative and cheaply computable problem instance features provide the basis for effective per-instance algorithm selection systems, we also provide an overview of such features for discrete and continuous problems. Finally, we provide perspectives on future work in the area and discuss a number of open research challenges.

scholarly journals Speeding Up Incomplete GDL-based Algorithms for Multi-agent Optimization with Dense Local Utilities

2020 ◽  
Author(s):  
Yanchen Deng ◽  
Bo An
Keyword(s):  
Utility Function ◽  
Branch And Bound ◽  
State Of The Art ◽  
Search Space ◽  
Computational Effort ◽  
The State ◽  
Computational Overhead ◽  
Multi Agent

Incomplete GDL-based algorithms including Max-sum and its variants are important methods for multi-agent optimization. However, they face a significant scalability challenge as the computational overhead grows exponentially with respect to the arity of each utility function. Generic Domain Pruning (GDP) technique reduces the computational effort by performing a one-shot pruning to filter out suboptimal entries. Unfortunately, GDP could perform poorly when dealing with dense local utilities and ties which widely exist in many domains. In this paper, we present several novel sorting-based acceleration algorithms by alleviating the effect of densely distributed local utilities. Specifically, instead of one-shot pruning in GDP, we propose to integrate both search and pruning to iteratively reduce the search space. Besides, we cope with the utility ties by organizing the search space of tied utilities into AND/OR trees to enable branch-and-bound. Finally, we propose a discretization mechanism to offer a tradeoff between the reconstruction overhead and the pruning efficiency. We demonstrate the superiorities of our algorithms over the state-of-the-art from both theoretical and experimental perspectives.

scholarly journals Unifying Search-based and Compilation-based Approaches to Multi-agent Path Finding through Satisfiability Modulo Theories

2019 ◽  
Author(s):  
Pavel Surynek
Keyword(s):  
Undirected Graph ◽  
State Of The Art ◽  
The State ◽  
Satisfiability Modulo Theories ◽  
Path Finding ◽  
Low Level ◽  
Multi Agent ◽  
High Level ◽  
Novel Algorithm

We unify search-based and compilation-based approaches to multi-agent path finding (MAPF) through satisfiability modulo theories (SMT). The task in MAPF is to navigate agents in an undirected graph to given goal vertices so that they do not collide. We rephrase Conflict-Based Search (CBS), one of the state-of-the-art algorithms for optimal MAPF solving, in the terms of SMT. This idea combines SAT-based solving known from MDD-SAT, a SAT-based optimal MAPF solver, at the low-level with conflict elimination of CBS at the high-level. Where the standard CBS branches the search after a conflict, we refine the propositional model with a disjunctive constraint. Our novel algorithm called SMT-CBS hence does not branch at the high-level but incrementally extends the propositional model. We experimentally compare SMT-CBS with CBS, ICBS, and MDD-SAT.

scholarly journals AI for Explaining Decisions in Multi-Agent Environments

2020 ◽  
Vol 34 (09) ◽  
pp. 13534-13538
Author(s):  
Sarit Kraus ◽  
Amos Azaria ◽  
Jelena Fiosina ◽  
Maike Greve ◽  
Noam Hazon ◽  
...  
Keyword(s):  
User Satisfaction ◽  
State Of The Art ◽  
Research Direction ◽  
The State ◽  
The Other ◽  
Research Directions ◽  
Multi Agent ◽  
New Research

Explanation is necessary for humans to understand and accept decisions made by an AI system when the system's goal is known. It is even more important when the AI system makes decisions in multi-agent environments where the human does not know the systems' goals since they may depend on other agents' preferences. In such situations, explanations should aim to increase user satisfaction, taking into account the system's decision, the user's and the other agents' preferences, the environment settings and properties such as fairness, envy and privacy. Generating explanations that will increase user satisfaction is very challenging; to this end, we propose a new research direction: Explainable decisions in Multi-Agent Environments (xMASE). We then review the state of the art and discuss research directions towards efficient methodologies and algorithms for generating explanations that will increase users' satisfaction from AI systems' decisions in multi-agent environments.

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