Conflict History Based Branching Heuristic for CSP Solving

International audienceAn important feature in designing algorithms to solve Constraint Satisfaction Problems (CSP) is the definition of a branching heuristic to explore efficiently the search space and exploit the problem structure. We propose Conflict-History Search (CHS), a new dynamic and adaptive branching heuristic for CSP solving. It is based on the search history by considering the temporality of search failures. To achieve that, we use the exponential recency weighted average to estimate the evolution of the hardness of constraints throughout the search. The experimental evaluation on XCSP3 instances shows that integrating CHS to solvers based on MAC obtains competitive results and can improve those obtained through other heuristics of the state of the art

Conflict History based Search for Constraint Satisfaction Problem

International audienc

Combining VSIDS and CHB Using Restarts in SAT

Conflict Driven Clause Learning (CDCL) solvers are known to be efficient on structured instances and manage to solve ones with a large number of variables and clauses. An important component in such solvers is the branching heuristic which picks the next variable to branch on. In this paper, we evaluate different strategies which combine two state-of-the-art heuristics, namely the Variable State Independent Decaying Sum (VSIDS) and the Conflict History-Based (CHB) branching heuristic. These strategies take advantage of the restart mechanism, which helps to deal with the heavy-tailed phenomena in SAT, to switch between these heuristics thus ensuring a better and more diverse exploration of the search space. Our experimental evaluation shows that combining VSIDS and CHB using restarts achieves competitive results and even significantly outperforms both heuristics for some chosen strategies

Monte Carlo Forest Search: UNSAT Solver Synthesis via Reinforcement learning

We introduce Monte Carlo Forest Search (MCFS), an offline algorithm for automatically synthesizing strong tree-search solvers for proving \emph{unsatisfiability} on given distributions, leveraging ideas from the Monte Carlo Tree Search (MCTS) algorithm that led to breakthroughs in AlphaGo. The crucial difference between proving unsatisfiability and existing applications of MCTS, is that policies produce trees rather than paths. Rather than finding a good path (solution) within a tree, the search problem becomes searching for a small proof tree within a forest of candidate proof trees. We introduce two key ideas to adapt to this setting. First, we estimate tree size with paths, via the unbiased approximation from Knuth (1975). Second, we query a strong solver at a user-defined depth rather than learning a policy across the whole tree, in order to focus our policy search on early decisions, which offer the greatest potential for reducing tree size. We then present MCFS-SAT, an implementation of MCFS for learning branching policies for solving the Boolean satisfiability (SAT) problem that required many modifications from AlphaGo. We matched or improved performance over a strong baseline on two well-known SAT distributions (\texttt{sgen}, \texttt{random}). Notably, we improved running time by 9\% on \texttt{sgen} over the \texttt{kcnfs} solver and even further over the strongest UNSAT solver from the 2021 SAT competition

Proceedings of the 2022 XCSP3 Competition

This document represents the proceedings of the 2022 XCSP3 Competition. The results of this competition of constraint solvers were presented at FLOC (Federated Logic Conference) 2022 Olympic Games, held in Haifa, Israel from 31th July 2022 to 7th August, 2022.Comment: arXiv admin note: text overlap with arXiv:1901.0183

Towards 40 years of constraint reasoning

Research on constraints started in the early 1970s. We are approaching 40 years since the beginning of this successful field, and it is an opportunity to revise what has been reached. This paper is a personal view of the accomplishments in this field. We summarize the main achievements along three dimensions: constraint solving, modelling and programming. We devote special attention to constraint solving, covering popular topics such as search, inference (especially arc consistency), combination of search and inference, symmetry exploitation, global constraints and extensions to the classical model. For space reasons, several topics have been deliberately omitted.Partially supported by the Spanish project TIN2009-13591-C02-02 and Generalitat de Catalunya grant 2009-SGR-1434.Peer Reviewe

Proceedings of SAT Competition 2020 : Solver and Benchmark Descriptions

Non peer reviewe