Standard Linear Programming Methods Research Articles

INSTABILITY OF CLOUD INFRASTRUCTURE RESOURCES AND SERVICES

Increasing non-stationarity of cloud infrastructure resources and services leads to a significant decrease in its productivity. Therefore, the purpose of the article is to identify the reasons for non-stationarity of cloud infrastructure resources and services; finding ways to reduce the level of non-stationarity . As a result of the research, the following results were obtained . Sources leading to the specified non-stationarity are identified . Existing approaches to reducing non-stationarity are analyzed . An example of basic resource allocation using standard linear programming methods is given. Variants of application of these methods for dynamic redistribution of resources are shown. Conclusion. Allocation and dynamic redistribution of resources in the cloud infrastructure can be done using standard linear programming methods. But due to the significant non-stationarity of the cloud environment, the proposed approach will reduce the productivity of cloud resources. At the same time, with an increase in the number of variables and restrictions, the computational complexity of the proposed algorithm will grow exponentially . Therefore, it is necessary to look for other approaches for the distribution and redistribution of cloud resources in conditions of significant non-stationarity .

Minimal Cycle Representatives in Persistent Homology Using Linear Programming: An Empirical Study With User's Guide.

Cycle representatives of persistent homology classes can be used to provide descriptions of topological features in data. However, the non-uniqueness of these representatives creates ambiguity and can lead to many different interpretations of the same set of classes. One approach to solving this problem is to optimize the choice of representative against some measure that is meaningful in the context of the data. In this work, we provide a study of the effectiveness and computational cost of several minimization optimization procedures for constructing homological cycle bases for persistent homology with rational coefficients in dimension one, including uniform-weighted and length-weighted edge-loss algorithms as well as uniform-weighted and area-weighted triangle-loss algorithms. We conduct these optimizations via standard linear programming methods, applying general-purpose solvers to optimize over column bases of simplicial boundary matrices. Our key findings are: 1) optimization is effective in reducing the size of cycle representatives, though the extent of the reduction varies according to the dimension and distribution of the underlying data, 2) the computational cost of optimizing a basis of cycle representatives exceeds the cost of computing such a basis, in most data sets we consider, 3) the choice of linear solvers matters a lot to the computation time of optimizing cycles, 4) the computation time of solving an integer program is not significantly longer than the computation time of solving a linear program for most of the cycle representatives, using the Gurobi linear solver, 5) strikingly, whether requiring integer solutions or not, we almost always obtain a solution with the same cost and almost all solutions found have entries in and therefore, are also solutions to a restricted optimization problem, and 6) we obtain qualitatively different results for generators in Erdős-Rényi random clique complexes than in real-world and synthetic point cloud data.

Bell nonlocality using tensor networks and sparse recovery

Bell's theorem, stating that quantum predictions are incompatible with a local hidden variable description, is a cornerstone of quantum theory and at the center of many quantum information processing protocols. Over the years, different perspectives on non-locality have been put forward as well as different ways to to detect non-locality and quantify it. Unfortunately and in spite of its relevance, as the complexity of the Bell scenario increases, deciding whether a given observed correlation is non-local becomes computationally intractable. Here, we propose to analyse a Bell scenario as a tensor network, a perspective permitting to test and quantify non-locality resorting to very efficient algorithms originating from compressed sensing and that offer a significant speedup in comparison with standard linear programming methods. Furthermore, it allows to prove that non-signalling correlations can be described by hidden variable models governed by a quasi-probability.

Modelling multi-packet multi-receiver spectrum sharing using D-OFDM in software-defined networks

Cognitive radio (CR) technology has been proposed to solve the inefficient spectrum utilization resulted from the traditional fixed spectrum allocation strategy used in wireless systems. Through dynamic and opportunistic spectrum access, CR users can significantly improve spectrum utilization. Most of existing spectrum access schemes designed for CR networks (CRNs) targeted either uni-cast transmission or multi-cast transmission paradigm. Such transmission paradigms allow a CR user to transmit the same data packet over multiple channels to a receiver or a group of receivers. However, existing designs cannot support simultaneous transmissions of multiple distinct packets to different receivers. This new transmission paradigm can be realised using the Discrete Orthogonal Frequency Division Multiplexing (D-OFDM) technology, where each CR transmitter can send multiple different packets to several (multiple) receivers over different channels. In this paper, we investigate the problem of assigning channels to CR transmitters with D-OFDM capabilities, each with multiple packets to be simultaneously sent to multiple receivers. Specifically, we formulate the channel assignment problem as an optimization problem with the goal of achieving the maximum possible network sum-rate. Then, we optimally solve the optimization problem based on standard linear programming methods. To realize our channel assignment in a distributed way, we propose an admission control spectrum access mechanism that allows communicating CR users to exchange their control information. Simulation experiments are carried out to reveal the effectiveness of the proposed protocol compared to previous protocols. The results reveal that significant performance improvement can be achieved by utilizing the D-OFDM technology, in which CR users are allowed to simultaneously transmit multiple packets to multiple receivers.

A market‐oriented wind power dispatch strategy using adaptive price thresholds and battery energy storage

AbstractIn this paper, an adaptive dispatch strategy is presented to maximize the revenue for grid‐tied wind power plant coupled with a battery energy storage system (BESS). The proposed idea is mainly based on time‐varying market‐price thresholds, which are varied according to the proposed algorithm in an adaptive manner. The variable nature of wind power and market price signals leads to the idea of storing energy at low price periods and consequently selling it at high prices. In fact, the wind farm operators can take advantage of the price variability to earn additional income and to maximize the operational profit based on the choice of best price thresholds at each instant of time. This research study proposes an efficient strategy for intermittent power dispatch along with the optimal operation of a BESS in the presence of physical limits and constraints. The strategy is tested and validated with different BESSs, and the percentage improvement of income is calculated. The simulation results, based on actual wind farm and market‐price data, depict the proficiency of the proposed methodology over standard linear programming methods.

Optimal Mixing Enhancement

We introduce a general-purpose method for optimizing the mixing rate of advective fluid flows. An existing velocity field is perturbed in a $C^1$ neighborhood to maximize the mixing rate for flows generated by velocity fields in this neighborhood. Our numerical approach is based on the infinitesimal generator of the flow and is solved by standard linear programming methods. The perturbed flow may be easily constrained to preserve the same steady state distribution as the original flow, and various natural geometric constraints can also be simply applied. The same technique can also be used to optimize the mixing rate of advection-diffusion flow models by manipulating the drift term in a small neighborhood.

Portfolio Construction Based on Stochastic Dominance and Empirical Likelihood

We develop and apply a portfolio optimization framework based on the Stochastic Dominance (SD) decision criterion and the Empirical Likelihood (EL) estimation method. SD and EL share a distribution-free assumption structure that allows for dynamic and non-Gaussian return distributions. The combination of SD and EL can be implemented with standard convex optimization and Linear Programming methods. We apply the SD/EL framework to a range of equity industry momentum strategies. Our moment conditions are based on stylized facts about common risk factors in the stock market. SD/EL yields important ex-ante performance improvements relative to heuristic diversification and optimization based on the Mean-Variance criterion and/or plug-in estimates. Relative to the CRSP all-share index, SD/EL improves average out-of-sample return by more than eight percentage points per annum, with less downside risk, semi-annual rebalancing and no short sales.

Mathematical Modeling of Multiphase Chemical Equilibrium

Prediction of chemical equilibrium conditions is fundamental to modeling in many aerospace applications including rocket performance and ablation heat transfer. Although legacy equilibrium approaches have been in place for some time, improved methodologies are needed to address solution limitations, instabilities, and better code coupling. In support of this, we have developed general mathematical formulations that provide solutions for chemical composition in equilibrium states. Our methods consider both linear and nonlinear objective functions, allowing for any combination of gas- and condensed-phase products, a generality not available in other codes. Our methods are based on the minimization of Gibb’s function subject to mass balance constraints of element conservation. Standard linear programming methods are used for linear problems, and the method of Lagrange multipliers is used for nonlinear problems. We provide unique mathematical derivations in consistent matrix-vector form to provide clarity and to support modern program implementation. This mathematical clarity has allowed us to identify and correct solution instabilities common in other equilibrium codes. We have implemented our approach into a computer code named Chemics, and we provide demonstration cases to verify accuracy and stability. This code provides a stable platform for improved modeling capabilities for important aerospace applications.

Regularized Discrete Optimal Transport

This article introduces a generalization of the discrete optimal transport, with applications to color image manipulations. This new formulation includes a relaxation of the mass conservation constraint and a regularization term. These two features are crucial for image processing tasks where one must take into account families of multimodal histograms with large mass variation across modes. The corresponding relaxed and regularized transportation problem is the solution of a convex optimization problem. Depending on the regularization used, this minimization can be solved using standard linear programming methods or first order proximal splitting schemes. The resulting transportation plan can be used as a color transfer map, which is robust to mass variation across image color palettes. Furthermore, the regularization of the transport plan helps remove colorization artifacts due to noise amplification. We also extend this framework to compute the barycenter of distributions. The barycenter is the solution of an optimization problem, which is separately convex with respect to the barycenter and the transportation plans, but not jointly convex. A block coordinate descent scheme converges to a stationary point of the energy. We show that the resulting algorithm can be used for color normalization across several images. The relaxed and regularized barycenter defines a common color palette for those images. Applying color transfer toward this average palette performs a color normalization of the input images.

Modelling Convex Shape Priors and Matching Based on the Gromov-Wasserstein Distance

We present a novel convex shape prior functional with potential for application in variational image segmentation. Starting point is the Gromov-Wasserstein Distance which is successfully applied in shape recognition and classification tasks but involves solving a non-convex optimization problem and which is non-convex as a function of the involved shape representations. In two steps we derive a convex approximation which takes the form of a modified transport problem and inherits the ability to incorporate vast classes of geometric invariances beyond rigid isometries. We propose ways to counterbalance the loss of descriptiveness induced by the required approximations and to process additional (non-geometric) feature information. We demonstrate combination with a linear appearance term and show that the resulting functional can be minimized by standard linear programming methods and yields a bijective registration between a given template shape and the segmented foreground image region. Key aspects of the approach are illustrated by numerical experiments.

A Network Flow Algorithm for the Cell-Based Single-Destination System Optimal Dynamic Traffic Assignment Problem

The cell-transmission model-based single-destination system optimal dynamic traffic assignment problem proposed by Ziliaskopoulos was mostly solved by standard linear programming (LP) methods, e.g., simplex and interior point methods, which produce link-based flows involving vehicle-holding phenomenon. In this paper we present a network flow algorithm for this problem. We show that the problem is equivalent to the earliest arrival flow and then solve the earliest arrival flow on a time-expanded network. In particular, a scaled flow scheme is proposed to deal with the situation in which the ratio of backward wave speed to forward wave speed is less than one. The proposed algorithm produces path-based flows exhibiting realistic nonvehicle-holding properties. Complexity and numerical analyses show that the algorithm runs more efficiently than LP.

Exact optimization for the [formula omitted]-Compressive Sensing problem using a modified Dantzig–Wolfe method

This paper considers the l 1 -Compressive Sensing problem and presents an efficient algorithm that computes an exact solution. The idea consists in reformulating the problem such that it yields a modified Dantzig–Wolfe decomposition that allows to efficiently apply all standard simplex pivoting rules. Experimental results show the superiority of our approach compared to standard linear programming methods.

A Deterministic Smart Market Model for Groundwater

Efficient management of water requires balancing environmental needs, externality considerations, and economic efficiency. Toward that end, this paper presents a deterministic linear program that could be used to operate a smart spot market for groundwater. The market design uses the existing hydrological programs MODFLOW and GWM along with standard linear programming methods. In principle, a market could be set up anywhere that a MODFLOW model is available. The market design has parallels to markets in the electricity and gas sectors, which we discuss. We present a case study with notional bids for Marlborough, New Zealand. Our approach would reduce transaction costs for a water market, reduce users' risk, and increase the reliability of environmental flows. We discuss a number of cautions and limitations to the model and recommend further work on introducing a stochastic framework to the model.

Quantized Control Allocation of Reaction Control Jets and Aerodynamic Control Surfaces

Amixed-integer linear programming approach tomixing continuous andpulsed control effectors is proposed. The method is aimed at applications involving reentry vehicles that are transitioning from exoatmospheric flight to endoatmospheric flight. In this flight phase, aerodynamic surfaces are weak and easily saturated, and vehicles typically rely on pulsed reaction control jets for attitude control. Control laws for these jets have historically been designed using single-axis phase-plane analysis, which has proven to be sufficient formany applications wheremultiaxis coupling is insignificant and when failures have not been encountered. Here, we propose using a mixed-integer linear programming technique to blend continuous control effectors and pulsed jets to generate moments commanded by linear or nonlinear control laws. When coupled with fault detection and isolation logic, the control effectors can be reconfigured to minimize the impact of control effector failures or damage. When the continuous effectors can provide the desired moments, standard linear programming methods can be used to mix the effectors; however, when the pulsed effectors must be used to augment the aerodynamic surfaces, mixed-integer linear programming techniques are used to determine the optimal combination of jets to fire. The reaction jet control allocator acts as a nonuniformquantizer that applies amoment vector to the vehicle, which approximates the desired moment generated by a continuous control law. Lyapunov theory is applied to develop amethod for determining the region of attraction associated with a quantized vehicle attitude control system.

Chunking for massive nonlinear kernel classification†

A chunking procedure [Bradley, P.S. and Mangasarian, O.L., 2000, Massive data discrimination via linear support vector machines. Optimization Methods and Software, 13, 1–10. Available online at: ftp://ftp.cs.wisc.edu/mathprog/tech-reports/98-05.ps] utilized in [Mangasarian, O.L. and Thompson, M.E., 2006, Massive data classification via unconstrained support vector machines. Journal of Optimization Theory and Applications, 131, 315–325. Available online at: ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/06-01.pdf] for linear classifiers is proposed here for nonlinear kernel classification of massive datasets. A highly accurate algorithm based on nonlinear support vector machines that utilize a linear programming formulation [Mangasarian, O.L., 2000, Generalized support vector machines. In: A. Smola, P. Bartlett, B. Schölkopf and D. Schuurmans (Eds) Advances in Large Margin Classifiers (Cambridge, MA: MIT Press), pp. 135–146. Available online at: ftp://ftp.cs.wisc.edu/math-prog/tech-reports/98-14.ps] is developed here as a completely unconstrained minimization problem [Mangasarian, O.L., 2005, Exact 1-Norm support vector machines via unconstrained convex differentiable minimization. Technical Report 05-03, Data Mining Institute, Computer Sciences Department, University of Wisconsin, Madison, Wisconsin. Available online at: ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/05-03.ps. Journal of Machine Learning Research, 7, 1517–1530, 2006.]. This approach together with chunking leads to a simple and accurate method for generating nonlinear classifiers for a 250,000-point dataset that typically exceeds machine capacity when standard linear programming methods such as CPLEX [ILOG, 2003, ILOG CPLEX 9.0 User's Manual, Incline Village, Nevada. Available online at: http://www.ilog.com/products/cplex/] are used. Because a 1-norm support vector machine underlies the proposed method, the approach together with a reduced support vector machine formulation [Lee, Y.-J. and Mangasarian, O.L., 2001, RSVM: reduced support vector machines. Proceedings of the First SIAM International Conference on Data Mining, Chicago, 5–7 April, CD-ROM. Available online at: ftp://ftp.cs.wisc.edu/pub/dmi/tech-reports/00-07.ps] minimizes the number of kernel functions utilized to generate a simplified nonlinear classifier. †Data Mining Institute Technical Report 06-07, December 2006.

Computation of some stochastic linear programming problems with Cauchy and extreme value distributions

Stochastic programming is concerned with optimization problems in which some or all parameters are treated as random variables in order to capture the uncertainty which is almost always an inherent feature of the system being modelled. It is a methodology for allocating today’s resources to meet tomorrow’s unknown demands. A general approach to deal with uncertainty is to assign a probability distribution to the unknown parameters. The basic idea used in stochastic optimization is to convert the probabilistic model to an equivalent deterministic model. The resulting model is then solved by standard linear or non-linear programming methods. In this paper two probability distributions, the Cauchy distribution and the extreme value distribution, are introduced for stochastic programming. Two different approaches are applied to transform the probabilistic multi-objective linear programming problem into deterministic models. The computational procedures of the models are discussed.

Control of Discrete-Event Systems Modelled by Continuous Petri Nets Case of Closed Manufacturing Lines

In this work, a methodology to study the control of a class of discrete-event systems, more precisely of closed manufacturing lines is proposed. Our contribution is based on the variable speeds and the controlled maximal speeds continuous Petri net model. The computation of the control is made using standard linear programming methods. Through illustrative examples, the simplicity as well as the efficiency of this method will be put in a prominent. Dans ce travail, on propose une méthodologie pour I'étude de la commande d'une Glasse de systémes á événements discrets, plus précisément des lignes de fabrication fermécs. Notre contribution est basée sur le modèle réseau de Petri continu á vitesses variabes et á vitesses maximales contrôlées. Le calcul de la commande se fait par le biais de méthodes standards de programmation linéaire. A travers des exemples illustratifs, la simplcité aussi bien que I'efficacité de cette méthode seront mis en évidence

Incorporating interconnect, register, and clock distribution delays into the retiming process

A retiming algorithm is presented which includes the effects of variable register, clock distribution, and interconnect delays. These delay components are incorporated into the retiming process by assigning register electrical characteristics (RECs) to each edge in the graph representation of a synchronous circuit. A matrix, called the sequential adjacency matrix (SAM), is presented that contains all path delays. Timing constraints for each data path are derived from this matrix. Vertex lags are assigned ranges rather than single values as in existing retiming algorithms. The approach used in the proposed algorithm is to initialize these ranges with unbounded values and to continuously tighten these ranges using localized timing constraints until an optimal solution is obtained. A branch and bound method is offered for the general retiming problem where the REC values are arbitrary. Certain monotonicity constraints can be placed on the REC values to permit the use of standard linear programming methods, thereby requiring significantly less computational time. These conditions and the feasibility of their application to practical circuits are presented. The algorithm is demonstrated on modified benchmark circuits and both increased clock frequencies and the elimination of all race conditions are observed.

A Solution Procedure for the Sort Yard Location Problem in Forest Operations

Abstract Sort yards placed at selected intermediate points between timber cutting sites and mills have potential for increasing the value of logs or trees destined for processing into different products. A two-phase modeling procedure is presented for identifying the efficient placement of sort yards using computations much simpler than those in standard linear mixed-integer programming methods. For. Sci. 33(3):750-762.

Investigation on the use of chemical mass balance receptor model: Numerical computations

Abstract Cheng, M.D. and Hopke, P.K., 1986. Investigation on the use of chemical mass balance receptor model: numerical computations. Chemometrics and Intelligent Laboratory Systems , 1: 33–50. The use of various numerical techniques in the chemical mass balance receptor model leads to different estimations of mass contributions by the identified sources for an ambient air quality data set. Weighted-constrained L 1 (called least absolute deviations in statistics), ordinary weighted least squares, effective variance weighted least squares, and two variants of standard linear programming methods based on the maximized allocation of aerosol mass were studied. The data sets used in this study were the simulated aerosol composition data generated by the National Bureau of Standards for the EPA workshop on mathematical and empirical receptor modeling held at Quail Roost, NC, U.S.A. in 1982. The ensemble reliability of the numerical solutions for these test data sets were evaluated. The weighted-constrained L 1 solutions were found highly stable compared to those from the least-squares methods subject to various complexities of the simulated data sets. The effective variance weighted least squares was found to be ineffective in improving the quality of aerosol mass apportionment by the chemical mass balance model. The results of the standard linear programming methods were insensitive to the lognormal random variations present in the source compositions in Set 3, but gave less precise results than those obtained with the L 1 or least squares methods.