Many NP-hard graph problems can be solved in polynomial time for graphs with bounded treewidth. Equivalent results are known for pathwidth and branchwidth. In recent years, several studies have shown that this result is not only of theoretical interest but can successfully be applied to find (almost) optimal solutions or lower bounds for many optimization … Read more
Given two finite sets of points $X^+$ and $X^-$ in $\R^n$, the maximum box problem consists in finding an interval (“box”) $B=\{x : l \leq x \leq u\}$ such that $B\cap X^-=\emptyset$, and the cardinality of $B\cap X^+$ is maximized. A simple generalization can be obtained by instead maximizing a weighted sum of the elements … Read more
Wireless communication is used in many different situations such as mobile telephony, radio and TV broadcasting, satellite communication, and military operations. In each of these situations a frequency assignment problem arises with application specific characteristics. Researchers have developed different modeling ideas for each of the features of the problem, such as the handling of interference … Read more
A new simple generalization of the Motzkin-Straus theorem for the maximum weight clique problem is formulated and directly proved. Within this framework a new trust region heuristic is developed. In contrast to usual trust region methods, it regards not only the global optimum of a quadratic objective over a sphere, but also a set of … Read more
We present a Branch-and-Cut algorithm where the Volume Algorithm is applied to the linear programming relaxations arising at each node of the search tree. This means we use fast approximate solutions to these linear programs instead of exact but slower solutions given by the traditionally used dual simplex method. Our claim is that such a … Read more
We provide two algorithms for computing the volume of the convex polytope $\Omega:=\{x\in \R^n_+ \,|\,Ax\leq b\}$, for $A\in\R^{m\times n}, b\in\R^n$. The computational complexity of both algorithms is essentially described by $n^m$, which makes them especially attractive for large $n$ and relatively small $m$, when the other methods with $O(m^n)$ complexity fail. The methodology which differs … Read more
This paper illustrates results obtained by a new metaheuristic approach, Greedy Randomized Adaptive Path Relinking, applied to solve static power transmission network design problems. This new approach consists of a generalization of GRASP concepts to explore different trajectories between two CitationAT&T Labs Research Report, December 2001 Submitted to PSCC’02.ArticleDownload View PDF
The Dedicated Aircraft Recovery Problem (DARP) involves decisions concerning aircraft to flight assignments in situations where unforeseen events have disrupted the existing flight schedule, e.g. bad weather causing flight delays. The dedicated aircraft recovery problem aims to recover these flight schedules through a series of reassignments of aircraft to flights, delaying of flights and cancellations … Read more
We present a heuristic method for general 0-1 mixed integer programming, intended for eventual incorporation into parallel branch-and-bound methods for solving such problems exactly. The core of the heuristic is a rounding method based on simplex pivots, employing only gradient information, for a strictly concave, differentiable merit function measuring integer feasibility. When local minima of … Read more
In the job shop scheduling problem (JSP), a finite set of jobs is processed on a finite set of machines. Each job is required to complete a set of operations in a fixed order. Each operation is processed on a specific machine for a fixed duration. A machine can process no more than one job … Read more