A Reliable Affine Relaxation Method for Global Optimization

An automatic method for constructing linear relaxations of constrained global optimization problems is proposed. Such a construction is based on affine and interval arithmetics and uses operator overloading. These linear programs have exactly the same numbers of variables and of inequality constraints as the given problems. Each equality constraint is replaced by two inequalities. This … Read more

Reformulation of a model for hierarchical divisive graph modularity maximization

Finding clusters, or communities, in a graph, or network is a very important problem which arises in many domains. Several models were proposed for its solution. One of the most studied and exploited is the maximization of the so called modularity, which represents the sum over all communities of the fraction of edges within these … Read more

On the impact of symmetry-breaking constraints on spatial Branch-and-Bound for circle packing in a square

We study the problem of packing equal circles in a square from the mathematical programming point of view. We discuss different formulations, we analyse formulation symmetries, we propose some symmetry breaking constraints and show that not only do they tighten the convex relaxation bound, but they also ease the task of local NLP solution algorithms … Read more

Exact and heuristic solutions of the global supply chain problem with transfer pricing

We examine the example of a multinational corporation that attempts to maximize its global after tax profits by determining the flow of goods, the transfer prices, and the transportation cost allocation between each of its subsidiaries. Vidal and Goetschalckx (2001) proposed a bilinear model of this problem and solved it by an Alternate heuristic. We … Read more

Set covering and packing formulations of graph coloring: algorithms and first polyhedral results

We consider two (0,1)-linear programming formulations of the graph (vertex-)coloring problem, in which variables are associated to stable sets of the input graph. The first one is a set covering formulation, where the set of vertices has to be covered by a minimum number of stable sets. The second is a set packing formulation, in … Read more