Machine learning (ML) has been recently introduced to solving optimization problems, especially for combinatorial (CO) tasks. In this paper, we survey the trend of leveraging ML solve mixed-integer programming problem (MIP). Theoretically, MIP is an NP-hard problem, and most CO problems can be formulated as MIP. Like other human-designed heuristic algorithms rely on good initial solutions cost ...

Multistage stochastic programs can be approximated by restricting policies to follow decision rules. Directly applying this idea problems with integer decisions is difficult because of the need for rules that lead integral decisions. In work, we introduce Lagrangian dual (LDDRs) multistage mixed-integer programming (MSMIP) which overcome difficulty in a MSMIP. We propose two new bounding techni...

• Mixed-integer linear programming formulations for influence diagrams are presented. Even problems in which the no-forgetting assumption does not hold can be solved. Many kinds of resource, logical and risk constraints accommodated. All non-dominated strategies computed with multiple objectives. Support project porfolio selection under endogenous uncertainties is given. Influence widely employ...