Solving Multi-objective Pseudo-Boolean Problems

Integer Linear Programs are widely used in areas such as routing problems, scheduling analysis and optimization, logic synthesis, and partitioning problems. As many of these problems have a Boolean nature, i.e., the variables are restricted to 0 and 1, so called Pseudo-Boolean solvers have been proposed. They are mostly based on SAT solvers which took continuous improvements over the past years. However, Pseudo-Boolean solvers are only able to optimize a single linear function while fulfilling several constraints. Unfortunately many realworld optimization problems have multiple objective functions which are often conflicting and have to be optimized simultaneously, resulting in general in a set of optimal solutions. As a consequence, a single-objective Pseudo-Boolean solver will not be able to find this set of optimal solutions. As a remedy, we propose three different algorithms for solving multi-objective Pseudo-Boolean problems. Our experimental results will show the applicability of these algorithms on the basis of several test cases.