  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.
