David Di Lorenzo

Machine learning for global optimization

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 (although different machine learning tools might be employed) to learn the relationship between the starting point of an algorithm and the final outcome (which is usually related to the function value at the point returned by the procedure). Numerical experiments performed both on classical test functions and on difficult space trajectory planning problems show that the proposed approach can be very effective in identifying good starting points for global optimization.

On the convergence of inexact block coordinate descent methods for constrained optimization

We consider the problem of minimizing a smooth function over a feasible set defined as the Cartesian product of convex compact sets. We assume that the dimension of each factor set is huge, so we are interested in studying inexact block coordinate descent methods (possibly combined with column generation strategies). We define a general decomposition framework where different line search based methods can be embedded, and we state global convergence results. Specific decomposition methods based on gradient projection and Frank–Wolfe algorithms are derived from the proposed framework. The numerical results of computational experiments performed on network assignment problems are reported.

A concave optimization-based approach for sparse portfolio selection

This paper considers a portfolio selection problem in which portfolios with minimum number of active assets are sought. This problem is motivated by the need of inducing sparsity on the selected portfolio to reduce transaction costs, complexity of portfolio management, and instability of the solution. The resulting problem is a difficult combinatorial problem. We propose an approach based on the definition of an equivalent smooth concave problem. In this way, we move the difficulty of the original problem to that of solving a concave global minimization problem. We present as global optimization algorithm a specific version of the monotonic basin hopping method which employs, as local minimizer, an efficient version of the Frank–Wolfe method. We test our method on various data sets (of small, medium, and large dimensions) involving real-world capital market from major stock markets. The obtained results show the effectiveness of the presented methodology in terms of global optimization. Furthermore, also the out-of-sample performances of the selected portfolios, as measured by Sharpe ratio, appear satisfactory.

A convergent inexact solution method for equilibrium problems

We consider equilibrium problems with differentiable bifunctions. We adopt the well-known approach based on the reformulation of the equilibrium problem as a global optimization problem through an appropriate gap function. We propose a solution method based on the inexact (and hence, less expensive) evaluation of the gap function and on the employment of a nonmonotone line search. We prove global convergence properties of the proposed inexact method under standard assumptions. Some preliminary numerical results show the potential computational advantages of the inexact method compared with a standard exact descent method.

Global Optimization Approaches for Optimal Trajectory Planning

Optimal trajectory design for interplanetary space missions is an extremely hard problem, mostly because of the very large number of local minimizers that real problems present. Despite the challenges of the task, it is possible, in the preliminary phase, to design low-cost high-energy trajectories with little or no human supervision. In many cases, the discovered paths are as cheap, or even cheaper, as the ones found by experts through lengthy and difficult processes. More interestingly, many of the tricks that experts used to design the trajectories, like, e.g., traveling along an orbit in fractional resonance with a given planet, naturally emerge from the computed solutions, despite neither the model nor the solver have been explicitly designed in order to exploit such knowledge. In this chapter we will analyze the modelling techniques that computational experiments have shown to be most successful, along with some of the algorithms that might be used to solve such problems.

Operating Room Joint Planning and Scheduling

In this paper we suggest a mixed approach in which medium term planning for surgery is combined with short term scheduling of resources. Combining scheduling with planning has the beneficial effect of producing feasible schedules for the next week taking into account waiting lists. Experiments performed with real data from the Careggi Hospital in Florence support the evidence that a significant improvement of waiting list management can be obtained this way.

A convergent and efficient decomposition method for the traffic assignment problem

In this work we consider the 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 decomposition-based approach suitably combined with a column generation strategy. We present an inexact block-coordinate descent method and we prove the global convergence of the algorithm. The results of computational experiments performed on medium-large dimensional problems show that the proposed algorithm is at least competitive with state of the art algorithms.

Exploiting sets of independent moves in VRP

Most heuristic methods for VRP and its variants are based on the partial exploration of large neighborhoods, typically by means of single, simple moves applied to the current solution. In this paper we define an extended concept of independent moves and show how even a very standard heuristic method can significantly improve when considering the simultaneous application of carefully chosen sets of moves. We show in particular that, when choosing a set such that the total cost variation is equal to the sum of the variations induced by each single move, the quality of solutions obtained is in general very high. When compared with numerical results obtained by some of the best available heuristics on challenging, large scale, problems, our simple algorithm equipped with the application of optimally chosen independent moves displayed very good quality.

Path Clustering Based on a Novel Dissimilarity Function for Ride-Sharing Recommenders

Ride-sharing practice represents one of the possible answers to the traffic congestion problem in todays cities. In this scenario, recommenders aim to determine similarity among different paths with the aim of suggesting possible ride shares. In this paper, we propose a novel dissimilarity function between pairs of paths based on the construction of a shared path, which visits all points of the two paths by respecting the order of sequences within each of them. The shared path is computed as the shortest path on a directed acyclic graph with precedence constraints between the points of interest defined in the single paths. The dissimilarity function evaluates how much a user has to extend his/her path for covering the overall shared path. After computing the dissimilarity between any pair of paths, we execute a fuzzy relational clustering algorithm for determining groups of similar paths. Within these groups, the recommenders will choose users who can be invited to share rides. We show and discuss the results obtained by our approach on 45 paths.

A novel convex power adaptation strategy for multicast communications using Random Linear Network Coding schemes

3GPPs Long Term Evolution (LTE) represents the one of the most valuable alternatives to offer a wireless broadband access in fully mobile network context. In particular LTE is able to manage several communication flows characterized by different QoS constrains. This paper deals with a network topology where the mobile users are clustered in Multicast Groups and the base station broadcasts a different traffic flow to each cluster. In order to improve the network throughput on a per-user basis, all communications rely on a Random Linear Network Coding (RLNC) scheme. A key aspect in the QoS management is represented by the power adaptation strategy in use. This paper proposes a novel convex formulation to the power adaptation problem for the downlink phase taking into account the specific RLNC scheme adopted by each communication flow. By the proposed convex formalization, an optimal solution of the problem can be early found in real time. Moreover, the proposed power adaptation strategy shows good performance for what concern throughput and fairness among the users when compared with other alternatives.