1 research outputs found
Generating Weighted MAX-2-SAT Instances of Tunable Difficulty with Frustrated Loops
Many optimization problems can be cast into the maximum satisfiability
(MAX-SAT) form, and many solvers have been developed for tackling such
problems. To evaluate a MAX-SAT solver, it is convenient to generate hard
MAX-SAT instances with known solutions. Here, we propose a method of generating
weighted MAX-2-SAT instances inspired by the frustrated-loop algorithm used by
the quantum annealing community. We extend the algorithm for instances of
general bipartite couplings, with the associated optimization problem being the
minimization of the restricted Boltzmann machine (RBM) energy over the nodal
values, which is useful for effectively pre-training the RBM. The hardness of
the generated instances can be tuned through a central parameter known as the
frustration index. Two versions of the algorithm are presented: the random- and
structured-loop algorithms. For the random-loop algorithm, we provide a
thorough theoretical and empirical analysis on its mathematical properties from
the perspective of frustration, and observe empirically a double phase
transition behavior in the hardness scaling behavior driven by the frustration
index. For the structured-loop algorithm, we show that it offers an improvement
in hardness over the random-loop algorithm in the regime of high loop density,
with the variation of hardness tunable through the concentration of frustrated
weights.Comment: 38 pages, 9 figure