Roni Stern

Conflict-based search for optimal multi-agent pathfinding

In the multi agent path finding problem (MAPF) paths should be found for several agents, each with a different start and goal position such that agents do not collide. Previous optimal solvers applied global A*-based searches. We present a new search algorithm called Conflict Based Search (CBS). CBS is a two-level algorithm. At the high level, a search is performed on a tree based on conflicts between agents. At the low level, a search is performed only for a single agent at a time. In many cases this reformulation enables CBS to examine fewer states than A* while still maintaining optimality. We analyze CBS and show its benefits and drawbacks. Experimental results on various problems shows a speedup of up to a full order of magnitude over previous approaches.

The increasing cost tree search for optimal multi-agent pathfinding

We address the problem of optimal pathfinding for multiple agents. Given a start state and a goal state for each of the agents, the task is to find minimal paths for the different agents while avoiding collisions. Previous work on solving this problem optimally, used traditional single-agent search variants of the A* algorithm. We present a novel formalization for this problem which includes a search tree called the increasing cost tree (ICT) and a corresponding search algorithm, called the increasing cost tree search (ICTS) that finds optimal solutions. ICTS is a two-level search algorithm. The high-level phase of ICTS searches the increasing cost tree for a set of costs (cost per agent). The low-level phase of ICTS searches for a valid path for every agent that is constrained to have the same cost as given by the high-level phase. We analyze this new formalization, compare it to the A* search formalization and provide the pros and cons of each. Following, we show how the unique formalization of ICTS allows even further pruning of the state space by grouping small sets of agents and identifying unsolvable combinations of costs. Experimental results on various domains show the benefits and limitations of our new approach. A speedup of up to 3 orders of magnitude was obtained in some cases.

Enhanced partial expansion A

When solving instances of problem domains that feature a large branching factor, A* may generate a large number of nodes whose cost is greater than the cost of the optimal solution. We designate such nodes as surplus. Generating surplus nodes and adding them to the OPEN list may dominate both time and memory of the search. A recently introduced variant of A* called Partial Expansion A* (PEA*) deals with the memory aspect of this problem. When expanding a node n, PEA* generates all of its children and puts into OPEN only the children with f = f(n). n is reinserted in the OPEN list with the f-cost of the best discarded child. This guarantees that surplus nodes are not inserted into OPEN. In this paper, we present a novel variant of A* called Enhanced Partial Expansion A* (EPEA*) that advances the idea of PEA* to address the time aspect. Given a priori domain-and heuristic-specific knowledge, EPEA* generates only the nodes with f = f(n). Although EPEA* is not always applicable or practical, we study several variants of EPEA*, which make it applicable to a large number of domains and heuristics. In particular, the ideas of EPEA* are applicable to IDA* and to the domains where pattern databases are traditionally used. Experimental studies show significant improvements in run-time and memory performance for several standard benchmark applications. We provide several theoretical studies to facilitate an understanding of the new algorithm.

PHA*: finding the shortest path with A* in an unknown physical environment

We address the problem of finding the shortest path between two points in an unknown real physical environment, where a traveling agent must move around in the environment to explore unknown territory. We introduce the Physical-A* algorithm (PHA*) for solving this problem. PHA* expands all the mandatory nodes that A* would expand and returns the shortest path between the two points. However. due to the physical nature of the problem, the complexity of the algorithm is measured by the traveling effort of the moving agent and not by the number of generated nodes, as in standard A*. PHA* is presented a a two-level algorithm, such that its high level, A*, chooses the next node to be expanded and its low level directs the agent to that node in order to explore it. We present a number of variations for both the high-level and low-level procedures and evaluate their performance theoretically and experimentally. We show that the travel cost of our best variation is fairly dose to the optimal travel cost, assuming that the mandatory nodes of A* are known in advance. We then generalize our algorithm to the multi-agent case, where a number of cooperative agents are designed to solve the problem. Specifically, we provide an experimental implementation for such a system. It should be noted that the problem addressed here is not a navigation problem, but rather a problem of finding the shortest path between two points for future usage.

Suboptimal variants of the conflict-based search algorithm for the multi-agent pathfinding problem

The task in the multi-agent path finding problem (MAPF) is to find paths for multiple agents, each with a different start and goal position, such that agents do not collide. A successful optimal MAPF solver is the conflict-based search (CBS) algorithm. CBS is a two level algorithm where special conditions ensure it returns the optimal solution. Solving MAPF optimally is proven to be NP-hard, hence CBS and all other optimal solvers do not scale up. We propose several ways to relax the optimality conditions of CBS trading solution quality for runtime as well as bounded-suboptimal variants, where the returned solution is guaranteed to be within a constant factor from optimal solution cost. Experimental results show the benefits of our new approach; a massive reduction in running time is presented while sacrificing a minor loss in solution quality. Our new algorithms outperform other existing algorithms in most of the cases.

A novel SAT-based approach to model based diagnosis

This paper introduces a novel encoding of Model Based Diagnosis (MBD) to Boolean Satisfaction (SAT) focusing on minimal cardinality diagnosis. The encoding is based on a combination of sophisticated MBD preprocessing algorithms and the application of a SAT compiler which optimizes the encoding to provide more succinct CNF representations than obtained with previous works. Experimental evidence indicates that our approach is superior to all published algorithms for minimal cardinality MBD. In particular, we can determine, for the first time, minimal cardinality diagnoses for the entire standard ISCAS-85 and 74XXX benchmarks. Our results open the way to improve the state-of-the-art on a range of similar MBD problems.

Privacy preserving landmark detection

In many cases several entities, such as commercial companies, need to work together towards the achievement of joint goals, while hiding certain private information. Multi-agent STRIPS (MA-STRIPS) is a new and attractive model for describing collaborative multi-agent privacy preserving planning, which is appropriate for such problems. In single agent classical planning, landmarks are key to constructing strong heuristics for state space search. In this paper we propose a method for identifying landmarks in MA-STRIPS in a privacy preserving distributed setting. The agents collaborate to find sound landmarks without revealing their private actions or goals. In addition, we also propose a novel MA-STRIPS planner that uses these landmarks. We empirically show that our detected landmarks improve the performance of previous approaches, and that our new planner is faster than all existing planners for multi-agent problems.

PHA*: performing A* in unknown physical environments

We address the problem of finding the shortest path between two points in an unknown real physical environment, where a traveling agent must move around in the environment to explore unknown territories. We present the Physical-A* algorithm (PHA*) to solve such a problem. PHA* is a two-level algorithm in which the upper level is A*, which chooses the next node to expand and the lower level directs the agent to that node in order to explore it. The complexity of this algorithm is measured by the traveling effort of the moving agent and not by the number of generated nodes as in classical A*. We present a number of variations of both the upper level and lower level algorithms and compare them both experimentally and theoretically. We then generalize our algorithm to the multi-agent case where a number of cooperative agents are designed to solve this problem and show experimental implementation for such a system.

Collaborative privacy preserving multi-agent planning

In many cases several entities, such as commercial companies, need to work together towards the achievement of joint goals, while hiding certain private information. To collaborate effectively, some sort of plan is needed to coordinate the different entities. We address the problem of automatically generating such a coordination plan while preserving the agents’ privacy. Maintaining privacy is challenging when planning for multiple agents, especially when tight collaboration is needed and a global high-level view of the plan is required. In this work we present the Greedy Privacy-Preserving Planner (GPPP), a privacy preserving planning algorithm in which the agents collaboratively generate an abstract and approximate global coordination plan and then individually extend the global plan to executable plans. To guide GPPP, we propose two domain independent privacy preserving heuristics based on landmarks and pattern databases, which are classical heuristics for single agent search. These heuristics, called privacy-preserving landmarks and privacy preserving PDBs, are agnostic to the planning algorithm and can be used by other privacy-preserving planning algorithms. Empirically, we demonstrate on benchmark domains the benefits of using these heuristics and the advantage of GPPP over existing privacy preserving planners for the multi-agent STRIPS formalism.

Bandit Algorithms for Social Network Queries

In many cases the best way to find a profile or a set of profiles matching some criteria in a social network is via targeted crawling. An important challenge in targeted crawling is to choose the next profile to explore. Existing heuristics for targeted crawling are usually tailored for specific search criterion and could lead to short-sighted crawling decisions. In this paper we propose and evaluate a generic approach for guiding a social network crawler that aims to provide a proper balance between exploration and exploitation based on the recently introduced variant of the Multi-Armed Bandit problem with volatile arms (VMAB). Our approach is general-purpose. In addition, it provides provable performance guarantees. Experimental results indicate that our approach compares favorably with the best existing heuristics on two different domains.