Separation Constraints Research Articles

Multiple Time Series Forecasting Using Quasi-Randomized Functional Link Neural Networks

We are interested in obtaining forecasts for multiple time series, by taking into account the potential nonlinear relationships between their observations. For this purpose, we use a specific type of regression model on an augmented dataset of lagged time series. Our model is inspired by dynamic regression models (Pankratz 2012), with the response variable’s lags included as predictors, and is known as Random Vector Functional Link (RVFL) neural networks. The RVFL neural networks have been successfully applied in the past, to solving regression and classification problems. The novelty of our approach is to apply an RVFL model to multivariate time series, under two separate regularization constraints on the regression parameters.

Asynchronous consensus for optimal power flow control in smart grid with zero power mismatch

The heterogeneous nature of smart grid components and the desire for smart grids to be scalable, stable and respect customer privacy have led to the need for more distributed control paradigms. In this paper we provide a distributed optimal power flow solution for a smart distribution network with separable global costs, separable non-convex constraints, and inseparable linear constraints, while considering important aspects of network operation such as distributed generation and load mismatch, and nodal voltage constraints. An asynchronous averaging consensus protocol is developed to estimate the values of inseparable global information. The consensus protocol is then combined with a fully distributed primal dual optimization utilizing an augmented Lagrange function to ensure convergence to a feasible solution with respect to power flow and power mismatch constraints. The presented algorithm uses only local and neighbourhood communication to simultaneously find the mismatch between power generation, line loss and loads, to calculate nodal voltages, and to minimize distributed costs, leading to a completely distributed solution of the global problem. An IEEE test feeder system with a reasonable number of nodes is used to illustrate the proposed method and efficiency.

Analysis of Model and Iteration Dependencies in Distributed Feasible-Point Algorithms for Optimal Control Computation

The problem of computing optimal control inputs is studied for networks of dynamical linear systems, with respect to separable input constraints and a separable quadratic cost over a finite time-horizon. The main results concern network structures for which the iterates of three feasible-point algorithms can be computed exactly on a subsystem-by-subsystem basis with access restricted to local model-data and algorithm-state information. In particular, hop-based network proximity bounds are investigated for algorithms based on projected gradient, random co-ordinate descent and Jacobi iterations, via graph-based characterisations of various aspects of an equivalent static formulation of the optimal control problem.

Distributionally Robust Chance Constrained Optimal Power Flow with Renewables: A Conic Reformulation

The uncertainty associated with renewable energy sources introduces significant challenges in optimal power flow (OPF) analysis. A variety of new approaches have been proposed that use chance constraints to limit line or bus overload risk in OPF models. Most existing formulations assume that the probability distributions associated with the uncertainty are known a priori or can be estimated accurately from empirical data, and/or use separate chance constraints for upper and lower line/bus limits. In this paper, we propose a data driven distributionally robust chance constrained optimal power flow model (DRCC-OPF), which ensures that the worst-case probability of violating both the upper and lower limit of a line/bus capacity under a wide family of distributions is small. Assuming that we can estimate the first and second moments of the underlying distributions based on empirical data, we propose an exact reformulation of DRCC-OPF as a tractable convex program. The key theoretical result behind this reformulation is a second-order cone programming (SOCP) reformulation of a general two-sided distributionally robust chance constrained set by lifting the set to a higher dimensional space. Our numerical study shows that the proposed SOCP formulation can be solved efficiently and that the results of our model are quite robust.

The BAHAMAS project: the CMB–large-scale structure tension and the roles of massive neutrinos and galaxy formation

Recent studies have presented evidence for tension between the constraints on Omega_m and sigma_8 from the cosmic microwave background (CMB) and measurements of large-scale structure (LSS). This tension can potentially be resolved by appealing to extensions of the standard model of cosmology and/or untreated systematic errors in the modelling of LSS, of which baryonic physics has been frequently suggested. We revisit this tension using, for the first time, carefully-calibrated cosmological hydrodynamical simulations, which thus capture the back reaction of the baryons on the total matter distribution. We have extended the BAHAMAS simulations to include a treatment of massive neutrinos, which currently represents the best motivated extension to the standard model. We make synthetic thermal Sunyaev-Zel'dovich effect, weak galaxy lensing, and CMB lensing maps and compare to observed auto- and cross-power spectra from a wide range of recent observational surveys. We conclude that: i) in general there is tension between the primary CMB and LSS when adopting the standard model with minimal neutrino mass; ii) after calibrating feedback processes to match the gas fractions of clusters, the remaining uncertainties in the baryonic physics modelling are insufficient to reconcile this tension; and iii) if one accounts for internal tensions in the Planck CMB dataset (by allowing the lensing amplitude, A_Lens, to vary), invoking a non-minimal neutrino mass, typically of 0.2-0.4 eV, can resolve the tension. This solution is fully consistent with separate constraints from the primary CMB and baryon acoustic oscillations.

Intermediate DC-Link Capacitor Reduction in a Two-Stage Cascaded AC/DC Converter for More Electric Aircrafts

In this paper, an innovative method to minimize the intermediate dc-link capacitance in a cascaded two-stage combination of a three-phase six-switch power factor correction (PFC) and phase-shifted full-bridge (PSFB) dc/dc stage is introduced and analyzed. The proposed strategy has a significant impact on the minimization of the overall system weight and volume. Fundamentally, the method is based on minimizing the switching fundamental component of the dc-link current and is established by imposing a separate constraint on the phase duty ratios without compromising the unity PFC action. Furthermore, the control loop takes care of regulating the intermediate dc-link voltage along with the final output voltage. A 6 kW laboratory prototype of the integrated three-phase PFC and PSFB dc/dc as a part of auxiliary power unit in more-electric airplanes is developed and designed to validate the proposed algorithm. The experimental results show a conversion efficiency of 95.4% at full load, input total harmonic distortion of 4.1%, power factor of 0.998, output voltage ripple of ±1%, and a reduction of dc-link capacitor by 60%.

Scalable methods for Bayesian selective inference

Modeled along the truncated approach in [20], selection-adjusted inference in a Bayesian regime is based on a selective posterior. Such a posterior is determined together by a generative model imposed on data and the selection event that enforces a truncation on the assumed law. The effective difference between the selective posterior and the usual Bayesian framework is reflected in the use of a truncated likelihood. The normalizer of the truncated law in the adjusted framework is the probability of the selection event; this typically lacks a closed form expression leading to the computational bottleneck in sampling from such a posterior. The current work provides an optimization problem that approximates the otherwise intractable selective posterior and leads to scalable methods that give valid post-selective Bayesian inference. The selection procedures are posed as data-queries that solve a randomized version of a convex learning program which have the advantage of preserving more left-over information for inference. We propose a randomization scheme under which the approximating optimization has separable constraints that result in a partially separable objective in lower dimensions for many commonly used selective queries. We show that the proposed optimization gives a valid exponential rate of decay for the selection probability on a large deviation scale under a Gaussian randomization scheme. On the implementation side, we offer a primal-dual method to solve the optimization problem leading to an approximate posterior; this allows us to exploit the usual merits of a Bayesian machinery in both low and high dimensional regimes when the underlying signal is effectively sparse. We show that the adjusted estimates empirically demonstrate better frequentist properties in comparison to the unadjusted estimates based on the usual posterior, when applied to a wide range of constrained, convex data queries.

Hybrid Jacobian and Gauss--Seidel Proximal Block Coordinate Update Methods for Linearly Constrained Convex Programming

Recent years have witnessed the rapid development of block coordinate update (BCU) methods, which are particularly suitable for problems involving large-sized data and/or variables. In optimization, BCU first appears as the coordinate descent method that works well for smooth problems or those with separable nonsmooth terms and/or separable constraints. As nonseparable constraints exist, BCU can be applied under primal-dual settings. In the literature, it has been shown that for weakly convex problems with nonseparable linear constraints, BCU with fully Gauss--Seidel updating rule may fail to converge and that with fully Jacobian rule can converge sublinearly. However, empirically the method with Jacobian update is usually slower than that with Gauss--Seidel rule. To maintain their advantages, we propose a hybrid Jacobian and Gauss--Seidel BCU method for solving linearly constrained multiblock structured convex programming, where the objective may have a nonseparable quadratic term and separable nonsmooth...

Exact Second-Order Cone Programming Relaxations for Some Nonconvex Minimax Quadratic Optimization Problems

In this paper, we study, for the first time, nonconvex minimax separable quadratic optimization problems with multiple separable quadratic constraints and their second-order cone programming (SOCP)...

Nonlinear Conflict Resolution and Flow Management Using Particle Swarm Optimization

A new optimization problem to resolve conflicts by allowing aircraft to change both their heading angle and speed is considered. The performance index in the optimization problem is formulated to reduce the variation of the aircraft arrival time that is caused by conflict resolution maneuvers. To achieve both conflict resolution and flow management, metering constraints are introduced together with separation constraints. Even though the performance index and constraints are nonlinear, the optimal solution can be easily obtained by utilizing particle swarm optimization. Numerical simulations are performed to evaluate the performance of the proposed algorithm, and the numerical experimental results showed a significant reduction in the variation of the aircraft arrival time as well as the magnitude of heading angle and speed changes.

Distance multi‐labelling of graphs with weighted vertices

The channel assignment problem (CAP) which finds an efficient assignment of channels to the transmitters of a wireless network is applicable to cellular mobile system (CMS). There are lots of results on CAP for CMS where the channel separation constraint is represented by a symmetric matrix or a graph. In particular, the Philadelphia instances and the 49-cell system are benchmark CAP for CMS and are treated in many papers. The distance multi-labelling (DM) problem on a graph with weighted vertices is an effective mathematical model of CAP for CMS in which a CMS is represented by a graph with weighted vertices, where a vertex corresponds to a cell with the number of calls on it as its weight. A DM on a graph with weighted vertices is an assignment of a set of non-negative numbers to each vertex. These numbers, which are called labels, represent the channels assigned to the demand calls in each cell. DM is a generalisation of both distance labelling and graph multi-colouring. In this study, the author introduce a new method called the layering method to find a DM on a graph with weighted vertices. Using this method, we obtain optimal DM for two Philadelphia instances. For each of them, the authors obtain a DM according to the range of separation conditions, and it includes known optimal results which are individually obtained under one separation condition.

The projected Barzilai–Borwein method with fall-back for strictly convex QCQP problems with separable constraints

A variant of the projected Barzilai–Borwein method for solving the strictly convex QCQP problems with separable constraints is presented. The convergence is enforced by a combination of the fall-back strategy and the fixed step-length gradient projection. Using the recent results on the decrease of the convex quadratic function along the projected-gradient path, we prove that the algorithm enjoys the R-linear convergence. The algorithm is plugged into our scalable TFETI based domain decomposition algorithm for the solution of contact problems and its performance is demonstrated on the solution of contact problems, including a frictionless problem and the problems with the isotropic and orthotropic Tresca friction.

Valid inequalities for separable concave constraints with indicator variables

We study valid inequalities for optimization models that contain both binary indicator variables and separable concave constraints. These models reduce to a mixed-integer linear program (MILP) when the concave constraints are ignored, or to a nonconvex global optimization problem when the binary restrictions are ignored. In algorithms designed to solve these problems to global optimality, cutting planes to strengthen the relaxation are traditionally obtained using valid inequalities for the MILP only. We propose a technique to obtain valid inequalities that are based on both the MILP constraints and the concave constraints. We begin by characterizing the convex hull of a four-dimensional set consisting of a single binary indicator variable, a single concave constraint, and two linear inequalities. Using this analysis, we demonstrate how valid inequalities for the single node flow set and for the lot-sizing polyhedron can be “tilted” to give valid inequalities that also account for separable concave functions of the arc flows. We present computational results demonstrating the utility of the new inequalities for nonlinear transportation problems and for lot-sizing problems with concave costs. To our knowledge, this is one of the first works that simultaneously convexifies both nonconvex functions and binary variables to strengthen the relaxations of practical mixed-integer nonlinear programs.

Semi-Decentralized Nash Equilibrium Seeking in Aggregative Games With Separable Coupling Constraints and Non-Differentiable Cost Functions

We study the Nash equilibrium seeking problem for noncooperative agents whose decision making process can be modeled as a generalized aggregative game. Specifically, we consider players with convex local cost functions, convex local constraints, and convex separable coupling constraints, and we extend the literature on generalized aggregative games by handling possibly non-differentiable cost functions. We recast the Nash equilibrium seeking problem as the problem to find a zero of a set-valued monotone operator and show that the variational Nash equilibria correspond to KKT solutions of the original game where the shared constraints have the same Lagrange multipliers for all the players. Finally, we design a semi-decentralized algorithm with global convergence guarantee for generalized Nash equilibrium seeking.

Revisiting Stress Majorization as a Unified Framework for Interactive Constrained Graph Visualization.

We present an improved stress majorization method that incorporates various constraints, including directional constraints without the necessity of solving a constraint optimization problem. This is achieved by reformulating the stress function to impose constraints on both the edge vectors and lengths instead of just on the edge lengths (node distances). This is a unified framework for both constrained and unconstrained graph visualizations, where we can model most existing layout constraints, as well as develop new ones such as the star shapes and cluster separation constraints within stress majorization. This improvement also allows us to parallelize computation with an efficient GPU conjugant gradient solver, which yields fast and stable solutions, even for large graphs. As a result, we allow the constraint-based exploration of large graphs with 10K nodes - an approach which previous methods cannot support.

Divide and update: towards single-shot object and probe retrieval for near-field holography.

We present a phase reconstruction scheme for X-ray near-field holographic imaging based on a separability constraint for probe and object. In order to achieve this, we have devised an algorithm which requires only two measurements - with and without an object in the beam. This scheme is advantageous if the standard flat-field correction fails and a full ptychographic dataset can not be acquired, since either object or probe are dynamic. The scheme is validated by numerical simulations and by a proof-of-concept experiment using highly focused undulator radiation of the beamline ID16a of the European Synchrotron Radiation Facility (ESRF).

Combination of optimal control approaches for aircraft conflict avoidance via velocity regulation

SummaryThis paper deals with optimal control applied to one of the most crucial and challenging problems in Air Traffic Management that of aircraft conflict avoidance. We propose an optimal control model where aircraft separation is achieved by changing the speeds of aircraft, and the integral over a time window of their squared accelerations is minimized. Pairwise aircraft separation constraints constitute the main difficulties to be handled. We propose an original decomposition of the problem into 3 zones, in such a way that in two of them, no conflict occurs. Then, using the Pontryagin maximum principle, 2 new formulations of the original optimal control problem are proposed and solved via direct shooting methods. Thanks to our decomposition, these numerical methods are applied on subproblems having reduced size with respect to the original one, thus improving the efficiency of the solution process. Thirty problem instances are numerically solved, showing the effectiveness of the proposed approaches.

Designing spatially cohesive nature reserves with backup coverage

ABSTRACTNatural habitats continue to dwindle due to a variety of natural and human-induced stressors. In response, sufficient land must be set aside for conservation to preserve long-term biodiversity. In this paper, we propose a bi-objective optimization model to form spatially cohesive nature reserves by minimizing the distance from habitat patches to the center of their reserve, while simultaneously maximizing the ecological condition of the patches set aside for preservation. Our model can accommodate multiple reserves which, combined with a minimum separation distance requirement, enforces backup coverage to mitigate the possible effects of natural and anthropogenic stressors. The model fully capitalizes on GIS functionalities to extract information on spatial relationships and visualize optimization results. Given the complexity of the separation constraint, we propose a genetic algorithm (GA) and a two-phase heuristic where the GA solves the selection of the reserves, while a solver attempts to optimize the allocation of patches to the selected reserves. The behavior of our model and its sensitivity to the parameters are illustrated on a simulated data set, while its real-world problem-solving capabilities are demonstrated on a case study in New Hampshire. Our model provides an alternative modeling tool for conservation planning, particularly when backup reserves are desired.

Frequency assignment problem with net filter discrimination constraints

Managing radio spectrum resources is a crucial issue. The frequency assignment problem (FAP) basically aims to allocate limited number of frequencies to communication links in an efficient manner. Geographically close links, however, cause interference, which complicates the assignment, imposing frequency separation constraints. The FAP is closely related to the graph-coloring problem and it is an NP-hard problem. In this paper, we propose to incorporate the randomization into greedy and fast heuristics. As far as being implemented, the proposed algorithms are quite straight forward and are unencumbered by system parameters that need to be tuned whenever the system changes. The proposed algorithms significantly improve, quickly and effectively, the solutions obtained by greedy algorithms in terms of the number of assigned frequencies and the range. The enhanced versions of the proposed algorithms perform close to the lower bounds while running in a reasonable duration. Another novelty of our study is its consideration of the net filter discrimination effects in the communication model. Performance analysis is done by synthetic and measured data, where the measurement data includes the effect of the real 3-dimensional (3D) geographical features in the Daejeon region in Korea. In both cases, we observe a significant improvement by employing randomized heuristics.

Reciprocal Geometric Conflict Resolution on Unmanned Aerial Vehicles by Heading Control

This paper presents a novel geometry-based distributed cooperative conflict resolution method for unmanned aerial vehicles to autonomously handle distributed multiple encounters in an integrated airspace. First, the safe separation constraint of pairwise conflicts is studied, with consideration given to the periodic features of the tangent function. Second, the nonlinear safe separation constraint is transformed into a linear constraint through mapping the constraint relationship from the degree space into the sin value space. A consensus-guaranteed rule is designed to decouple the conflict resolution responsibilities of pairwise conflict-related unmanned aerial vehicles from the obtained linear constraint. Each unmanned aerial vehicle can compute its feasible maneuver range individually. Third, a short-term conflict resolution object function is designed, and a reciprocal geometric conflict resolution algorithm is proposed. The proposed method is tested in several simulations and compared with existing algorithms. The results show that the reciprocal geometric conflict resolution method is capable of resolving various conflicts, is robust to time delay, and outperforms existing algorithms in reducing conflict avoidance cost.