Aircraft deconfliction with speed regulation: new models from mixed-integer optimization

Detecting and solving aircraft conflicts, which occur when aircraft sharing the same airspace are too close to each other according to their predicted trajectories, is a crucial problem in Air Traffic Management. We focus on mixed-integer optimization models based on speed regulation. We first solve the problem to global optimality by means of an exact … 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 feasibility based bounds tightening

Mathematical programming problems involving nonconvexities are usually solved to optimality using a (spatial) Branch-and-Bound algorithm. Algorithmic efficiency depends on many factors, among which the widths of the bounding box for the problem variables at each Branch-and-Bound node naturally plays a critical role. The practically fastest box-tightening algorithm is known as FBBT (Feasibility-Based Bounds Tightening): an … Read more

Optimal Design of Electrical Machines: Mathematical Programming Formulations

The optimal design of electrical machines can be mathematically modeled as a mixed-integer nonlinear optimization problem. We present six variants of such a problem, and we show, through extensive computational experiments, that, even though they are mathematically equivalent, the differences in the formulations may have an impact on the numerical performances of a local optimization … Read more

On convex relaxations of quadrilinear terms

The best known method to find exact or at least epsilon-approximate solutions to polynomial programming problems is the spatial Branch-and-Bound algorithm, which rests on computing lower bounds to the value of the objective function to be minimized on each region that it explores. These lower bounds are often computed by solving convex relaxations of the … Read more