The Power of Semidefinite Programming Relaxations for MAX-SAT

Gomes, Carla P.; Hoeve, Willem‐Jan van; Leahu, Lucian

doi:10.1007/11757375_10

Cited by 10 publications

(8 citation statements)

References 19 publications

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“…We are using the LP relaxation for partioning the variables, as this is readily available. Other relaxations might be more efficient, as stated by Gomes et al (2006). They show that in their case (MAX SAT) the predictive power of variable fixing based on semi-definite relaxations is much higher than that of LP relaxations.…”

Section: Remarkmentioning

confidence: 93%

Alternating control tree search for knapsack/covering problems

et al. 2008

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The Multidimensional Knapsack/Covering Problem (KCP) is a 0-1 Integer Programming Problem containing both knapsack and weighted covering constraints, subsuming the well-known Multidimensional Knapsack Problem (MKP) and the Generalized (weighted) Covering Problem. We propose an Alternating Control Tree Search (ACT) method for these problems that iteratively transfers control between the following three components: (1) ACT-1, a process that solves an LP relaxation of the current form of the KCP. (2) ACT-2, a method that partitions the variables according to 0, 1, and fractional values to create sub-problems that can be solved with relatively high efficiency. (3) ACT-3, an updating procedure that adjoins inequalities to produce successively more constrained versions of KCP, and in conjunction with the solution processes of ACT-1 and ACT-2, ensures finite convergence to optimality. The ACT method can also be used as a heuristic approach using early termination rules. Computational results show that the ACT-framework successfully enhances the performance of three widely different heuristics for the KCP. Our ACT-method involving scatter search performs better than any other known method on a large set of KCP-instances from the literature. The ACT-based methods are also found to be highly effective on the MKP.

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Section: Remarkmentioning

confidence: 93%

Alternating control tree search for knapsack/covering problems

et al. 2008

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“…Although several authors have noted the effectiveness of the SDP relaxation for the MAX2SAT problem (Lotgering, 2012;Gomes, van Hoeve, and Leahu, 2006) in terms of the approximation quality, no previous works we are aware of have succeeded at turning this into a practical algorithm. Several efforts were made: Anjos (2004) investigated the effectiveness of different SDPs for the MAXSAT problems, but didn't consider their integration into an exact solver.…”

Section: Approximation Algorithms For Maxsatmentioning

confidence: 99%

Low-Rank Semidefinite Programming for the MAX2SAT Problem

Wang

Kolter

2019

AAAI

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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.

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“…The second approach concerns approximation algorithms which do not guarantee the optimality of the solutions but return a result of good quality in a reasonable time. Such algorithms include semi-definite programming, pseudo Boolean optimization, etc [5], [6], [7]. Local search (LS) methods, efficient when dealing with SAT, belong also to these approximation methods.…”

Section: Introductionmentioning

confidence: 99%

Inference Rules in Local Search for Max-SAT

Abramé

Habet

2012

2012 IEEE 24th International Conference on Tools With Artificial Intelligence

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In the last years, many advances were accomplished in the exact solving of the Max-SAT problem, especially by the definition of new inference rules and a better estimation of lower bounds in branch and bound based methods. However, and oppositely to the SAT problem, fewer works exist on approximate methods for Max-SAT, mainly local search ones which have shown their potency for SAT. In this paper, we illustrate that including inference rules in a classical local search solver for SAT improves its performances when solving the Max-SAT problem. The obtained results confirm the efficiency of our approach.

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The Power of Semidefinite Programming Relaxations for MAX-SAT

Cited by 10 publications

References 19 publications

Alternating control tree search for knapsack/covering problems

Alternating control tree search for knapsack/covering problems

Low-Rank Semidefinite Programming for the MAX2SAT Problem

Inference Rules in Local Search for Max-SAT

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