Perfect graphs constitute a well-studied graph class with a rich structure, reflected by many characterizations with respect to different concepts. Perfect graphs are, for instance, precisely those graphs $G$ where the stable set polytope $STAB(G)$ coincides with the fractional stable set polytope $QSTAB(G)$. For all imperfect graphs $G$ it holds that $STAB(G) \subset QSTAB(G)$. It … Read more
Wasps, bees, ants and termites all make effective use of their environment and resources by displaying collective “swarm” intelligence. Termite colonies – for instance – build nests with a complexity far beyond the comprehension of the individual termite, while ant colonies dynamically allocate labor to various vital tasks such as foraging or defense without any … Read more
Our goal in this paper is to demonstrate that branch-and-bound algorithms for combinatorial optimization can be effectively implemented on a relatively new type of multiprocessor platform known as a computational grid. We will argue that to easily and effectively harness the power of computational grids for branch-and-bound algorithms, the master-worker paradigm should be used to … Read more
This papers describes a perl language program to create time-to-target solution value plots for measured CPU times that are assumed to fit a shifted exponential distribution. This is often the case in local search based heuristics for combinatorial optimization, such as simulated annealing, genetic algorithms, iterated local search, tabu search, WalkSAT, and GRASP. Such plots … Read more
We consider the problem of interconnecting a set of customer sites using SONET rings of equal capacity, which can be defined as follows: Given an undirected graph G=(V,E) with nonnegative edge weight d(u,v), (u,v) in E, and two integers K and B, find a partition of the nodes of G into K subsets so that … Read more
The k-traveling salesman problem, or k-TSP is: given a graph with edge weights and an integer k, find a simple cycle of minimum weight visiting exactly k nodes. To obtain lower bounds for the traveling salesman problem the 2-matching relaxation and the 1-tree relaxation can be used. We generalize these two relaxations for the k-TSP. … Read more
We address a multi-item capacitated lot-sizing problem with setup times and shortage costs that arises in real-world production planning problems. Demand cannot be backlogged, but can be totally or partially lost. The problem is NP-hard. A mixed integer mathematical formulation is presented. Our approach in this paper is to propose some classes of valid inequalities … Read more
Semidefinite optimization, commonly referred to as semidefinite programming, has been a remarkably active area of research in optimization during the last decade. For combinatorial problems in particular, semidefinite programming has had a truly significant impact. This paper surveys some of the results obtained in the application of semidefinite programming to satisfiability and maximum-satisfiability problems. The … Read more
Nonlinear optimization deals with the problem of optimizing a single objective function, such as physical weight or cost, in the presence of equality and inequality constraints. Usually engineering design applications are highly non-linear and engineers are always interested in not finding a feasible design that is locally optimal in the design space, but globally optimal … Read more
We study the problem of maximizing the second smallest eigenvalue of the Laplace matrix of a graph over all nonnegative edge weightings with bounded total weight. The optimal value is the \emph{absolute algebraic connectivity} introduced by Fiedler, who proved tight connections of this value to the connectivity of the graph. Using semidefinite programming techniques and … Read more