borealis —A generalized global update algorithm for Boolean optimization problems

Optimization problems with Boolean variables that fall into the nondeterministic polynomial (NP) class when cast as decision problems are of fundamental importance in computer science, mathematics, physics and industrial applications. Most notably, solving constraint-satisfaction problems, which are related to spin-glass-like Hamiltonians in physics, remains a difficult numerical task. As such, there has been great interest in designing efficient heuristics to solve these computationally difficult problems. Inspired by parallel tempering Monte Carlo in conjunction with the rejection-free isoenergetic cluster algorithm developed for Ising spin glasses, we present a generalized global update optimization heuristic that can be applied to different NP-complete problems with Boolean variables. The global cluster updates allow for a wide-spread sampling of phase space, thus considerably speeding up optimization. By carefully tuning the pseudo-temperature (needed to randomize the configurations) of the problem, we show that the method can efficiently tackle optimization problems with over-constraints or on topologies with a large site percolation threshold. We illustrate the efficiency of the heuristic on paradigmatic optimization problems, such as the maximum satisfiability problem and the vertex cover problem. Because this physics-based algorithm is an algorithm that searches solutions globally, it performs best for random Max-k-SAT instances.