Computational evaluation of ranking models in an automatic decomposition framework

A data driven Dantzig–Wolfe decomposition framework

“…Even if our preliminary investigations showed data driven methods to be promising in specific tasks, the results of [21,22] are not directly applicable as a full computational tool. In detail, [21] shows how to rank decompositions in terms of distance from the Pareto front on the space of bound and computing time, but the problem of actually generating and selecting a specific decomposition of good rank in an overall optimization framework is only sketched. Neither the results of [22] are sufficient to be directly integrated in an overall framework, the main drawback being the computing time: the algorithms of [22] might take as long as the optimization phase itself.…”

“…In [21] we propose supervised learning models, mapping static decomposition features to bound and time scores, exploiting a dataset including about 1000 decompositions for each of 36 base MIP problems from the MIPLIB. These decompositions were sampled by a randomized greedy algorithm that iteratively picks constraints with a probability directly proportional to their sparsity, builds well-formed blocks and possibly aborts and restarts the process if the structure of the tentative decomposition is not satisfying certain criteria (in our implementation, at least three distinct blocks must be present).…”

“…In this paper we fill the gap between the concepts of [21,22] and their actual use in a full decomposition-based MIP resolution framework, proving its effectiveness in realistic contexts. We also describe and share a library of more than 31 thousands decompositions of MIPLIB instances, generated by a randomized greedy algorithm and scored by their root node computation.…”

“…Preliminary investigations. In two preparatory workshop papers [21,22] we have experimented the potential of machine learning tools in this context. We have mainly focused on two very specific tasks.…”

“…First, from a given set of generic MIP instances and a set of decompositions produced for them by a randomized greedy algorithm, whose relaxation at the root node is actually computed by column generation, we trained regression and classification models. We found them to be able to predict bound and computing time for other random decompositions over the same set of MIP instances, or limited perturbations of them [21]. Second, we used these models for choosing how to improve decompositions by simple local changes [22].…”