Optimal control problems including partial differential equation (PDE) as well integer constraints merge the combinatorial difficulties of programming and challenges related to large-scale systems resulting from discretized PDEs. So far, branch-and-bound framework has been most common solution strategy for such problems. In order provide an alternative approach, especially in a context, this ar...

• 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...

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...

This thesis presents methods for finding optimal trajectories for vehicles subjected to avoidance and assignment requirements. The former include avoidance of collisions with obstacles or other vehicles and avoidance of thruster plumes from spacecraft. Assignment refers to the inclusion of decisions about terminal constraints in the optimization, such as assignment of waypoints to UAVs and the ...

Performance aspects of a Lagrangian relaxation based heuristic for solving large 0-1 integer linear programs are discussed. In particular, we look at its application to airline and railway crew scheduling problems. We present a scalable paralleliza-tion of the original algorithm used in production at Carmen Systems AB, GG oteborg, Sweden, based on distributing the variables. A lazy variant of t...

Performance aspects of a Lagrangian relaxation based heuris-tic for solving large 0-1 integer linear programs are discussed. In particular , we look at its application to airline and railway crew scheduling problems. We present a scalable parallelization of the original algorithm used in production at Carmen Systems AB, GG oteborg, Sweden, based on distributing the variables and a new sequentia...

Generalizing both mixed-integer linear optimization and convex optimization, mixed-integer convex optimization possesses broad modeling power but has seen relatively few advances in general-purpose solvers in recent years. In this paper, we intend to provide a broadly accessible introduction to our recent work in developing algorithms and software for this problem class. Our approach is based o...

It is well-known that the Lagrangian dual of an Integer Linear Program (ILP) provides the same bound as a continuous relaxation involving the convex hull of all the optimal solutions of the Lagrangian relaxation. It is less often realized that this equivalence is effective, in that basically all known algorithms for solving the Lagrangian dual either naturally compute an (approximate) optimal s...