25 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
Improving WalkSAT for Random 3-SAT Problems
Stochastic local search (SLS) algorithms are well known for their ability to efficiently find models of random instances of the Boolean satisfiability (SAT) problems. One of the most famous SLS algorithms for SAT is called WalkSAT, which has wide influence and performs well on most of random 3-SAT instances. However, the performance of WalkSAT lags far behind on random 3-SAT instances equal to or greater than the phase transition ratio. Motivated by this limitation, in the present work, firstly an allocation strategy is introduced and utilized in WalkSAT to determine the initial assignment, leading to a new algorithm called WalkSATvav. The experimental results show that WalkSATvav significantly outperforms the state-of-the-art SLS solvers on random 3-SAT instances at the phase transition for SAT Competition 2017. However, WalkSATvav cannot rival its competitors on random 3-SAT instances greater than the phase transition ratio. Accordingly, WalkSATvav is further improved for such instances by utilizing a combination of an improved genetic algorithm and an improved ant colony algorithm, which complement each other in guiding the search direction. The resulting algorithm, called WalkSATga, is far better than WalkSAT and significantly outperforms some previous known SLS solvers on random 3-SAT instances greater than the phase transition ratio from SAT Competition 2017. Finally, a new SAT solver called WalkSATlg, which combines WalkSATvav and WalkSATga, is proposed, which is competitive with the winner of random satisfiable category of SAT competition 2017 on random 3-SAT problem
Effect of Initial Assignment on Local Search Performance for Max Sat
In this paper, we explore the correlation between the quality of initial assignments provided to local search heuristics and that of the corresponding final assignments. We restrict our attention to the Max r-Sat problem and to one of the leading local search heuristics - Configuration Checking Local Search (CCLS). We use a tailored version of the Method of Conditional Expectations (MOCE) to generate initial assignments of diverse quality.
We show that the correlation in question is significant and long-lasting. Namely, even when we delve deeper into the local search, we are still in the shadow of the initial assignment. Thus, under practical time constraints, the quality of the initial assignment is crucial to the performance of local search heuristics.
To demonstrate our point, we improve CCLS by combining it with MOCE. Instead of starting CCLS from random initial assignments, we start it from excellent initial assignments, provided by MOCE. Indeed, it turns out that this kind of initialization provides a significant improvement of this state-of-the-art solver. This improvement becomes more and more significant as the instance grows
Local Search For SMT On Linear and Multilinear Real Arithmetic
Satisfiability Modulo Theories (SMT) has significant application in various
domains. In this paper, we focus on quantifier-free Satisfiablity Modulo Real
Arithmetic, referred to as SMT(RA), including both linear and non-linear real
arithmetic theories. As for non-linear real arithmetic theory, we focus on one
of its important fragments where the atomic constraints are multi-linear. We
propose the first local search algorithm for SMT(RA), called LocalSMT(RA),
based on two novel ideas. First, an interval-based operator is proposed to
cooperate with the traditional local search operator by considering the
interval information. Moreover, we propose a tie-breaking mechanism to further
evaluate the operations when the operations are indistinguishable according to
the score function. Experiments are conducted to evaluate LocalSMT(RA) on
benchmarks from SMT-LIB. The results show that LocalSMT(RA) is competitive with
the state-of-the-art SMT solvers, and performs particularly well on
multi-linear instances
An Iterative Path-Breaking Approach with Mutation and Restart Strategies for the MAX-SAT Problem
Although Path-Relinking is an effective local search method for many
combinatorial optimization problems, its application is not straightforward in
solving the MAX-SAT, an optimization variant of the satisfiability problem
(SAT) that has many real-world applications and has gained more and more
attention in academy and industry. Indeed, it was not used in any recent
competitive MAX-SAT algorithms in our knowledge. In this paper, we propose a
new local search algorithm called IPBMR for the MAX-SAT, that remedies the
drawbacks of the Path-Relinking method by using a careful combination of three
components: a new strategy named Path-Breaking to avoid unpromising regions of
the search space when generating trajectories between two elite solutions; a
weak and a strong mutation strategies, together with restarts, to diversify the
search; and stochastic path generating steps to avoid premature local optimum
solutions. We then present experimental results to show that IPBMR outperforms
two of the best state-of-the-art MAX-SAT solvers, and an empirical
investigation to identify and explain the effect of the three components in
IPBMR