4,382 research outputs found
Low-rank semidefinite programming for the MAX2SAT problem
This paper proposes a new algorithm for solving MAX2SAT problems based on
combining search methods with semidefinite programming approaches. Semidefinite
programming techniques are well-known as a theoretical tool for approximating
maximum satisfiability problems, but their application has traditionally been
very limited by their speed and randomized nature. Our approach overcomes this
difficult by using a recent approach to low-rank semidefinite programming,
specialized to work in an incremental fashion suitable for use in an exact
search algorithm. The method can be used both within complete or incomplete
solver, and we demonstrate on a variety of problems from recent competitions.
Our experiments show that the approach is faster (sometimes by orders of
magnitude) than existing state-of-the-art complete and incomplete solvers,
representing a substantial advance in search methods specialized for MAX2SAT
problems.Comment: Accepted at AAAI'19. The code can be found at
https://github.com/locuslab/mixsa
Solving the Resource Constrained Project Scheduling Problem with Generalized Precedences by Lazy Clause Generation
The technical report presents a generic exact solution approach for
minimizing the project duration of the resource-constrained project scheduling
problem with generalized precedences (Rcpsp/max). The approach uses lazy clause
generation, i.e., a hybrid of finite domain and Boolean satisfiability solving,
in order to apply nogood learning and conflict-driven search on the solution
generation. Our experiments show the benefit of lazy clause generation for
finding an optimal solutions and proving its optimality in comparison to other
state-of-the-art exact and non-exact methods. The method is highly robust: it
matched or bettered the best known results on all of the 2340 instances we
examined except 3, according to the currently available data on the PSPLib. Of
the 631 open instances in this set it closed 573 and improved the bounds of 51
of the remaining 58 instances.Comment: 37 pages, 3 figures, 16 table
A Logical Approach to Efficient Max-SAT solving
Weighted Max-SAT is the optimization version of SAT and many important
problems can be naturally encoded as such. Solving weighted Max-SAT is an
important problem from both a theoretical and a practical point of view. In
recent years, there has been considerable interest in finding efficient solving
techniques. Most of this work focus on the computation of good quality lower
bounds to be used within a branch and bound DPLL-like algorithm. Most often,
these lower bounds are described in a procedural way. Because of that, it is
difficult to realize the {\em logic} that is behind.
In this paper we introduce an original framework for Max-SAT that stresses
the parallelism with classical SAT. Then, we extend the two basic SAT solving
techniques: {\em search} and {\em inference}. We show that many algorithmic
{\em tricks} used in state-of-the-art Max-SAT solvers are easily expressable in
{\em logic} terms with our framework in a unified manner.
Besides, we introduce an original search algorithm that performs a restricted
amount of {\em weighted resolution} at each visited node. We empirically
compare our algorithm with a variety of solving alternatives on several
benchmarks. Our experiments, which constitute to the best of our knowledge the
most comprehensive Max-sat evaluation ever reported, show that our algorithm is
generally orders of magnitude faster than any competitor
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