2 research outputs found
On Solving Boolean Multilevel Optimization Problems
Many combinatorial optimization problems entail a number of hierarchically
dependent optimization problems. An often used solution is to associate a
suitably large cost with each individual optimization problem, such that the
solution of the resulting aggregated optimization problem solves the original
set of hierarchically dependent optimization problems. This paper starts by
studying the package upgradeability problem in software distributions.
Straightforward solutions based on Maximum Satisfiability (MaxSAT) and
pseudo-Boolean (PB) optimization are shown to be ineffective, and unlikely to
scale for large problem instances. Afterwards, the package upgradeability
problem is related to multilevel optimization. The paper then develops new
algorithms for Boolean Multilevel Optimization (BMO) and highlights a large
number of potential applications. The experimental results indicate that the
proposed algorithms for BMO allow solving optimization problems that existing
MaxSAT and PB solvers would otherwise be unable to solve
Algorithms for Weighted Boolean Optimization
The Pseudo-Boolean Optimization (PBO) and Maximum Satisfiability (MaxSAT)
problems are natural optimization extensions of Boolean Satisfiability (SAT).
In the recent past, different algorithms have been proposed for PBO and for
MaxSAT, despite the existence of straightforward mappings from PBO to MaxSAT
and vice-versa. This papers proposes Weighted Boolean Optimization (WBO), a new
unified framework that aggregates and extends PBO and MaxSAT. In addition, the
paper proposes a new unsatisfiability-based algorithm for WBO, based on recent
unsatisfiability-based algorithms for MaxSAT. Besides standard MaxSAT, the new
algorithm can also be used to solve weighted MaxSAT and PBO, handling
pseudo-Boolean constraints either natively or by translation to clausal form.
Experimental results illustrate that unsatisfiability-based algorithms for
MaxSAT can be orders of magnitude more efficient than existing dedicated
algorithms. Finally, the paper illustrates how other algorithms for either PBO
or MaxSAT can be extended to WBO.Comment: 14 pages, 2 algorithms, 3 tables, 1 figur