This paper explores the use of Answer Set Programming (ASP) in solving Distributed Constraint Optimization Problems (DCOPs). The paper provides the following novel contributions: (1) It shows how one can formulate DCOPs as logic programs; (2) It introduces ASP-DPOP, the first DCOP algorithm that is based on logic programming; (3) It experimentally shows that ASP-DPOP can be up to two orders of magnitude faster than DPOP (its imperative programming counterpart) as well as solve some problems that DPOP fails to solve, due to memory limitations; and (4) It demonstrates the applicability of ASP in a wide array of multi-agent problems currently modeled as DCOPs. Under consideration in Theory and Practice of Logic Programming (TPLP).
This note considers how to modify BnB-ADOPT, a well-known algorithm for optimally solving distributed constraint optimization problems, with a double aim: (i) to avoid sending most of the redundant messages and (ii) to handle cost functions of any arity. Some of the messages exchanged by BnB-ADOPT turned out to be redundant. Removing most of the redundant messages increases substantially communication efficiency: the number of exchanged messages is -in most cases-at least three times fewer (keeping the other measures almost unchanged), and termination and optimality are maintained. On the other hand, handling n-ary cost functions was addressed in the original work, but the presence of thresholds makes their practical usage more complex. Both issues -removing most of the redundant messages and efficiently handling n-ary cost functions- can be combined, producing the new version BnB-ADOPT+. Experimentally, we show the benefits of this version over the original one. The DCOP model has gained momentum in recent years thanks to its ability to capture problems that are naturally distributed and cannot be realistically addressed in a centralized manner. Dynamic programming based techniques have been recognized to be among the most effective techniques for building complete DCOP solvers (e.g., DPOP). Unfortunately, they also suffer from a widely recognized drawback: their messages are exponential in size. Another limitation is that most current DCOP algorithms do not actively exploit hard constraints, which are common in many real problems. This paper addresses these two limitations by introducing an algorithm, called BrC-DPOP, that exploits arc consistency and a form of consistency that applies to paths in pseudo-trees to reduce the size of the messages. Experimental results shows that BrC-DPOP uses messages that are up to one order of magnitude smaller than DPOP, and that it can scale up well, being able to solve problems that its counterpart can not. Gutierrez and Meseguer show how to enforce consistency in BnB-ADOPT+ for distributed constraint optimization, but they consider unconditional deletions only. However, during search, more values can be pruned conditionally according to variable instantiations that define subproblems. Enforcing consistency in these subproblems can cause further search space reduction. We introduce efficient methods to maintain soft arc consistencies in every subproblem during search, a non trivial task due to asynchronicity and induced overheads. Experimental results show substantial benefits on three different benchmarks. We are grateful to the anonymous referees for their constructive comments. The work of Lei and Lee was generously supported by grants CUHK413808, CUHK413710 and CUHK413713 from the Research Grants Council of Hong Kong SAR. The work of Gutierrez and Meseguer was partially supported by the Spanish project TIN2009-13591-C02-02 and Generalitat de Catalunya 2009-SGR-1434. The work of Gutierrez, Lee and Meseguer was also jointly supported by the CSIC RGC Joint Research Scheme grants S-HK003 12 and 2011HK0017. The work of Mak was performed while he was at CUHK. Several multiagent tasks can be formulated and solved as DCOPs. BnB-ADOPT+-AC is one of the most efficient algorithms for optimal DCOP solving. It is based on BnB-ADOPT, removing redundant messages and maintaining soft arc consistency during search. In this paper, we present several improvements for this algorithm, namely (i) a better implementation, (ii) processing exactly simultaneous deletions, and (iii) searching on arc consistent cost functions. We present empirical results showing the benefits of these improvements on several benchmarks. Distributed constraint optimization (DCOP) problems are a popular way of formulating and solving agent-coordination problems. A DCOP problem is a problem where several agents coordinate their values such that the sum of the resulting constraint costs is minimal. It is often desirable to solve DCOP problems with memory-bounded and asynchronous algorithms. We introduce Branch-and-Bound ADOPT (BnB-ADOPT), a memory-bounded asynchronous DCOP search algorithm that uses the message-passing and communication framework of ADOPT (Modi, Shen, Tambe, & Yokoo, 2005), a well known memory-bounded asynchronous DCOP search algorithm, but changes the search strategy of ADOPT from best-first search to depth-first branch-and-bound search. Our experimental results show that BnB-ADOPT finds cost-minimal solutions up to one order of magnitude faster than ADOPT for a variety of large DCOP problems and is as fast as NCBB, a memory-bounded synchronous DCOP search algorithm, for most of these DCOP problems. Additionally, it is often desirable to find bounded-error solutions for DCOP problems within a reasonable amount of time since finding cost-minimal solutions is NP-hard. The existing bounded-error approximation mechanism allows users only to specify an absolute error bound on the solution cost but a relative error bound is often more intuitive. Thus, we present two new bounded-error approximation mechanisms that allow for relative error bounds and implement them on top of BnB-ADOPT. ADOPT and BnB-ADOPT are two optimal DCOP search algorithms that are similar except for their search strategies: the former uses best-first search and the latter uses depth-first branch-and-bound search. In this paper, we present a new algorithm, called ADOPT(k), that generalizes them. Its behavior depends on the k parameter. It behaves like ADOPT when k = 1, like BnB-ADOPT when k = ∞ and like a hybrid of ADOPT and BnB-ADOPT when 1 < k < ∞. We prove that ADOPT(k) is a correct and complete algorithm and experimentally show that ADOPT(k) outperforms ADOPT and BnB-ADOPT on several benchmarks across several metrics. In distributed constraint optimization problems, dynamic programming methods have been recently proposed (e.g. DPOP). In dynamic programming many valuations are grouped together in fewer messages, which produce much less networking overhead than search. Nevertheless, these messages are exponential in size. The basic DPOP always communicates all possible assignments, even when some of them may be inconsistent due to hard constraints. Many real problems contain hard constraints that significantly reduce the space of feasible assignments. This paper introduces H-DPOP, a hybrid algorithm that is based on DPOP, which uses Constraint Decision Diagrams (CDD) to rule out infeasible assignments, and thus compactly represent UTIL messages. Experimental results show that H-DPOP requires several orders of magnitude less memory than DPOP, especially for dense and tightly-constrained problems. In the centralized context, global constraints have been essential for the advancement of constraint reasoning. In this paper we propose to include soft global constraints in distributed constraint optimization problems (DCOPs). Looking for efficiency, we study possible decompositions of global constraints, including the use of extra variables. We extend the distributed search algorithm BnB-ADOPT+ to support these representations of global constraints. In addition, we explore the relation of global constraints with soft local consistency in DCOPs, in particular for the generalized soft arc consistency (GAC) level. We include specific propagators for some well-known soft global constraints. Finally, we provide empirical results on several benchmarks.