Integer linear programming (ILP) is widely utilized for various combinatorial optimization problems. Primal heuristics play a crucial role in quickly finding feasible solutions for NP-hard ILP. Although $\textit{end-to-end learning}$-based primal heuristics (E2EPH) have recently been proposed, they are typically unable to independently generate feasible solutions and mainly focus on binary variables. Ensuring feasibility is critical, especially when handling non-binary integer variables. To address this challenge, we propose RL-SPH, a novel reinforcement learning-based start primal heuristic capable of independently generating feasible solutions, even for ILP involving non-binary integers. Experimental results demonstrate that RL-SPH rapidly obtains high-quality feasible solutions, achieving on average a 44x lower primal gap and a 2.3x lower primal integral compared to existing primal heuristics.

翻译：整数线性规划（ILP）被广泛应用于各类组合优化问题。原始启发式方法在快速求解NP难整数线性规划可行解方面起着关键作用。尽管近期已提出基于端到端学习的原始启发式方法（E2EPH），但它们通常无法独立生成可行解，且主要针对二元变量处理。确保可行性至关重要，尤其是在处理非二元整数变量时。为应对这一挑战，我们提出RL-SPH——一种基于强化学习的新型起始原始启发式方法，能够独立生成可行解，即使对于包含非二元整数的整数线性规划问题亦如此。实验结果表明，相较于现有原始启发式方法，RL-SPH能以更快的速度获得高质量可行解，其原始间隙平均降低44倍，原始积分平均降低2.3倍。