The proposed HEM framework can be extended to handle more complex MILP problems by incorporating additional components and techniques. For MILP problems with non-linear constraints, the framework can be adapted to include non-linear constraint handling methods such as convex relaxation techniques, piecewise linear approximations, or nonlinear programming solvers. This would involve modifying the state representation to include information about non-linear constraints and updating the policy network architecture to accommodate the handling of non-linearities.
For MILP problems with multiple objectives, the framework can be extended to support multi-objective optimization by incorporating multi-objective optimization algorithms such as weighted sum method, epsilon-constraint method, or Pareto optimization. The policy network can be modified to output a set of solutions that represent the Pareto front, capturing the trade-offs between different objectives. Additionally, the reward function can be adjusted to consider multiple objectives and evaluate the quality of the selected cuts based on all objectives simultaneously.