In the quadratic traveling salesman problem a cost is associated with any three nodes traversed in succession. This structure arises, e.g., if the succession of two edges represents energetic conformations, a change of direction or a possible change of transportation means. In the symmetric case, costs do not depend on the direction of traversal. We … Read more
Computational molecular biology has emerged as one of the most exciting interdisciplinary fields. It has currently benefited from concepts and theoretical results obtained by different scientific research communities, including genetics, biochemistry, and computer science. In the past few years it has been shown that a large number of molecular biology problems can be formulated as … Read more
This paper surveys several applications of biased random-key genetic algorithms (BRKGA) in optimization problems that arise in telecommunications. We first review the basic concepts of BRKGA. This is followed by a description of BRKGA-based heuristics for routing in IP networks, design of survivable IP networks, redundant server location for content distribution, regenerator location in optical … Read more
Given an undirected node-weighted graph and a positive integer k, the maximum k-colorable subgraph probem is to select a k-colorable induced subgraph of largest weight. The natural integer programming formulation for this problem exhibits a high degree of symmetry which arises by permuting the color classes. It is well known that such symmetry has negative … Read more
We show that half-integral polytopes obtained as the convex hull of a random set of half-integral points of the 0/1 cube have rank as high as Ω(logn/loglogn) with positive probability — even if the size of the set relative to the total number of half-integral points of the cube tends to 0. The high rank … Read more
We present a biased random-key genetic algorithm (BRKGA) for finding small covers of computationally difficult set covering problems that arise in computing the 1-width of incidence matrices of Steiner triple systems. Using a parallel implementation of the BRKGA, we compute improved covers for the two largest instances in a standard set of test problems used … Read more
In this paper we describe an algorithm to approximately solve a class of semidefinite programs called covering semidefinite programs. This class includes many semidefinite programs that arise in the context of developing algorithms for important optimization problems such as sparsest cut, wireless multicasting, and pattern classification. We give algorithms for covering SDPs whose dependence on … Read more
We show how we can linearize probabilistic linear constraints with binary variables when all coefficients are distributed according to either $\mathcal{N}(\mu_i,\lambda \mu_i)$, for some $\lambda >0$ and $\mu_i>0$, or $\Gamma(k_i,\theta)$ for some $\theta >0$ and $k_i>0$. The constraint can also be linearized when the coefficients are independent and identically distributed if they are, besides, either … Read more
Copositive optimization problems are particular conic programs: extremize linear forms over the copositive cone subject to linear constraints. Every quadratic program with linear constraints can be formulated as a copositive program, even if some of the variables are binary. So this is an NP-hard problem class. While most methods try to approximate the copositive cone … Read more
We report on a growing class of assignment problems that are increasingly of interest and very challenging in terms of the difficulty they pose to attempts at exact solution. These problems address economic issues in the location and design of factories, hospitals, depots, transportation hubs and military bases. Others involve improvements in communication network design. … Read more