Andrea Cassioli In the last years, the gap between solution methods in literature and optimization running in production has increased. Agile development practices, DevOps and modern cloud-based infrastructure call for a revisit of how optimization software is developed. We review the state-of-the-art, propose a development framework that can be applied across different programming languages and modeling frameworks … Read more
When a weighted graph is an instance of the Distance Geometry Problem (DGP), certain types of vertex orders (called discretization orders) allow the use of a very efficient, precise and robust discrete search algorithm (called Branch-and-Prune). Accordingly, finding such orders is critically important in order to solve DGPs in practice. We discuss three types of … Read more
In this work we consider the symmetric network equilibrium problem formulated as convex minimization problem whose variables are the path flows. In order to take into account the difficulties related to the large dimension of real network problems we adopt a column generation strategy and we employ a gradient projection method within an inexact decomposition … Read more
In this paper we propose an algorithm for the global optimization of computationally expensive black–box functions. For this class of problems, no information, like e.g. the gradient, can be obtained and function evaluation is highly expensive. In many applications, however, a lower bound on the objective function is known; in this situation we derive a … Read more
In this paper we consider a mathematical model for magmatic mixtures based on the Gibbs free energy. Different reformulations of the problem are presented and some theoretical results about the existence and number of solutions are derived. Finally, two homotopy methods and a global optimization one are introduced and computationally tested. One of the homotopy … Read more
In this paper we propose a heuristic approach for the problem of packing equal rectangles within a convex region. The approach is based on an Iterated Local Search scheme (or, using a terminology employed for continuous problems, a Monotonic Basin Hopping), in which the key step is the perturbation move. Different perturbation moves, both combinatorial … Read more
In this paper we introduce the LeGO (Learning for Global Optimization) approach for global optimization in which machine learning is used to predict the outcome of a computationally expensive global optimization run, based upon a suitable training performed by standard runs of the same global optimization method. We propose to use a Support Vector Machine … Read more
The Sensor Network Localization Problem (SNLP), arising from many applied fields related with environmental monitoring, has attracted much research during the last years. Solving the SNLP deals with the reconstruction of a geometrical structure from incomplete pairwise distances between sensors. In this paper we present an heuristic multistage approach in which the solving strategy is … Read more
The problem of optimally designing a trajectory for a space mission is considered in this paper. Actual mission design is a complex, multi-disciplinary and multi-objective activity with relevant economic implications. In this paper we will consider some simplified models proposed by the European Space Agency as test problems for global optimization. We show that many … Read more
Very hard optimization problems, i.e., problems with a large number of variables and local minima, have been effectively attacked with algorithms which mix local searches with heuristic procedures in order to widely explore the search space. A Population Based Approach based on a Monotonic Basin Hopping optimization algorithm has turned out to be very effective … Read more