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...

Network security defenses evolve, responding to real-time attack incidents, modifying the underlying topology, or reallocating defense systems across network. The present work emphasizes reducing time compute new optimal reallocations of systems, emerging remote attacks. proposed heuristic method utilizes parallel processing by slicing graphical model representing network solving in multiple mi...

Abstract The last milestone achievement for the roundoff-error-free solution of general mixed integer programs over rational numbers was a hybrid-precision branch-and-bound algorithm published by Cook, Koch, Steffy, and Wolter in 2013. We describe substantial revision extension this framework that integrates symbolic presolving, features an exact repair step solutions from primal heuristics, em...

Bilevel optimization is a field of mathematical programming in which some variables are constrained to be the solution another problem. As consequence, bilevel able model hierarchical decision processes. This appealing for modeling real-world problems, but it also makes resulting models hard solve theory and practice. The scientific interest computational increased lot over last decade still gr...

the set covering problem (scp) is a well-known combinatorial optimization problem. this paper investigates development of a local branching approach for the scp. this solution strategy is exact in nature, though it is designed to improve the heuristic behavior of the mixed integer programming solver. the algorithm parameters are tuned by design of experiments approach. the proposed method is te...