Recent studies employ collections of binary decision diagrams (BDDs) to solve combinatorial optimization problems. This paper focuses on the problem of optimally aligning two BDDs, i.e., transforming them to enforce a common order of variables while keeping the total size of the diagrams as small as possible. We address this problem, which is known to … Read more
Feature selection is a fundamental process to avoid overfitting and to reduce the size of databases without significant loss of information that applies to hierarchical clustering. Dendrograms are graphical representations of hierarchical clustering algorithms that for single linkage clustering can be interpreted as minimum spanning trees in the complete network defined by the database. In … Read more
\(\) In 1994, Kranakis et al. published a conjecture about the minimum link-length of every rectilinear covering path for the \(k\)-dimensional grid \(P(n,k) := \{0,1, \dots, n-1\} \times \{0,1, \dots, n-1\} \times \cdots \times \{0,1, \dots, n-1\}\). In this paper we consider the general, NP-complete, Line-Cover problem, where the edges are not required to be … Read more
Given a graph, the maximum clique problem (MCP) asks for determining a complete subgraph with the largest possible number of vertices. We propose a new exact algorithm, called CliSAT, to solve the MCP to proven optimality. This problem is of fundamental importance in graph theory and combinatorial optimization due to its practical relevance for a … Read more
In this paper, we look at the tool indexing problem in which a single copy of each tool is allowed in the tool magazine. We develop problem specific methods to search the neighborhood efficiently and design a Tabu Search algorithm based on them. Computational experiments show that our algorithm is competent. Citation Indian Institute of … Read more
We consider combinatorial optimization problems with interval uncertainty in the cost vector. Recently a new approach was developed to deal with such uncertainties: instead of a single one absolute robust solution, obtained by solving a min max problem, a set of cardinality predefined and minimal absolute regret, obtained by solving a min max min problem, … Read more
The Total Matching Polytope generalizes the Stable Set Polytope and the Matching Polytope. In this paper, we give the perfect formulation for Trees and we derive two new families of valid inequalities, the balanced biclique inequalities which are always facet-defining and the non-balanced lifted biclique inequalities obtained by a lifting procedure, which are facet-defining for … Read more
Since its introduction in the early 2000s, robust optimization with budget uncertainty has received a lot of attention. This is due to the intuitive construction of the uncertainty sets and the existence of a compact robust reformulation for (mixed-integer) linear programs. However, despite its compactness, the reformulation performs poorly when solving robust integer problems due … Read more
In this article we address the problem of finding lower bounds for small Ramsey numbers $R(m,n)$ using circulant graphs. Our constructive approach is based on finding feasible colorings of circulant graphs using Integer Programming (IP) techniques. First we show how to model the problem as a Stackelberg game and, using the tools of bilevel optimization, … Read more
In this paper, we compute the tightest possible bounds on the probability that the optimal value of a combinatorial optimization problem in maximization form with a random objective exceeds a given number, assuming only knowledge of the marginal distributions of the objective coefficient vector. The bounds are “extremal” since they are valid across all joint … Read more