Asynchronous PFC-MRDAC±Adopt —Consistency-Maintenance in Adopt—

Each agent has private problems. Private concerns can often be formulated in a general framework such as constraint satisfaction (where everything is modeled by either variables, values, or constraints). Often agents need to find agreement with others for the allocation of final resources. The constraint satisfaction (CSPs) is only a special case of optimization. Here it is shown how a very general technique for Distributed CSPs, Replicabased Multiply Asynchronous Search (R-MAS) (comprising ABT,ABTR,AAS,DMAC,DMAC-ABT), can be extended and applied to optimization problems in distributed Weighted CSPs (WCSPs). Centralized WCSPs can be seen as MAXCSPs where several constraints can link the same variables. PFC-MRDAC is a good approach to MAX-CSPs. How to asynchronize and adapt it to distributed WCSPs? This article describes how asynchronous consistency maintenance can be introduced in Adopt and in Asynchronous Branch&Bound1. The main new ideas proposed in this article are that: (a) a concept called Weighted Consistency Nogood (WCN) allows to maintain consistency in DisWCSPs, (b) leading to an asynchronous equivalent of PFC-MRDAC. (c) The feedback that Adopt needs about low bounds can be extracted from such WCNs.