High Performance Decomposition Algorithms for Combinatorial Optimization and Machine Learning – ADHOC

Decomposition techniques in mathematical programming (Dantzig-Wolf, Benders) are among the most effective methods to date to solve large scale combinatorial optimization problems. For example, such problems are typically encountered in logistics. Vehicle Routing Problems are a spectacular example of the success of Dantzig-Wolf decomposition while Benders decomposition are at the heart of recent advances for service network design problems. Although these techniques allow a drastic increase in the size of the problems that can be solved, they need a more important computational effort than the standard methods such as polyhedral approaches, heuristics and meta-heuristics. In the continuation of recent works, the project aims to promote the use of machine learning to guide and speed up the convergence of decomposition methods while exploiting high performance computing by supercomputer and hardware acceleration (GPU, FPGA). The main objective of the project is therefore the identification of the key factors and criterions allowing the hybridization of decomposition algorithms with recent advances in machine learning and to propose innovative solutions allowing to solve larger instances than nowadays thanks to massive parallel computing.