Limited discrepancy AND/OR search and its application to optimization tasks in graphical models

Many combinatorial problems are solved with a Depth-First search (DFS) guided by a heuristic and it is well-known that this method is very fragile with respect to heuristic mistakes. One standard way to make DFS more robust is to search by increasing number of discrepancies. This approach has been found useful in several domains where the search structure is a height-bounded OR tree. In this paper we investigate the generalization of discrepancy-based search to AND/OR search trees and propose an extension of the Limited Discrepancy Search (LDS) algorithm. We demonstrate the relevance of our proposal in the context of Graphical Models. In these problems, which can be solved with either a standard OR search tree or an AND/OR tree, we show the superiority of our approach. For a fixed number of discrepancies, the search space visited by the AND/OR algorithm strictly contains the search space visited by standard LDS, and many more nodes can be visited due to the multiplicative effect of the AND/OR decomposition. Besides, if the AND/OR tree achieves a significant size reduction with respect to the standard OR tree, the cost of each iteration of the AND/OR algorithm is asymptotically lower than in standard LDS. We report experiments on the minsum problem on different domains and show that the AND/OR version of LDS usually obtains better solutions given the same CPU time.Peer ReviewedPostprint (published version

Look-ahead with mini-bucket heuristics for MPE

The paper investigates the potential of look-ahead in the con-text of AND/OR search in graphical models using the Mini-Bucket heuristic for combinatorial optimization tasks (e.g., MAP/MPE or weighted CSPs). We present and analyze the complexity of computing the residual (a.k.a Bellman update) of the Mini-Bucket heuristic and show how this can be used to identify which parts of the search space are more likely to benefit from look-ahead and how to bound its overhead. We also rephrase the look-ahead computation as a graphical model, to facilitate structure exploiting inference schemes. We demonstrate empirically that augmenting Mini-Bucket heuristics by look-ahead is a cost-effective way of increasing the power of Branch-And-Bound search.Postprint (published version

Partial lazy forward checking

Partial forward checking (PFC) may perform more consistency checks than really needed to detect dead-ends in MAX-CSP. After analyzing PFC, we have identified four causes of redundant check computation: (a) unnecessary lookahead when detecting an empty domain, (b) not always using the better bounds for future value pruning, (c) computing in advance inconsistency counts, and (d) lookahead is performed on the whole set of future variables. We present the partial lazy forward checking (PLFC) algorithm, which follows a lazy approach delaying as much as possible inconsistency count computation, keeping updated the contribution of future variables to the lower bound. This algorithm avoids the causes of redundant checks identified for PFC. It can be easily combined with DACs, producing the PLFC-DAC algorithm. Empirical results on random problems show that PLFC-DAC outperforms previous algorithms in both consistency checks and CPU time.Postprint (published version

Residual-guided look-ahead in AND/OR search for graphical models

We introduce the concept of local bucket error for the mini-bucket heuristics and show how it can be used to improve the power of AND/OR search for combinatorial optimization tasks in graphical models (e.g. MAP/MPE or weighted CSPs). The local bucket error illuminates how the heuristic errors are distributed in the search space, guided by the mini-bucket heuristic. We present and analyze methods for compiling the local bucket-errors (exactly and approximately) and show that they can be used to yield an effective tool for balancing look-ahead overhead during search. This can be especially instrumental when memory is restricted, accommodating the generation of only weak compiled heuristics. We illustrate the impact of the proposed schemes in an extensive empirical evaluation for both finding exact solutions and anytime suboptimal solutions.Peer ReviewedPostprint (published version

Generic CSP techniques for the job-shop problem

The job-shop is a classical problem in manufacturing, arising daily in factories and workshops. From an AI perspective, the job-shop is a constraint satisfaction problem (CSP), and many specific techniques have been developed to solve it efficiently. In this context, one may believe that generic search and CSP methods (which typically are better understood and easier to develop, codify and maintain than specific approaches) are not appropriated for this problem. In this paper, we contradict this belief. We show that generic search and CSP algorithms and heuristics can be successfully applied to job-shop problem instances that have been considered challenging by the job-shop community. In particular, we use forward checking with support-based heuristics, a combination of a generic CSP algorithm with generic heuristics. We improve this combination replacing the depth-first search strategy of forward checking by a discrepancy-based schema, a generic search strategy recently developed. Our approach obtains similar results to specific approaches in terms of the number of solved problems, with reasonable requirements in computational resources.Postprint (published version

Dinamització d'aules informàtiques a Senegal i Mali

Postprint (published version

Dinamització d'aules informàtiques a Senegal i Mali

Postprint (published version

Augmenting the power of (partial) MaxSat resolution with extension

The refutation power of SAT and MaxSAT resolution is challenged by problems like the soft and hard Pigeon Hole Problem PHP for which short refutations do not exist. In this paper we augment the MaxSAT resolution proof system with an extension rule. The new proof system MaxResE is sound and complete, and more powerful than plain MaxSAT resolution, since it can refute the soft and hard PHP in polynomial time. We show that MaxResE refutations actually subtract lower bounds from the objective function encoded by the formulas. The resulting formula is the residual after the lower bound extraction. We experimentally show that the residual of the soft PHP (once its necessary cost of 1 has been efficiently subtracted with MaxResE) is a concise, easy to solve, satisfiable problem.This work was funded partially by the Spanish MINECO and MICINN projects TIN2015-69175-C4-3-R and RTI2018-094403-B-C33.Peer ReviewedPostprint (published version