Interior-point solver for convex separable block-angular problems

Constraints matrices with block-angular structures are pervasive in Optimization. Interior-point methods have shown to be competitive for these structured problems by exploiting the linear algebra. One of these approaches solved the normal equations using sparse Cholesky factorizations for the block constraints, and a preconditioned conjugate gradient (PCG) for the linking constraints. The preconditioner is based on a power series expansion which approximates the inverse of the matrix of the linking constraints system. In this work we present an efficient solver based on this algorithm. Some of its features are: it solves linearly constrained convex separable problems (linear, quadratic or nonlinear); both Newton and second-order predictor-corrector directions can be used, either with the Cholesky+PCG scheme or with a Cholesky factorization of normal equations; the preconditioner may include any number of terms of the power series; for any number of these terms, it estimates the spectral radius of the matrix in the power series (which is instrumental for the quality of the precondi- tioner). The solver has been hooked to SML, a structure-conveying modelling language based on the popular AMPL modeling language. Computational results are reported for some large and/or difficult instances in the literature: (1) multicommodity flow problems; (2) minimum congestion problems; (3) statistical data protection problems using l1 and l2 distances (which are linear and quadratic problems, respectively), and the pseudo-Huber function, a nonlinear approximation to l1 which improves the preconditioner. In the largest instances, of up to 25 millions of variables and 300000 constraints, this approach is from two to three orders of magnitude faster than state-of-the-art linear and quadratic optimization solvers.Preprin

A specialized interior-point algorithm for huge minimum convex cost flows in bipartite networks

Research Report UPC-DEIO DR 2018-01. November 2018The computation of the Newton direction is the most time consuming step of interior-point methods. This direction was efficiently computed by a combination of Cholesky factorizations and conjugate gradients in a specialized interior-point method for block-angular structured problems. In this work we apply this algorithmic approach to solve very large instances of minimum cost flows problems in bipartite networks, for convex objective functions with diagonal Hessians (i.e., either linear, quadratic or separable nonlinear objectives). After analyzing the theoretical properties of the interior-point method for this kind of problems, we provide extensive computational experiments with linear and quadratic instances of up to one billion arcs and 200 and five million nodes in each subset of the node partition. For linear and quadratic instances our approach is compared with the barriers algorithms of CPLEX (both standard path-following and homogeneous-self-dual); for linear instances it is also compared with the different algorithms of the state-of-the-art network flow solver LEMON (namely: network simplex, capacity scaling, cost scaling and cycle canceling). The specialized interior-point approach significantly outperformed the other approaches in most of the linear and quadratic transportation instances tested. In particular, it always provided a solution within the time limit and it never exhausted the 192 Gigabytes of memory of the server used for the runs. For assignment problems the network algorithms in LEMON were the most efficient option.Peer ReviewedPreprin

Revisiting interval protection, a.k.a. partial cell suppression, for tabular data

The final publication is available at link.springer.comInterval protection or partial cell suppression was introduced in “M. Fischetti, J.-J. Salazar, Partial cell suppression: A new methodology for statistical disclosure control, Statistics and Computing, 13, 13–21, 2003” as a “linearization” of the difficult cell suppression problem. Interval protection replaces some cells by intervals containing the original cell value, unlike in cell suppression where the values are suppressed. Although the resulting optimization problem is still huge—as in cell suppression, it is linear, thus allowing the application of efficient procedures. In this work we present preliminary results with a prototype implementation of Benders decomposition for interval protection. Although the above seminal publication about partial cell suppression applied a similar methodology, our approach differs in two aspects: (i) the boundaries of the intervals are completely independent in our implementation, whereas the one of 2003 solved a simpler variant where boundaries must satisfy a certain ratio; (ii) our prototype is applied to a set of seven general and hierarchical tables, whereas only three two-dimensional tables were solved with the implementation of 2003.Peer ReviewedPostprint (author's final draft

A linear optimization based method for data privacy in statistical tabular data

National Statistical Agencies routinely disseminate large amounts of data. Prior to dissemination these data have to be protected to avoid releasing confidential information. Controlled tabular adjustment (CTA) is one of the available methods for this purpose. CTA formulates an optimization problem that looks for the safe table which is closest to the original one. The standard CTA approach results in a mixed integer linear optimization (MILO) problem, which is very challenging for current technology. In this work we present a much less costly variant of CTA that formulates a multiobjective linear optimization (LO) problem, where binary variables are pre-fixed, and the resulting continuous problem is solved by lexicographic optimization. Extensive computational results are reported using both commercial (CPLEX and XPRESS) and open source (Clp) solvers, with either simplex or interior-point methods, on a set of real instances. Most instances were successfully solved with the LO-CTA variant in less than one hour, while many of them are computationally very expensive with the MILO-CTA formulation. The interior-point method outperformed simplex in this particular application.Peer ReviewedPreprin

Collective intelligence: aggregation of information from neighbors in a guessing game

Complex systems show the capacity to aggregate information and to display coordinated activity. In the case of social systems the interaction of different individuals leads to the emergence of norms, trends in political positions, opinions, cultural traits, and even scientific progress. Examples of collective behavior can be observed in activities like the Wikipedia and Linux, where individuals aggregate their knowledge for the benefit of the community, and citizen science, where the potential of collectives to solve complex problems is exploited. Here, we conducted an online experiment to investigate the performance of a collective when solving a guessing problem in which each actor is endowed with partial information and placed as the nodes of an interaction network. We measure the performance of the collective in terms of the temporal evolution of the accuracy, finding no statistical difference in the performance for two classes of networks, regular lattices and random networks. We also determine that a Bayesian description captures the behavior pattern the individuals follow in aggregating information from neighbors to make decisions. In comparison with other simple decision models, the strategy followed by the players reveals a suboptimal performance of the collective. Our contribution provides the basis for the micro-macro connection between individual based descriptions and collective phenomena.Comment: 9 pages, 9 figure

Voltage noise analysis with ring oscillator clocks

Voltage noise is the main source of dynamic variability in integrated circuits and a major concern for the design of Power Delivery Networks (PDNs). Ring Oscillators Clocks (ROCs) have been proposed as an alternative to mitigate the negative effects of voltage noise as technology scales down and power density increases. However, their effectiveness highly depends on the design parameters of the PDN, power consumption patterns of the system and spatial locality of the ROCs within the clock domains. This paper analyzes the impact of the PDN parameters and ROC location on the robustness to voltage noise. The capability of reacting instantaneously to unpredictable voltage droops makes ROCs an attractive solution, which allows to reduce the amount of decoupling capacitance without downgrading performance. Tolerance to voltage noise and related benefits can be increased by using multiple ROCs and reducing the size of the clock domains. The analysis shows that up to 83% of the margins for voltage noise and up to 27% of the leakage power can be reduced by using local ROCs.Peer ReviewedPostprint (author's final draft

Stabilized Benders methods for large-scale combinatorial optimization, with appllication to data privacy

The Cell Suppression Problem (CSP) is a challenging Mixed-Integer Linear Problem arising in statistical tabular data protection. Medium sized instances of CSP involve thousands of binary variables and million of continuous variables and constraints. However, CSP has the typical structure that allows application of the renowned Benders’ decomposition method: once the “complicating” binary variables are fixed, the problem decomposes into a large set of linear subproblems on the “easy” continuous ones. This allows to project away the easy variables, reducing to a master problem in the complicating ones where the value functions of the subproblems are approximated with the standard cutting-plane approach. Hence, Benders’ decomposition suffers from the same drawbacks of the cutting-plane method, i.e., oscillation and slow convergence, compounded with the fact that the master problem is combinatorial. To overcome this drawback we present a stabilized Benders decomposition whose master is restricted to a neighborhood of successful candidates by local branching constraints, which are dynamically adjusted, and even dropped, during the iterations. Our experiments with randomly generated and real-world CSP instances with up to 3600 binary variables, 90M continuous variables and 15M inequality constraints show that our approach is competitive with both the current state-of-the-art (cutting-plane-based) code for cell suppression, and the Benders implementation in CPLEX 12.7. In some instances, stabilized Benders is able to quickly provide a very good solution in less than one minute, while the other approaches were not able to find any feasible solution in one hour.Peer ReviewedPreprin

Improving an interior-point algorithm for multicommodity flows by quadratic regularizations

One of the best approaches for some classes of multicommodity flow problems is a specialized interior-point method that solves the normal equations by a combination of Cholesky factorizations and preconditioned conjugate gradient. Its efficiency depends on the spectral radius—in [0,1)—of a certain matrix in the definition of the preconditioner. In a recent work the authors improved this algorithm (i.e., reduced the spectral radius) for general block-angular problems by adding a quadratic regularization to the logarithmic barrier. This barrier was shown to be self-concordant, which guarantees the convergence and polynomial complexity of the algorithm. In this work we focus on linear multicommodity problems, a particular case of primal block-angular ones. General results are tailored for multicommodity flows, allowing a local sensitivity analysis on the effect of the regularization. Extensive computational results on some standard and some difficult instances, testing several regularization strategies, are also provided. These results show that the regularized interior-point algorithm is more efficient than the nonregularized one. From this work it can be concluded that, if interior-point methods based on conjugate gradients are used, linear multicommodity flow problems are most efficiently solved as a sequence of quadratic ones.Preprin

Waveform flexibility in database-oriented cognitive wireless systems

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes,creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.In this paper we discuss the idea of waveform flexibility in future wireless networks utilizing cognitive radio functionality. Mainly, we consider the possibility to adjust the shape of the waveform based on the information about the surrounding environment stored in a dedicated context-information database. In our approach, the cognitive terminal has an option to select one of four available waveforms to adapt itself in the best way to the constraints delivered by the database. In this paper we present the key concept of waveform flexibility, the proposed algorithm for waveform selection and the achieved simulation results.Peer ReviewedPostprint (author's final draft