We present a branch-and-cut algorithm for solving discrete bilevel linear programs where the upper-level variables are binary and the lower-level variables are either pure integer or pure binary. This algorithm performs local search to find improved bilevel feasible solutions. We strengthen the relaxed node subproblems in the branch-and-cut search tree by generating cuts to eliminate … Read more
Interior point methods (IPM) are the most popular approaches to solve Second Order Cone Optimization (SOCO) problems, due to their theoretical polynomial complexity and practical performance. In this paper, we present a warm-start method for primal-dual IPMs to reduce the number of IPM steps needed to solve SOCO problems that appear in a Branch and … Read more
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 … Read more
In this paper, we describe an algorithmic framework for solving mixed integer bilevel linear optimization problems (MIBLPs) by a generalized branch-and-cut approach. The framework presented merges features from existing algorithms (for both traditional mixed integer linear optimization and MIBLPs) with new techniques to produce a flexible and robust framework capable of solving a wide range … Read more
Cardinality constraints enforce an upper bound on the number of variables that can be nonzero. This article investigates linear programs with cardinality constraints that mutually overlap, i.e., share variables. We present the components of a branch-and-cut solution approach, including new branching rules that exploit the structure of the corresponding conflict hypergraph. We also investigate valid … Read more
In this work we introduce profit-oriented capacitated ring arborescence problems and present exact and heuristic algorithms. These combinatorial network design problems ask for optimized bi-level networks taking into account arc costs and node profits. Solutions combine circuits on the inner level with arborescences on the outer level of the networks. We consider the prize-collecting, the … Read more
The design of hub-and-spoke transport networks is a strategic planning problem, as the choice of hub locations has to remain unchanged for long time periods. However, strikes, disasters or traffic breakdown can lead to the unavailability of a hub for a short period of time. Therefore it is important to consider such events already in … Read more
The Min-up/min-down Unit Commitment Problem (MUCP) is to find a minimum-cost production plan on a discrete time horizon for a set of fossil-fuel units for electricity production. At each time period, the total production has to meet a forecasted demand. Each unit must satisfy minimum up-time and down-time constraints besides featuring production and start-up costs. … Read more
A linear program with linear complementarity constraints (LPCC) requires the minimization of a linear objective over a set of linear constraints together with additional linear complementarity constraints. This class has emerged as a modeling paradigm for a broad collection of problems, including bilevel programs, Stackelberg games, inverse quadratic programs, and problems involving equilibrium constraints. The … Read more
We present a generic branch-and-bound algorithm for finding all the Pareto solutions of a biobjective mixed-integer linear program. The main contributions are new algorithms for obtaining dual bounds at a node, checking node fathoming, presolve, and duality gap measurement. Our branch-and-bound is predominantly a decision space search method because the branching is performed on the … Read more