Systems of polynomial equations over the complex or real numbers can be used to model combinatorial problems. In this way, a combinatorial problem is feasible (e.g. a graph is 3-colorable, hamiltonian, etc.) if and only if a related system of polynomial equations has a solution. In the first part of this paper, we construct new … Read more
Valid inequalities for 0-1 knapsack polytopes often prove useful when tackling hard 0-1 Linear Programming problems. To use such inequalities effectively, one needs separation algorithms for them, i.e., routines for detecting when they are violated. We show that the separation problems for the so-called extended cover and weight inequalities can be solved exactly in O(nb) … Read more
In this paper we study capacitated network design problems, differentiating directed, bidirected and undirected link capacity models. We complement existing polyhedral results for the three variants by new classes of facet-defining valid inequalities and unified lifting results. For this, we study the restriction of the problems to a cut of the network. First, we show … Read more
In the paper we consider the quadratic ssignment problem arising from channel coding in communications where one coefficient matrix is the adjacency matrix of a hypercube in a finite dimensional space. By using the geometric structure of the hypercube, we first show that there exist at least $n$ different optimal solutions to the underlying QAPs. … Read more
In a paper published 1978, McEliece, Rodemich and Rumsey improved Lov\’asz’ bound for the Maximum Clique Problem. This strengthening has become well-known under the name Lov\’asz-Schrijver bound and is usually denoted by $\theta’$. This article now deals with situations where this bound is not exact. To provide instances for which the gap between this bound … Read more
This paper presents a robust branch-cut-and-price algorithm for the Heterogeneous Fleet Vehicle Routing Problem (HFVRP), vehicles may have various capacities and fixed costs. The columns in the formulation are associated to $q$-routes, a relaxation of capacitated elementary routes that makes the pricing problem solvable in pseudo-polynomial time. Powerful new families of cuts are also proposed, … Read more
The largest possible average diameter of a bounded cell of a simple hyperplane arrangement is conjectured to be not greater than the dimension. We prove that this conjecture holds in dimension 2, and is asymptotically tight in fixed dimension. We give the exact value of the largest possible average diameter for all simple arrangements in … Read more
The central objective of this paper is to develop a transparent, consistent, self-contained, and stable country risk rating model, closely approximating the country risk ratings provided by Standard and Poor’s (S&P). The models should be non-recursive, i.e., they should not rely on the previous years’ S&P ratings. The selected set of variables includes not only … Read more
Recently, a general-purpose local-search heuristic method called Extremal Optimization (EO) has been successfully applied to some NP-hard combinatorial optimization problems. This paper presents an investigation on EO with its application in multiobjective optimization and proposes a new novel elitist multiobjective algorithm, called Multiobjective Extremal Optimization (MOEO). In order to extend EO to solve the multiobjective … Read more
In this paper a covering model for locating facilities with time-dependent demand is introduced. Not only the facility locations, but also the instants at which such facilities become operative, are considered as decision variables in order to determine the maximal-profit decision. Expressed as a mixed nonlinear integer program, structural properties are derived for particular demand … Read more