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).
ASP-DPOP is able to exploit problem structure by propagating hard constraints and using them to prune the search space efficiently. This reduces the memory requirement of the algorithm and improves the scalability of the system. Existing DCOP algorithms that also propagate hard and soft constraints to prune the search space include H-DPOP that propagates exclusively hard constraints @cite_68 , BrC-DPOP that propagates branch consistency @cite_21 , and variants of BnB-ADOPT @cite_59 @cite_48 @cite_15 that maintains soft-arc consistency @cite_17 @cite_57 @cite_56 . A key difference is that these algorithms require algorithm developers to explicitly implement the ability to reason about the hard and soft constraints and propagate them efficiently. In contrast, ASP-DPOP capitalizes on general purpose ASP solvers to do so.
@cite_48 @cite_21 @cite_56 @cite_57 @cite_59 @cite_15 @cite_68 @cite_17
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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. 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. 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. Distributed Constraint Optimization Problems (DCOPs) have been used to model a number of multi-agent coordination problems. In DCOPs, agents are assumed to have complete information about the utility of their possible actions. However, in many real-world applications, such utilities are stochastic due to the presence of exogenous events that are beyond the direct control of the agents. This paper addresses this issue by extending the standard DCOP model to Expected Regret DCOP (ER-DCOP) for DCOP applications with uncertainty in constraint utilities. Different from other approaches, ER-DCOPs aim at minimizing the overall expected regret of the problem. The paper proposes the ER-DPOP algorithm for solving ER-DCOPs, which is complete and requires a linear number of messages with respect to the number of agents in the problem. We further present two implementations of ER-DPOP---GPU- and ASP-based implementations---that orthogonally exploit the problem structure and present their evaluations on random networks and power network problems.