A complete distributed constraint optimization method for non-traditional pseudotree arrangements

Abstract

Distributed Constraint Optimization (DCOP) is a general framework that can model complex problems in multi-agent systems. Several current algorithms that solve general DCOP instances, including ADOPT and DPOP, arrange agents into a traditional pseudotree structure. We introduce an extension to the DPOP algorithm that handles an extended set of pseudotree arrangements. Our algorithm correctly solves DCOP instances for pseudotrees that include edges between nodes in separate branches. The algorithm also solves instances with traditional pseudotree arrangements using the same procedure as DPOP.We compare our algorithm with DPOP using several metrics including the induced width of the pseudotrees, the maximum dimensionality of messages and computation, and the maximum sequential path cost through the algorithm. We prove that for some problem instances it is not possible to generate a traditional pseudotree using edge-traversal heuristics that will outperform a cross-edged pseudotree. We use multiple heuristics to generate pseudotrees and choose the best pseudotree in linear space-time complexity. For some problem instances we observe significant improvements in message and computation sizes compared to DPOP.

Constructing a unifying theory of dynamic programming DCOP algorithms via the generalized distributive law

“…Secondly, notice that if two cliques C i and C j are connected by a separator s i j , the message from C i to C j is a table containing the values of function μ i j : D s i j → R. 3 When a clique C i sends a message to C j , it combines its local knowledge with all messages it has received from its neighbours other than C j , and transmits the result to C j . Following [1], we can regard a J T as a communication network where an edge from C i and C j is a transmission line that "filters out" dependence (by summarization in our case) on all variables but those common to C i and C j .…”

“…Messages/local knowledge K 3 Example of constraint graph, a pseudotree PT and its equivalent junction tree J T in Fig. 3.…”

“…In this section we show the generality of Action-GDL by showing that it unifies two state-of-the-art dynamic programming optimal DCOP algorithms that are based on the general distributed law (GDL): DPOP [15] and DCPOP [3].…”

“…DCPOP [3] is a generalization of DPOP based on an extension of PT s, namely crossedged PT s. A cross-edged PT (CT ) is a PT with the addition of cross-edges (dotted line). Figure 4b shows a CT for the constraint graph in Fig.…”

“…Dynamic programming algorithms, like the distributed pseudotree optimization procedure (DPOP) and its extensions [15], only require a linear number of messages, but their complexity lies on the message size, which may be very large. Recently, Atlas and Decker provided a generalization of DPOP, the so-called distributed cross-edged pseudotree optimization procedure (DCPOP) [3], which extends DPOP by handling an extended set of pseudotree arrangements. Moreover, researchers have also proposed hybrid algorithms that are able to preserve optimality whereas offering different trade-offs, as for instance MB-DPOP (message-size vs. memory) or PC-DPOP (number of messages vs partial centralisation) [14].…”