On Solving Boolean Multilevel Optimization Problems

TL;DR

This paper introduces new algorithms for Boolean Multilevel Optimization (BMO), effectively solving hierarchical combinatorial problems that traditional MaxSAT and PB methods struggle with, demonstrated through practical experiments.

Contribution

The paper develops novel algorithms for BMO, addressing scalability issues in hierarchical optimization problems and expanding potential application areas.

Findings

Proposed algorithms outperform existing MaxSAT and PB solvers.

Algorithms successfully solve large-scale hierarchical optimization problems.

Experimental results confirm the effectiveness of the new methods.

Abstract

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.