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Speeding up GDL-based distributed constraint optimization algorithms in cooperative multi-agent systems

Speeding up GDL-based distributed constraint optimization algorithms in cooperative multi-agent systems
Speeding up GDL-based distributed constraint optimization algorithms in cooperative multi-agent systems
Coping with an increasing number of agents, tasks and/or resources in a complex environment poses an onerous challenge for coordination algorithms that are developed to process constraints in multi-agent systems. In particular, Distributed Constraint Optimization Problems (DCOPs) are a widely studied constraint handling framework for coordinating interactions in cooperative multi-agent systems. For the past decade, a number of algorithms have been developed to solve DCOPs, and they have been applied to many real world applications. However, it is often observed that the outcome obtained from such algorithms becomes outdated or unusable as the optimization process takes too much time. The issue of taking too long to complete the internal operation of a DCOP algorithm is even more severe and commonplace as the system becomes larger. This, in turn, limits the practical scalability of such algorithms. In effect, an optimization algorithm can eventually handle larger systems if the completion time can be minimized. However, it is difficult to maintain the quality of solution and generic applicability whilst minimizing the completion time.

In this thesis, we investigate techniques that have been used to solve DCOPs and examine their efficacy in light of the above mentioned observation. Specifically, we identify that Generalized Distributive Law (GDL) based inference algorithms have a number of axiomatic benefits, and as such, are suited to deploy in practical multi-agent settings. However, scalability remains a widely acknowledged challenge for these algorithms owing to a number of potentially expensive phases. In the multi-agent systems literature, several attempts have sought to improve the scalability of GDL-based algorithms by typically speeding up one of the expensive phases of existing approaches. However, most of them focus on a specific application domain, and therefore cannot be applied to general DCOP settings. Although a few studies have been conducted to speed-up GDL-based algorithms for general settings, they typically experience lack of consistency in their performance.

Against this background, the central problem that this thesis aims to address is of speeding up GDL-based DCOP algorithms, so that they can be applied to general DCOP settings without compromising on solution quality. To accomplish this objective, we determine three of the expensive phases of such algorithms, then speed them up independently. Firstly, the maximization operation - which a GDL-based algorithm performs repetitively during its optimization process. Notably, each of these operates on a search space that grows exponentially with either, or both, of the corresponding constraint function's arity and its associated variables' domain size. Consequently, this particular phase has been considered as one of the main reasons GDL-based algorithms can be computationally infeasible in practice, which eventually incurs delay in producing the final outcome of these algorithms. To overcome this challenge, we develop a generic domain pruning technique so that the corresponding maximization operator can act upon a significantly reduced search space of 33% to 81%. Moreover, we theoretically prove that the pruned search space obtained by our approach does not affect the outcome of the algorithms.

Secondly, GDL-based algorithms follow the Standard Message Passing (SMP) protocol to exchange messages among the nodes of a corresponding graphical representation of a DCOP. We identify that this incurs a significant delay in the form of average waiting time for agents to attain the ultimate outcome. Building on this insight, we advance the state-of-the-art by developing a new way of speeding up GDL-based message passing algorithms. In particular, we propose a new cluster-based generic message passing protocol that minimizes the completion time of GDL-based algorithms by replacing the SMP protocol. To elaborate further, our approach utilizes partial decentralization and combines clustering with domain pruning. It also uses a regression method to determine the appropriate number of clusters for a given scenario. We empirically evaluate the performance of our proposed method in different possible settings, and find that it brings down the completion time by around 37 - 85% (1.6 - 6.5 times faster) for 100 - 900 nodes and by around 47-91% (1.9-11 times faster) for 3000-10000 nodes, compared to the current state-of-the-art.

Finally, the conventional DCOP model assumes that the sub-problem that each agent is responsible for (i.e. the mapping of nodes in the constraint graph to agents) is part of the model description. While this assumption is often reasonable, there are many applications where there is some flexibility in making this assignment. Specifically, we recognise that a poor mapping can increase an algorithm's completion time in a significant manner, and that finding an optimal mapping is an NP-hard problem. In the wake of this trade-off, we propose a new time-efficient heuristic to determine a near-optimal mapping of nodes to the participating agents of a DCOP. As a pre-processing step, it works prior to executing the optimization process of a GDL-based algorithm, and can be executed in a centralized or a decentralized manner, depending on the applications' suitability. We empirically demonstrate that it performs at a level of around 90%-100% of the optimal mapping. Our results also show a speed-up of 16%-40% when compared with the state-of-the-art. This means that a GDL-based algorithm can perform 1.2-1.7 times faster when using node-to-agent mapping obtained by our method. When taken together, the contributions presented in this thesis signify advancement in the state-of-the art of GDL-based DCOP algorithms, in terms of their scalability and applicability, by speeding up their optimization process.
University of Southampton
Khan, Md. Mosaddek
6c5cfdba-17fd-4b64-9c26-97e562071ed2
Khan, Md. Mosaddek
6c5cfdba-17fd-4b64-9c26-97e562071ed2
Jennings, Nicholas
ab3d94cc-247c-4545-9d1e-65873d6cdb30

Khan, Md. Mosaddek (2018) Speeding up GDL-based distributed constraint optimization algorithms in cooperative multi-agent systems. University of Southampton, Doctoral Thesis, 143pp.

Record type: Thesis (Doctoral)

Abstract

Coping with an increasing number of agents, tasks and/or resources in a complex environment poses an onerous challenge for coordination algorithms that are developed to process constraints in multi-agent systems. In particular, Distributed Constraint Optimization Problems (DCOPs) are a widely studied constraint handling framework for coordinating interactions in cooperative multi-agent systems. For the past decade, a number of algorithms have been developed to solve DCOPs, and they have been applied to many real world applications. However, it is often observed that the outcome obtained from such algorithms becomes outdated or unusable as the optimization process takes too much time. The issue of taking too long to complete the internal operation of a DCOP algorithm is even more severe and commonplace as the system becomes larger. This, in turn, limits the practical scalability of such algorithms. In effect, an optimization algorithm can eventually handle larger systems if the completion time can be minimized. However, it is difficult to maintain the quality of solution and generic applicability whilst minimizing the completion time.

In this thesis, we investigate techniques that have been used to solve DCOPs and examine their efficacy in light of the above mentioned observation. Specifically, we identify that Generalized Distributive Law (GDL) based inference algorithms have a number of axiomatic benefits, and as such, are suited to deploy in practical multi-agent settings. However, scalability remains a widely acknowledged challenge for these algorithms owing to a number of potentially expensive phases. In the multi-agent systems literature, several attempts have sought to improve the scalability of GDL-based algorithms by typically speeding up one of the expensive phases of existing approaches. However, most of them focus on a specific application domain, and therefore cannot be applied to general DCOP settings. Although a few studies have been conducted to speed-up GDL-based algorithms for general settings, they typically experience lack of consistency in their performance.

Against this background, the central problem that this thesis aims to address is of speeding up GDL-based DCOP algorithms, so that they can be applied to general DCOP settings without compromising on solution quality. To accomplish this objective, we determine three of the expensive phases of such algorithms, then speed them up independently. Firstly, the maximization operation - which a GDL-based algorithm performs repetitively during its optimization process. Notably, each of these operates on a search space that grows exponentially with either, or both, of the corresponding constraint function's arity and its associated variables' domain size. Consequently, this particular phase has been considered as one of the main reasons GDL-based algorithms can be computationally infeasible in practice, which eventually incurs delay in producing the final outcome of these algorithms. To overcome this challenge, we develop a generic domain pruning technique so that the corresponding maximization operator can act upon a significantly reduced search space of 33% to 81%. Moreover, we theoretically prove that the pruned search space obtained by our approach does not affect the outcome of the algorithms.

Secondly, GDL-based algorithms follow the Standard Message Passing (SMP) protocol to exchange messages among the nodes of a corresponding graphical representation of a DCOP. We identify that this incurs a significant delay in the form of average waiting time for agents to attain the ultimate outcome. Building on this insight, we advance the state-of-the-art by developing a new way of speeding up GDL-based message passing algorithms. In particular, we propose a new cluster-based generic message passing protocol that minimizes the completion time of GDL-based algorithms by replacing the SMP protocol. To elaborate further, our approach utilizes partial decentralization and combines clustering with domain pruning. It also uses a regression method to determine the appropriate number of clusters for a given scenario. We empirically evaluate the performance of our proposed method in different possible settings, and find that it brings down the completion time by around 37 - 85% (1.6 - 6.5 times faster) for 100 - 900 nodes and by around 47-91% (1.9-11 times faster) for 3000-10000 nodes, compared to the current state-of-the-art.

Finally, the conventional DCOP model assumes that the sub-problem that each agent is responsible for (i.e. the mapping of nodes in the constraint graph to agents) is part of the model description. While this assumption is often reasonable, there are many applications where there is some flexibility in making this assignment. Specifically, we recognise that a poor mapping can increase an algorithm's completion time in a significant manner, and that finding an optimal mapping is an NP-hard problem. In the wake of this trade-off, we propose a new time-efficient heuristic to determine a near-optimal mapping of nodes to the participating agents of a DCOP. As a pre-processing step, it works prior to executing the optimization process of a GDL-based algorithm, and can be executed in a centralized or a decentralized manner, depending on the applications' suitability. We empirically demonstrate that it performs at a level of around 90%-100% of the optimal mapping. Our results also show a speed-up of 16%-40% when compared with the state-of-the-art. This means that a GDL-based algorithm can perform 1.2-1.7 times faster when using node-to-agent mapping obtained by our method. When taken together, the contributions presented in this thesis signify advancement in the state-of-the art of GDL-based DCOP algorithms, in terms of their scalability and applicability, by speeding up their optimization process.

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Published date: April 2018

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Local EPrints ID: 421047
URI: http://eprints.soton.ac.uk/id/eprint/421047
PURE UUID: 791a25e0-8fe3-4aa1-b8b3-a3edac0fa943

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Date deposited: 21 May 2018 16:30
Last modified: 13 Mar 2019 18:31

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Contributors

Author: Md. Mosaddek Khan
Thesis advisor: Nicholas Jennings

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