7 research outputs found
Approximation Strategies for Incomplete MaxSAT
Incomplete MaxSAT solving aims to quickly find a solution
that attempts to minimize the sum of the weights of the unsati
sfied soft
clauses without providing any optimality guarantees. In th
is paper, we
propose two approximation strategies for improving incomp
lete MaxSAT
solving. In one of the strategies, we cluster the weights and
approximate
them with a representative weight. In another strategy, we b
reak up
the problem of minimizing the sum of weights of unsatisfiable
clauses
into multiple minimization subproblems. Experimental res
ults show that
approximation strategies can be used to find better solution
s than the
best incomplete solvers in the MaxSAT Evaluation 2017
Approximation Strategies for Incomplete MaxSAT
Incomplete MaxSAT solving aims to quickly find a solution that attempts to
minimize the sum of the weights of the unsatisfied soft clauses without
providing any optimality guarantees.
In this paper, we propose two approximation strategies for improving
incomplete MaxSAT solving. In one of the strategies, we cluster the weights and
approximate them with a representative weight. In another strategy, we break up
the problem of minimizing the sum of weights of unsatisfiable clauses into
multiple minimization subproblems. Experimental results show that approximation
strategies can be used to find better solutions than the best incomplete
solvers in the MaxSAT Evaluation 2017.Comment: 10 pages, 3 algorithms, 1 figure, International Conference on
Principles and Practice of Constraint Programming (CP) 201
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
A Tutorial on Clique Problems in Communications and Signal Processing
Since its first use by Euler on the problem of the seven bridges of
K\"onigsberg, graph theory has shown excellent abilities in solving and
unveiling the properties of multiple discrete optimization problems. The study
of the structure of some integer programs reveals equivalence with graph theory
problems making a large body of the literature readily available for solving
and characterizing the complexity of these problems. This tutorial presents a
framework for utilizing a particular graph theory problem, known as the clique
problem, for solving communications and signal processing problems. In
particular, the paper aims to illustrate the structural properties of integer
programs that can be formulated as clique problems through multiple examples in
communications and signal processing. To that end, the first part of the
tutorial provides various optimal and heuristic solutions for the maximum
clique, maximum weight clique, and -clique problems. The tutorial, further,
illustrates the use of the clique formulation through numerous contemporary
examples in communications and signal processing, mainly in maximum access for
non-orthogonal multiple access networks, throughput maximization using index
and instantly decodable network coding, collision-free radio frequency
identification networks, and resource allocation in cloud-radio access
networks. Finally, the tutorial sheds light on the recent advances of such
applications, and provides technical insights on ways of dealing with mixed
discrete-continuous optimization problems
Tailoring local search for partial MaxSAT
Partial MaxSAT (PMS) is a generalization to SAT and MaxSAT. Many real world problems can be encoded into PMS in a more natural and compact way than SAT and MaxSAT. In this paper, we propose new ideas for local search for PMS, which mainly rely on the distinction between hard and soft clauses. We use these ideas to develop a local search PMS algorithm called Dist. Experimental results on PMS benchmarks from MaxSAT Evaluation 2013 show that Dist significantly outperforms state-of-the-art PMS algorithms, including both local search algorithms and complete ones, on random and crafted benchmarks. For the industrial benchmark, Dist dramatically outperforms previous local search algorithms and is comparable with complete algorithms.Partial MaxSAT (PMS) is a generalization to SAT and MaxSAT. Many real world problems can be encoded into PMS in a more natural and compact way than SAT and MaxSAT. In this paper, we propose new ideas for local search for PMS, which mainly rely on the distinction between hard and soft clauses. We use these ideas to develop a local search PMS algorithm called Dist. Experimental results on PMS benchmarks from MaxSAT Evaluation 2013 show that Dist significantly outperforms state-of-the-art PMS algorithms, including both local search algorithms and complete ones, on random and crafted benchmarks. For the industrial benchmark, Dist dramatically outperforms previous local search algorithms and is comparable with complete algorithms