Aerospace applications on integer and combinatorial optimization

Research supported by NASA Langley Research Center includes many applications of aerospace design optimization and is conducted by teams of applied mathematicians and aerospace engineers. This paper investigates the benefits from this combined expertise in formulating and solving integer and combinatorial optimization problems. Applications range from the design of large space antennas to interior noise control. A typical problem. for example, seeks the optimal locations for vibration-damping devices on an orbiting platform and is expressed as a mixed/integer linear programming problem with more than 1500 design variables

ABACUS - A Branch-And-CUt System, Version 2.0, User's Guide and Reference Manual

ABACUS is a C++ framework for the implementation of branch-and-cut algorithms, branch-and-price algorithms, and their combination for linear mixed integer and combinatorial optimization problems. This manual explains the installation, the design, and the usage of the framework. Both the basic steps and advanced features are discussed. The reference manual describes all classes together with all members that are relevant for the user

A linear programming approach to general dataflow process network verification and dimensioning

In this paper, we present linear programming-based sufficient conditions, some of them polynomial-time, to establish the liveness and memory boundedness of general dataflow process networks. Furthermore, this approach can be used to obtain safe upper bounds on the size of the channel buffers of such a network.Comment: In Proceedings ICE 2010, arXiv:1010.530

Topological Additive Numbering of Directed Acyclic Graphs

We propose to study a problem that arises naturally from both Topological Numbering of Directed Acyclic Graphs, and Additive Coloring (also known as Lucky Labeling). Let $D$ be a digraph and $f$ a labeling of its vertices with positive integers; denote by $S(v)$ the sum of labels over all neighbors of each vertex $v$. The labeling $f$ is called \emph{topological additive numbering} if $S(u) < S(v)$ for each arc $(u,v)$ of the digraph. The problem asks to find the minimum number $k$ for which $D$ has a topological additive numbering with labels belonging to $\{ 1, \ldots, k \}$, denoted by $\eta_t(D)$. We characterize when a digraph has topological additive numberings, give a lower bound for $\eta_t(D)$, and provide an integer programming formulation for our problem, characterizing when its coefficient matrix is totally unimodular. We also present some families for which $\eta_t(D)$ can be computed in polynomial time. Finally, we prove that this problem is \np-Hard even when its input is restricted to planar bipartite digraphs

Combinatorial optimization tolerances calculated in linear time

For a given optimal solution to a combinatorial optimization problem, we show, under very natural conditions, the equality of the minimal values of upper and lower tolerances, where the upper tolerances are calculated for the given optimal solution and the lower tolerances outside the optimal solution. As a consequence, the calculation of such tolerances can now be done in linear time, while all current methods use quadratic time.