Extreme events such as disasters cause partial or total disruption of basic services such as water, energy, communication and transportation. In particular, roads can be damaged or blocked by debris, thereby obstructing access to certain affected areas. Thus, restoration of the damaged roads is necessary to evacuate victims and distribute emergency commodities to relief centers … Read more
We present a new tool for generating cutting planes for NP-hard combinatorial optimisation problems. It is based on the concept of gadgets — small subproblems that are “glued” together to form hard problems — which we borrow from the literature on computational complexity. Using gadgets, we are able to derive huge (exponentially large) new families … Read more
It is common knowledge that symmetries arising in integer programs could impair the solution process, in particular when symmetric solutions lead to an excessively large branch and bound (B&B) search tree. Techniques like isomorphic pruning [11], orbital branching [16] and orbitopal fixing [8] have been shown to be essential to solve very symmetric instances from … Read more
Problem instances found in the literature that are used in computational studies of the resource constrained project scheduling problem, typically include only a few resources. In some practical applications, however, the number of resources may be significantly higher. In this paper, problem instances with a large number of resources are considered and a Benders decomposition … Read more
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