Mohamed Wahbi

Nogood-based asynchronous forward checking algorithms

We propose two new algorithms for solving Distributed Constraint Satisfaction Problems (DisCSPs). The first algorithm, AFC-ng, is a nogood-based version of Asynchronous Forward Checking (AFC). Besides its use of nogoods as justification of value removals, AFC-ng allows simultaneous backtracks going from different agents to different destinations. The second algorithm, Asynchronous Forward Checking Tree (AFC-tree), is based on the AFC-ng algorithm and is performed on a pseudo-tree ordering of the constraint graph. AFC-tree runs simultaneous search processes in disjoint problem subtrees and exploits the parallelism inherent in the problem. We prove that AFC-ng and AFC-tree only need polynomial space. We compare the performance of these algorithms with other DisCSP algorithms on random DisCSPs and instances from real benchmarks: sensor networks and distributed meeting scheduling. Our experiments show that AFC-ng improves on AFC and that AFC-tree outperforms all compared algorithms, particularly on sparse problems.

Asynchronous inter-level forward-checking for DisCSPs

We propose two new asynchronous algorithms for solving Distributed Constraint Satisfaction Problems (DisCSPs). The first algorithm, AFC-ng, is a nogood-based version of Asynchronous Forward Checking (AFC). The second algorithm, Asynchronous Inter-Level Forward-Checking (AILFC), is based on the AFC-ng algorithm and is performed on a pseudo-tree ordering of the constraint graph. AFC-ng and AILFC only need polynomial space. We compare the performance of these algorithms with other DisCSP algorithms on random DisCSPs in two kinds of communication environments: Fast communication and slow communication. Our experiments show that AFC-ng improves on AFC and that AILFC outperforms all compared algorithms in communication load.

The Impact of Wireless Communication on Distributed Constraint Satisfaction

Distributed constraint satisfaction (DisCSP ) models decision problems where physically distributed agents control different decision variables, but must communicate with each other to agree on a global solution. Most DisCSP research assumes an abstract communication layer based on a peer-to-peer wired network. However, many practical applications of distributed reasoning require to be implemented over wireless networks, which impose different communication costs, and may affect the performance of DisCSP algorithms. We study the impact of wireless network topology and routing on two leading DisCSP algorithms – ABT and AFC-ng. We introduce a new framework for experiments which models different communication layers. We show that the communication layer has a significant impact on the messaging costs, which can vary by over an order of magnitude. We also show the impact on computation time, where the equivalent non-concurrent constraint checks can vary by a factor of 6. Finally, we show that given a fixed agent ordering, changing the communications topology can increase the number of messages by up to 50%.

Agile Asynchronous Backtracking for Distributed Constraint Satisfaction Problems

Asynchronous Backtracking is the standard search procedure for distributed constraint reasoning. It requires a total ordering on the agents. All polynomial space algorithms proposed so far to improve Asynchronous Backtracking by reordering agents during search only allow a limited amount of reordering. In this paper, we propose Agile-ABT, a search procedure that is able to change the ordering of agents more than previous approaches. This is done via the original notion of termination value, a vector of stamps labelling the new orders exchanged by agents during search. In Agile-ABT, agents can reorder themselves as much as they want as long as the termination value decreases as the search progresses. Our experiments show the good performance of Agile-ABT when compared to other dynamic reordering techniques.

Asynchronous forward bounding revisited

The Distributed Constraint Optimization Problem DCOP is a powerful framework for modeling and solving applications in multi-agent coordination. Asynchronous Forward Bounding AFB_BJ is one of the best algorithms to solve DCOPs.We propose AFB_BJ+, a revisited version of AFB_BJ in which we refine the lower bound computations. We also propose to compute lower bounds for the whole domain of the last assigned agent instead of only doing this for its current assignment. This reduces both the number of messages needed and the time future agents remain idle. In addition, these lower bounds can be used as a value ordering heuristic in AFB_BJ+. The experimental evaluation on standard benchmark problems shows the efficiency of AFB_BJ+ compared to other algorithms for DCOPs.

A distributed asynchronous solver for Nash Equilibria in hypergraphical games

Hypergraphical games provides a compact model of a network of self-interested agents, each involved in simultaneous subgames with its neighbors. The overall aim is for the agents in the network to reach a Nash Equilibrium, in which no agent has an incentive to change their response, but without revealing all their private information. Asymmetric Distributed constraint satisfaction (ADisCSP) has been proposed as a solution to this search problem. In this paper, we propose a new model of hypergraphical games as an ADisCSP based on a new global constraint, and a new asynchronous algorithm for solving ADisCSP that is able to find a Nash Equilibrium. We show empirically that we significantly reduce both message passing and computation time, achieving an order of magnitude improvement in messaging and in non-concurrent computation time on dense problems compared to state-of-the art algorithms.

A General Framework for Reordering Agents Asynchronously in Distributed CSP

Reordering agents during search is an essential component of the efficiency of solving a distributed constraint satisfaction problem. Termination values have been recently proposed as a way to simulate the min-domain dynamic variable ordering heuristic. The use of termination values allows the greatest flexibility in reordering agents dynamically while keeping polynomial space. In this paper, we propose a general framework based on termination values for reordering agents asynchronously. The termination values are generalized to represent various heuristics other than min-domain. Our general framework is sound, complete, terminates and has a polynomial space complexity. We implemented several variable ordering heuristics that are well-known in centralized CSPs but could not until now be applied to the distributed setting. Our empirical study shows the significance of our framework compared to state-of-the-art asynchronous dynamic ordering algorithms for solving distributed CSP.

Maintaining Arc Consistency Asynchronously in Synchronous Distributed Search

We recently proposed No good-Based Asynchronous Forward Checking (AFC-ng), an efficient and robust algorithm for solving Distributed Constraint Satisfaction Problems (DisCSPs). AFC-ng performs an asynchronous forward checking phase during synchronous search. In this paper, we propose two new algorithms based on the same mechanism as AFC-ng. However, instead of using forward checking as a filtering property, we propose to maintain arc consistency asynchronously (MACA). The first algorithm we propose, MACA-del, enforces arc consistency thanks to an additional type of messages, deletion messages. The second algorithm, MACA-not, achieves arc consistency without any new type of message. We provide a theoretical analysis and an experimental evaluation of the proposed approach. Our experiments show the good performance of MACA algorithms, particularly those of MACA-not.

Corrigendum to Min-domain retroactive ordering for asynchronous backtracking

The asynchronous backtracking algorithm with dynamic ordering (ABT_DO), proposed in Zivan and Meisels (Constraints 11(2–3):179–197, 2006), allows changing the order of agents during distributed asynchronous complete search. In a later study (Zivan et al., Constraints 14(2):177–198, 2009), retroactive heuristics which allowed more flexibility in the selection of new orders were introduced, resulting in the ABT_DO-Retro algorithm, and a relation between the success of heuristics and the min-domain property was identified. Unfortunately, the description of the time-stampping protocol used to compare orders in ABT_DO-Retro in Zivan et al. (Constraints 14(2):177–198, 2009) is confusing and may lead to an implementation in which ABT_DO-Retro may not terminate. In this corrigendum, we demonstrate the possible undesired outcome and give a detailed and formal description of the correct method for comparing time-stamps in ABT_DO-Retro.

A Distributed Optimization Method for the Geographically Distributed Data Centres Problem

The geographically distributed data centres problem (GDDC) is a naturally distributed resource allocation problem. The problem involves allocating a set of virtual machines (VM) amongst the data centres (DC) in each time period of an operating horizon. The goal is to optimize the allocation of workload across a set of DCs such that the energy cost is minimized, while respecting limitations on data centre capacities, migrations of VMs, etc. In this paper, we propose a distributed optimization method for GDDC using the distributed constraint optimization (DCOP) framework. First, we develop a new model of the GDDC as a DCOP where each DC operator is represented by an agent. Secondly, since traditional DCOP approaches are unsuited to these types of large-scale problem with multiple variables per agent and global constraints, we introduce a novel semi-asynchronous distributed algorithm for solving such DCOPs. Preliminary results illustrate the benefits of the new method.