Maintaining Soft Arc Consistencies in BnB-ADOPT+ During Search

Distributed Constraint Optimization Problems (DCOPs) have been applied in modeling and solving many multiagent coordination problems, such as meeting scheduling, sensor networks and traffic control. Several distributed algorithms for optimal DCOP solving have been proposed: ADOPT [Modi et al., 2005], DPOP [Petcu and Faltings, 2005], BnB-ADOPT [Yeoh et al., 2010]. BnB-ADOPT-AC and BnB-ADOPTFDAC [Gutierrez and Meseguer, 2010a] incorporate consistency enforcement during search into BnB-ADOPT [Gutierrez and Meseguer, 2010b], obtaining efficiency improvements. Enforcing consistency allows to prune some suboptimal values, making the search space smaller. This previous work considers unconditional deletions only, which avoids overhead in handling assignments and backtracking. However, values that could be deleted conditioned to some assignments will not be pruned with this strategy, so search space reduction opportunities are missed. A search-based constraint solving algorithm essentially forms subproblems of the original problem by variable assignments. Our goal is to maintain soft arc consistencies in each subproblem, so that variable assignments during search are also considered in consistency enforcement. As a result, we can explore more value pruning opportunities and thus further reduce the search space. An essential contribution in Gutierrez and Meseguer’s work is the introduction of an extra copy of cost functions in each agent, so that search and consistency enforcement are done asynchronously. Our contribution goes further maintaining soft arc consistencies in each subproblem during search, so that (i) search and consistency enforcement are done asynchronously, introducing some extra but finite and small number of variable domains and cost functions copies; (ii) the induced overhead caused by backtracking and undoing assignments and deletions is minimized. The asynchronicity requirement and different cost measurement (number of messages and NCCCs) require us to introduce novel techniques over those used in centralized CP. We show the benefits of our proposal on benchmarks usually unamenable to solvers without consistency.