Facility location decisions play a prominent role in strategic planning of many firms, companies and governmental organizations. Since in many real-world facility location problems, the data are subject to uncertainty, in this paper, we consider the P-center problem under uncertainty of demands. Using Bertsimas and Sim approach, we develop a robust model of the problem as an integer programming...

The k-center problem is a classical combinatorial optimization problem which asks to find k centers such that the maximum distance of any input point in a set P to its assigned center is minimized. The problem allows for elegant 2-approximations. However, the situation becomes significantly more difficult when constraints are added to the problem. We raise the question whether general methods c...

Microarray technology for profiling gene expression levels is a popular tool in modern biological research. Applications range from tissue classification to the detection of metabolic networks, from drug discovery to time-critical personalized medicine. Given the increase in size and complexity of the data sets produced, their analysis is becoming problematic in terms of time/quality trade-offs...

K-Means clustering is a well-known tool in unsupervised learning. The performance of K-Means clustering, measured by the F-ratio validity index, highly depends on selection of its initial partition. This problematic dependency always leads to a local optimal solution for k-center clustering. To overcome this difficulty, we present an intuitive approach that iteratively incorporates Fisher discr...

The convex ordered median problem is a generalization of the median, the k-centrum or the center problem. The task of the associated inverse problem is to change edge lengths at minimum cost such that a given vertex becomes an optimal solution of the location problem, i.e., an ordered median. It is shown that the problem is NP-hard even if the underlying network is a tree and the ordered median...