Smart Feasibility Pump: Reinforcement Learning for (Mixed) Integer Programming

In this work, we propose a deep reinforcement learning (DRL) model for finding a feasible solution for (mixed) integer programming (MIP) problems. Finding a feasible solution for MIP problems is critical because many successful heuristics rely on a known initial feasible solution. However, it is in general NP-hard. Inspired by the feasibility pump (FP), a well-known heuristic for searching feasible MIP solutions, we develop a smart feasibility pump (SFP) method using DRL. In addition to multi-layer perception (MLP), we propose a novel convolution neural network (CNN) structure for the policy network to capture the hidden information of the constraint matrix of the MIP problem. Numerical experiments on various problem instances show that SFP significantly outperforms the classic FP in terms of the number of steps required to reach the first feasible solution. Moreover, the CNN structure works without the projection of the current solution as the input, which saves the computational effort at each step of the FP algorithms to find projections. This highlights the representational power of the CNN structure.