DFS ordering in Nogood-based Asynchronous Distributed Optimization (ADOPT-ng)

This work proposes an asynchronous algorithm for solving Distributed Constraint Optimization problems (DCOPs) using a generalized kind of nogoods, called valued nogoods. The proposed technique is an extension of the asynchronous distributed optimization (ADOPT) where valued nogoods enable more flexible reasoning, leading to important speed-up. Valued nogoods are an extension of classic nogoods that associates each nogood with a threshold and optionally with a set of references to culprit constraints. ADOPT has the property of maintaining the initial distribution of the problem. ADOPT needs a preprocessing step consisting of computing a depth first search (DFS) tree on the agent graph. We show that besides bringing significant speed-up, valued nogoods allow for automatically detecting and exploiting DFS trees compatible with the current ordering since independent subproblems are now dynamically detected and exploited (DFS trees do not need to be specified/computed explicitly). However, not all possible orderings on variables are compatible with good DFS trees, and we find that on randomly ordered problems ADOPT-ng runs orders of magnitude slower than on orderings that are known to be compatible with short DFS trees. Being an extension of ABT, ADOPT-ng can also profit of the dynamic ordering heuristics enabled by Asynchronous Backtracking with Reordering (ABTR). However, our experiments imply that efficient dynamic ordering heuristics for ADOPT-ng will have to maintain compatibility with some DFS tree (e.g., to be decided by rebuilding DFS trees based on current search state). Experiments comparing ADOPT-ng with Valued Dynamic Backtracking show that ADOPT-ng also brings significant improvements over the old valued nogood-based algorithm.