Ordered Counterfactual Explanation by Mixed-Integer Linear Optimization

Integer convex minimization by mixed integer linear optimization

Minimizing a convex function over the integral points of a bounded convex set is polynomial in fixed dimension [6]. We provide an alternative, short, and geometrically motivated proof of this result. In particular, we present an oraclepolynomial algorithm based on a mixed integer linear optimization oracle.

Parallel Solvers for Mixed Integer Linear Optimization

In this article, we provide an overview of the current state of the art with respect to solution of mixed integer linear optimization problems (MILPS) in parallel. Sequential algorithms for solving MILPs have improved substantially in the last two decades and commercial MILP solvers are now considered effective off-the-shelf tools for optimization. Although concerted development of parallel MIL...

Trajectory Optimization using Mixed-Integer Linear Programming

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 ...

Mixed-Integer Nonlinear Optimization

Many optimal decision problems in scientific, engineering, and public sector applications involve both discrete decisions and nonlinear system dynamics that affect the quality of the final design or plan. These decision problems lead to mixed-integer nonlinear programming (MINLP) problems that combine the combinatorial difficulty of optimizing over discrete variable sets with the challenges of ...

Aspects of Time in Mixed-Integer (Non-) Linear Optimization