Improving Exact Algorithm for Pseudo Boolean Optimization with Two New Phase Selection Heuristics

Pseudo-Boolean optimization (PBO) problem involves optimizing a linear objective function under linear inequality constraints defined over Boolean variables. PBO is widely used for modeling many combinational optimization problems, particularly in some real-world scenarios. In core-guided CDCL-based exact solvers, the way branching variables are assigned, known as phase selection, significantly affects the solving efficiency. This paper introduces two strategies to enhance solver performance by improving phase selection. Firstly, we design a new phase selection strategy that actively guides variables in the objective function toward assignments closer to the optimal solution. Secondly, to prevent the solver from becoming trapped in local solutions, we propose a reinforcement learning-based rephase mechanism that dynamically updates and resets variable phases, increasing search diversity and encouraging exploration of high-quality solution spaces. We integrate two phase selection strategies into two state-of-the-art PBO solvers and compare them against top-performing solvers from the PB Competition 2024. The evaluation is conducted on benchmarks from the PB Competition 2016 and 2024. Experimental results show that our solvers outperform the PB Competition 2024 winning solver.