Alexandre Forel

A Hierarchy of Polyhedral Outer Approximations from Branch-and-Bound Trees

Categories (Mixed) Integer Linear Programming, Cutting Plane Approaches, Polyhedra Tags ,

This paper investigates the a posteriori analysis of Branch-and-Bound (BB) trees to extract structural information about the feasible region of mixed-binary linear programs. Using only the branching decisions of a tree and one dual bound per node, we introduce three polyhedral outer approximations of the feasible region, namely a disjunctive, a network-flow-based, and a mixing-set-based … Read more

Adaptive Partitioning for Chance-Constrained Problems with Finite Support

Categories Integer Programming, Stochastic Programming

This paper studies chance-constrained stochastic optimization problems with finite support. It presents an iterative method that solves reduced-size chance-constrained models obtained by partitioning the scenario set. Each reduced problem is constructed to yield a bound on the optimal value of the original problem. We show how to adapt the partitioning of the scenario set so … Read more