A learn-and-construct framework for general mixed-integer programming problems

Abstract

In this paper, we propose a new framework for finding an initial feasible solution from a mixed-integer programming (MIP) model. We call it learn-and-construct since it first exploits the structure of the model and its linear relaxation solution and then uses this knowledge to try to produce a feasible solution. In the learning phase, we use an unsupervised learning algorithm to cluster entities originating the MIP model. Such clusters are then used to decompose the original MIP in a number of easier sub-MIPs that are solved by using a black box solver. Computational results on three well-known problems show that our procedure is characterized by a success rate larger than both the feasibility pump heuristic and a state-of-the-art MIP solver. Furthermore, our approach is more scalable and uses less computing time on average.