Stefano Nasini

A cutting-plane approach for large-scale capacitated multi-period facility location using a specialized interior-point method

We propose a cutting-plane approach (namely, Benders decomposition) for a class of capacitated multi-period facility location problems. The novelty of this approach lies on the use of a specialized interior-point method for solving the Benders subproblems. The primal block-angular structure of the resulting linear optimization problems is exploited by the interior-point method, allowing the (either exact or inexact) efficient solution of large instances. The consequences of different modeling conditions and problem specifications on the computational performance are also investigated both theoretically and empirically, providing a deeper understanding of the significant factors influencing the overall efficiency of the cutting-plane method. The methodology proposed allowed the solution of instances of up to 200 potential locations, one million customers and three periods, resulting in mixed integer linear optimization problems of up to 600 binary and 600 millions of continuous variables. Those problems were solved by the specialized approach in less than one hour and a half, outperforming other state-of-the-art methods, which exhausted the (144xa0GB of) available memory in the largest instances.

Research impact in co-authorship networks: a two-mode analysis

In the context of research collaboration and co-authorship, we studied scholars’ scientific achievements and success, based on their collection of shared publications. By means of a novel regression model, which exploits the two-mode structure of co-authorship, we translated paper scientific impact into author professional achievement, to simultaneously account for the effect of paper properties (access status, funding bodies, etc.) as well as author demographic and behavioral characteristics (gender, nationality) on academic success and impact. After a detailed analysis of the proposed statistical procedure, we illustrated our approach with an empirical analysis of a co-authorship network based on 1007 scientific articles.

Mathematical programming approaches for classes of random network problems

Random simulations from complicated combinatorial sets are often needed in many classes of stochastic problems. This is particularly true in the analysis of complex networks, where researchers are usually interested in assessing whether an observed network feature is expected to be found within families of networks under some hypothesis (named conditional random networks, i.e., networks satisfying some linear constraints). This work presents procedures to generate networks with specified structural properties which rely on the solution of classes of integer optimization problems. We show that, for many of them, the constraints matrices are totally unimodular, allowing the efficient generation of conditional random networks by specialized interior-point methods. The computational results suggest that the proposed methods can represent a general framework for the efficient generation of random networks even beyond the models analyzed in this paper. This work also opens the possibility for other applications of mathematical programming in the analysis of complex networks.

A bi-level programming approach for global investment strategies with financial intermediation

Most mathematical programming models for investment selection and portfolio management rely on centralized decisions about both budget allocation in different (real and financial) investment options and portfolio composition within the different options. However, in more realistic market scenarios investors do not directly select the portfolio composition, but only provide guidelines and requirements for the investment procedure. Financial intermediaries are then responsible for the detailed portfolio management, resulting in a hierarchical investor-intermediary decision setting. In this work, a bi-level mixed-integer quadratic optimization problem is proposed for the decentralized selection of a portfolio of financial securities and real investments. Single-level reformulation techniques are presented, along with valid-inequalities which allow speeding-up their resolution procedure, when large-scale instances are taken into account. We conducted computational experiments on large historical stock market data from the Center for Research in Security Prices to validate and compare the proposed bi-level investment framework (and the resulting single-level reformulations), under different levels of investor’s and intermediary’s risk aversion and control. The empirical tests reveled the impact of decentralization on the investment performance, and provide a comparative analysis of the computational effort corresponding to the proposed solution approaches.

On Geometrical Properties of Preconditioners in IPMs for Classes of Block-Angular Problems

One of the most efficient interior-point methods for some classes of block-angular structured problems solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient for, respectively, the block and linking constraints. In this work we show that the choice of a good preconditioner depends on geometrical properties of the constraint structure. In particular, the principal angles between the subspaces generated by the diagonal blocks and the linking constraints can be used to estimate ex ante the efficiency of the preconditioner. Numerical validation is provided with some generated optimization problems. An application to the solution of multicommodity network flow problems with nodal capacities and equal flows of up to 64 million variables and up to 7.9 million constraints is also presented. These computational results also show that predictor-corrector directions combined with iterative system solves can be a competitive option for large instances.

A joint model for authors characteristics and collaboration pattern in bibliometric networks: a Bayesian approach

Demographic and behavioral characteristics of journal authors are important indicators of homophily in co-authorship networks. In the presence of correlations between adjacent nodes (assortative mixing), combining the estimation of the individual characteristics and the network structure results in a well-fitting model, which is capable to provide a deep understanding of the linkage between individual and social properties. This paper aims to propose a novel probabilistic model for the joint distribution of nodal properties (authors demographic and behavioral characteristics) and network structure (co-authorship connections), based on the nodal similarity effect. A Bayesian approach is used to estimate the model parameters, providing insights about the probabilistic properties of the observed data set. After a detailed analysis of the proposed statistical methodology, we illustrate our approach with an empirical analysis of co-authorship of 1007 journal articles indexed in the ISI Web of Science database in the field of neuroscience between 2009 and 2013.