We present an overview of noncommercial software tools for the solution of mixed-integer linear programs (MILPs). We first review solution methodologies for MILPs and then present an overview of the available software, including detailed descriptions of eight software packages available under open-source or other noncommercial licenses. Each package is categorized as a black-box solver, a calla...

This survey presents tools from polyhedral theory that are used in integer programming. It applies them to the study of valid inequalities for mixed integer linear sets, such as Gomory’s mixed integer cuts.

A wide range of problems can be modeled as Mixed Integer Linear Programming (MILP) problems using standard formulation techniques. However, in some cases the resulting MILP can be either too weak or to large to be effectively solved by state of the art solvers. In this survey we review advanced MILP formulation techniques that result in stronger and/or smaller formulations for a wide class of p...

Mixed integer linear programming (MILP) is a powerful representation often used to formulate decision-making problems under uncertainty. However, it lacks a natural mechanism to reason about objects, classes of objects, and relations. First-order logic (FOL), on the other hand, excels at reasoning about classes of objects, but lacks a rich representation of uncertainty. While representing propo...

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 ...

SelfSplit is a simple mechanism to convert a sequential tree-search code into a parallel one. In this paradigm, tree-search is distributed among a set of workers, each of which is able to autonomously determine—without any communication with the other workers—the job parts it has to process. SelfSplit already proved quite effective in parallelizing Constraint Programming solvers. In the present...

‎in this paper‎, ‎some kkt type sufficient global optimality conditions‎ ‎for general mixed integer nonlinear programming problems with‎ ‎equality and inequality constraints (minpp) are established‎. ‎we achieve‎ ‎this by employing a lagrange function for minpp‎. ‎in addition‎, ‎verifiable sufficient global optimality conditions for general mixed‎ ‎integer quadratic programming problems are der...