Frank Fischer We develop a fully asynchronous proximal bundle method for solving non-smooth, convex optimization problems. The algorithm can be used as a drop-in replacement for classic bundle methods, i.e., the function must be given by a first-order oracle for computing function values and subgradients. The algorithm allows for an arbitrary number of master problem processes computing … Read more
In this paper we consider the Double-Row Facility Layout Problem (DRFLP). Given a set of departments and pairwise transport weights between them the DRFLP asks for a non-overlapping arrangement of the departments along both sides of a common path such that the weighted sum of the center-to-center distances between the departments is minimized. Despite its … Read more
In this paper we investigate non-linear matroid optimization problems with polynomial objective functions where the monomials satisfy certain monotonicity properties. Indeed, we study problems where the set of non-linear monomials consists of all non-linear monomials that can be built from a given subset of the variables. Linearizing all non-linear monomials we study the respective polytope. … Read more
Recently, Buchheim and Klein suggested to study polynomial-time solvable optimisation problems with linear objective functions combined with exactly one additional quadratic monomial. They concentrated on special quadratic spanning tree or forest problems. We extend their results to general matroid optimisation problems with a set of nested monomials in the objective function. The monomials are linearised … Read more
The traveling salesman problem (TSP) asks for a shortest tour through all vertices of a graph with respect to the weights of the edges. The symmetric quadratic traveling salesman problem (SQTSP) associates a weight with every three vertices traversed in succession. If these weights correspond to the turning angles of the tour, we speak of … Read more
Given a set of departments, a number of rows and pairwise connectivities between these departments, the multi-row facility layout problem (MRFLP) looks for a non-overlapping arrangement of these departments in the rows such that the weighted sum of the center-to-center distances is minimized. As even small instances of the (MRFLP) are rather challenging, several special … Read more
An algorithmic framework is presented for optimising general convex functions by non synchronised parallel processes. Each process greedily picks a suitable adaptive subset of coordinates and runs a bundle method on a corresponding restricted problem stopping whenever a descent step is encountered or predicted decrease is reduced sufficiently. No prior knowledge on the dependencies between … Read more
We present a new lifting approach for strengthening arbitrary clique tree inequalities that are known to be facet defining for the symmetric traveling salesman problem in order to get stronger valid inequalities for the symmetric quadratic traveling salesman problem (SQTSP). Applying this new approach to the subtour elimination constraints (SEC) leads to two new classes … Read more
An algorithmic approach is proposed for exploiting parallelization possibilities in large scale optimization models of the following generic type. Objects change their state over time subject to a limited availability of common resources. These are modeled by linear coupling constraints and result in few objects competing for the same resource at each point in time. … Read more
The aim of operational train timetabling is to find a conflict free timetable for a set of passenger and freight trains with predefined stopping time windows along given routes in an infrastructure network so that station capacities and train dependent running and headway times are observed. Typical models for this problem are based on time-discretized … Read more