Learning Heuristics Approaches in Mixed Integer Linear Programing

Mixed Integer Linear Programming (MILP) technology is a versatile method used for formulating and solving combinatorial optimization problems. During the solving process, primal heuristics help to quickly find good feasible solutions, which can aid branch-and-bound (B&B) algorithms in reducing the primal-dual gap and pruning the B&B search tree. The heuristics employed by existing open-source solvers follow empirical rules summarized from real-world instances, enabling the solvers to achieve generally good performance but sometimes performing poorly on specific instances. In response, this paper proposes a method that uses hierarchical sequence models to learn the patterns of given instances and assigns a heuristic configuration for them. Compared to the default settings of the solver, the proposed method enables heuristic module to perform better, finding feasible solutions more quickly and reducing the primal-dual gap. Experimental results indicate that the proposed method can improve the solver's average performance on given instances by 27%.