Loandra, : Core-Boosted Linear Search for incomplete MaxSAT

Non peer reviewe

Core-Guided and Core-Boosted Search for CP

Peer reviewe

MaxSAT Evaluation 2021 : Solver and Benchmark Descriptions

Non peer reviewe

MaxSAT Evaluation 2022 : Solver and Benchmark Descriptions

Non peer reviewe

Incomplete MaxSAT Solving by Linear Programming Relaxation and Rounding

NP-hard optimization problems can be found in various real-world settings such as scheduling, planning and data analysis. Coming up with algorithms that can efficiently solve these problems can save various rescources. Instead of developing problem domain specific algorithms we can encode a problem instance as an instance of maximum satisfiability (MaxSAT), which is an optimization extension of Boolean satisfiability (SAT). We can then solve instances resulting from this encoding using MaxSAT specific algorithms. This way we can solve instances in various different problem domains by focusing on developing algorithms to solve MaxSAT instances. Computing an optimal solution and proving optimality of the found solution can be time-consuming in real-world settings. Finding an optimal solution for problems in these settings is often not feasible. Instead we are only interested in finding a good quality solution fast. Incomplete solvers trade guaranteed optimality for better scalability. In this thesis, we study an incomplete solution approach for solving MaxSAT based on linear programming relaxation and rounding. Linear programming (LP) relaxation and rounding has been used for obtaining approximation algorithms on various NP-hard optimization problems. As such we are interested in investigating the effectiveness of this approach on MaxSAT. We describe multiple rounding heuristics that are empirically evaluated on random, crafted and industrial MaxSAT instances from yearly MaxSAT Evaluations. We compare rounding approaches against each other and to state-of-the-art incomplete solvers SATLike and Loandra. The LP relaxation based rounding approaches are not competitive in general against either SATLike or Loandra However, for some problem domains our approach manages to be competitive against SATLike and Loandra

Preprocessing in Incomplete MaxSAT Solving

Peer reviewe

MaxSAT Evaluation 2020 : Solver and Benchmark Descriptions

Non peer reviewe

Rethinking the Soft Conflict Pseudo Boolean Constraint on MaxSAT Local Search Solvers

MaxSAT is an optimization version of the famous NP-complete Satisfiability problem (SAT). Algorithms for MaxSAT mainly include complete solvers and local search incomplete solvers. In many complete solvers, once a better solution is found, a Soft conflict Pseudo Boolean (SPB) constraint will be generated to enforce the algorithm to find better solutions. In many local search algorithms, clause weighting is a key technique for effectively guiding the search directions. In this paper, we propose to transfer the SPB constraint into the clause weighting system of the local search method, leading the algorithm to better solutions. We further propose an adaptive clause weighting strategy that breaks the tradition of using constant values to adjust clause weights. Based on the above methods, we propose a new local search algorithm called SPB-MaxSAT that provides new perspectives for clause weighting on MaxSAT local search solvers. Extensive experiments demonstrate the excellent performance of the proposed methods

Clause Redundancy and Preprocessing in Maximum Satisfiability

The study of clause redundancy in Boolean satisfiability (SAT) has proven significant in various terms, from fundamental insights into preprocessing and inprocessing to the development of practical proof checkers and new types of strong proof systems. We study liftings of the recently-proposed notion of propagation redundancy-based on a semantic implication relationship between formulas-in the context of maximum satisfiability (MaxSAT), where of interest are reasoning techniques that preserve optimal cost (in contrast to preserving satisfiability in the realm of SAT). We establish that the strongest MaxSAT-lifting of propagation redundancy allows for changing in a controlled way the set of minimal correction sets in MaxSAT. This ability is key in succinctly expressing MaxSAT reasoning techniques and allows for obtaining correctness proofs in a uniform way for MaxSAT reasoning techniques very generally. Bridging theory to practice, we also provide a new MaxSAT preprocessor incorporating such extended techniques, and show through experiments its wide applicability in improving the performance of modern MaxSAT solvers.Peer reviewe