A MIP flow model for crop-rotation planning in a context of forest sustainable development

We propose a Mixed-Integer Linear Programming model for a class of multi-period crop rotation optimization problems with demand constraints and incompatibility constraints between cultivation and fallow state on a land plot. This model is applied to a case study on Madagascan farms in the scope of a sustainable development campain against deforestation, where the objective is to better control agricultural space while covering seasonal needs of farmer. We propose an efficient upper bound computation and study the variation of the minimum number of plots and total space needed in function of the unitary surface area of a plot. Numerical results associated with the Madagascan case are reported.     

Displaying Variation in Large Datasets: Plotting a Visual Summary of Effect Sizes

Displaying the component-wise between-group differences high-dimensional datasets is problematic because widely used plots such as Bland–Altman and Volcano plots do not show what they are colloquially believed to show. Thus, it is difficult for the experimentalist to grasp why the between-group difference of one component is “significant” while that of another component is not. Here, we propose a type of “Effect Plot” that displays between-group differences in relation to respective underlying variability for every component of a high-dimensional dataset. We use synthetic data to show that such a plot captures the essence of what determines “significance” for between-group differences in each component, and provide guidance in the interpretation of the plot. Supplementary online materials contain the code and data for this article and include simple R functions to produce an effect plot from suitable datasets.     

Sustainable vegetable crop supply problem with perishable stocks

In this paper, we deal with a vegetable crop supply problem with two main particularities: (i) the production must respect certain ecologically-based constraints and (ii) harvested crops can be stocked but only for a limited period of time, given that they are perishable. To model these characteristics, we develop a linear formulation in which each variable is associated to a crop rotation plan. This model contains a very large number of variables and is therefore solved with the aid of a column generation approach. Moreover, we also propose a two-stage stochastic programming with recourse model which takes into consideration that information on the demands might be uncertain. We provide a discussion of the results obtained via computational tests run on instances adapted from real-world data.     

Tractable model discrimination for safety–critical systems with disjunctive and coupled constraints

This paper considers the model discrimination problem among a finite number of models in safety–critical systems that are subjected to constraints that can be disjunctive and where state and input constraints can be coupled with each other. In particular, we consider both the optimal input design problem for active model discrimination that is solved offline as well as the online passive model discrimination problem via a model invalidation framework. To overcome the issues associated with non-convex and generalized semi-infinite constraints due to the disjunctive and coupled constraints, we propose some techniques for reformulating these constraints in a computationally tractable manner by leveraging the Karush–Kuhn–Tucker (KKT) conditions and introducing binary variables, thus recasting the active and passive model discrimination problems into tractable mixed-integer linear/quadratic programming (MILP/MIQP) problems. When compared with existing approaches, our method is able to obtain the optimal solution and is observed in simulations to also result in less computation time. Finally, we demonstrate the effectiveness of the proposed active model discrimination approach for estimating driver intention with disjunctive safety constraints and state–input coupled curvature constraints, as well as for fault identification.     

Computational strategies for non-convex multistage MINLP models with decision-dependent uncertainty and gradual uncertainty resolution

In many planning problems under uncertainty the uncertainties are decision-dependent and resolve gradually depending on the decisions made. In this paper, we address a generic non-convex MINLP model for such planning problems where the uncertain parameters are assumed to follow discrete distributions and the decisions are made on a discrete time horizon. In order to account for the decision-dependent uncertainties and gradual uncertainty resolution, we propose a multistage stochastic programming model in which the non-anticipativity constraints in the model are not prespecified but change as a function of the decisions made. Furthermore, planning problems consist of several scenario subproblems where each subproblem is modeled as a nonconvex mixed-integer nonlinear program. We propose a solution strategy that combines global optimization and outer-approximation in order to optimize the planning decisions. We apply this generic problem structure and the proposed solution algorithm to several planning problems to illustrate the efficiency of the proposed method with respect to the method that uses only global optimization.     

A primal-dual active-set algorithm for bilaterally constrained total variation deblurring and piecewise constant Mumford-Shah segmentation problems

In this paper, we propose a fast primal-dual algorithm for solving bilaterally constrained total variation minimization problems which subsume the bilaterally constrained total variation image deblurring model and the two-phase piecewise constant Mumford-Shah image segmentation model. The presence of the bilateral constraints makes the optimality conditions of the primal-dual problem semi-smooth which can be solved by a semi-smooth Newton’s method superlinearly. But the linear system to solve at each iteration is very large and difficult to precondition. Using a primal-dual active-set strategy, we reduce the linear system to a much smaller and better structured one so that it can be solved efficiently by conjugate gradient with an approximate inverse preconditioner. Locally superlinear convergence results are derived for the proposed algorithm. Numerical experiments are also provided for both deblurring and segmentation problems. In particular, for the deblurring problem, we show that the addition of the bilateral constraints to the total variation model improves the quality of the solutions.     

A Crop Planning Problem with Fuzzy Random Profit Coefficients

The main purpose of this paper is to present a crop planning problem for agricultural management under uncertainty. It is significant that agricultural managers assign their limited farmlands to cultivation of which crops in a season. This planning is called the crop planning problem and influences their incomes for the season. Usually, the crop planning problem is formulated as a linear programming problem. But there are many uncertain factors in agricultural problems, so future profits for crops are not certain values. A linear programming model with constant profit coefficients may not reflect the environment of decision making properly. Therefore, we propose a model of crop planning with fuzzy profit coefficients, and an effective solution procedure for the model. Furthermore, we extend this fuzzy model, setting the profit coefficients as discrete randomized fuzzy numbers. We show concrete optimal solutions for each models.     

Simultaneous determination of capacities and load in parallel M/M/1 queues

In this paper, we address an analytical model to simultaneously determine the processing capacity and load assigned to each processor in a multiple processor configuration within the framework of M/M/1 queues. A queueing optimization model is formulated as a nonlinear programming problem having linear constraints. We then propose an optimization algorithm that utilizes the special structure of the problem. To illustrate the applicability of our method, a small sample system has been solved.     

Numerical analysis of a locking‐free mixed finite element method for a bending moment formulation of Reissner‐Mindlin plate model

This article deals with the approximation of the bending of a clamped plate, modeled by Reissner‐Mindlin equations. It is known that standard finite element methods applied to this model lead to wrong results when the thickness t is small. Here, we propose a mixed formulation based on the Hellinger‐Reissner principle which is written in terms of the bending moments, the shear stress, the rotations and the transverse displacement. To prove that the resulting variational formulation is well posed, we use the Babu?ka‐Brezzi theory with appropriate t ‐dependent norms. The problem is discretized by standard mixed finite elements without the need of any reduction operator. Error estimates are proved. These estimates have an optimal dependence on the mesh size h and a mild dependence on the plate thickness t. This allows us to conclude that the method is locking‐free. The proposed method yields direct approximation of the bending moments and the shear stress. A local postprocessing leading to H¹ ‐type approximations of transverse displacement and rotations is introduced. Moreover, we propose a hybridization procedure, which leads to solving a significantly smaller positive definite system. Finally, we report numerical experiments which allow us to assess the performance of the method. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013     

Construction of efficient experimental designs under multiple resource constraints

The aim of this paper is twofold. First, we introduce ‘resource constraints’ as a general concept that covers many practical restrictions on experimental design. Second, to compute optimal or near‐optimal exact designs of experiments under multiple resource constraints, we propose a tabu search heuristic related to the Detmax procedure. To illustrate the scope and performance of the proposed method, we chose the criterion of D‐optimality and computed efficient designs for (i) a block model with limits on the numbers of blocks and on the replications of treatments, (ii) a quadratic regression model with simultaneous marginal and cost constraints, and (iii) a non‐linear regression model with simultaneous direct and cost constraints. As we show, the proposed method generates similar or better results compared with algorithms specialized for computing optimal designs under less general constraints. Copyright © 2015 John Wiley & Sons, Ltd.     

An alternating direction method for linear‐constrained matrix nuclear norm minimization

The aim of the nuclear norm minimization problem is to find a matrix that minimizes the sum of its singular values and satisfies some constraints simultaneously. Such a problem has received more attention largely because it is closely related to the affine rank minimization problem, which appears in many control applications including controller design, realization theory, and model reduction. In this paper, we first propose an exact version alternating direction method for solving the nuclear norm minimization problem with linear equality constraints. At each iteration, the method involves a singular value thresholding and linear matrix equations which are solved exactly. Convergence of the proposed algorithm is followed directly. To broaden the capacity of solving larger problems, we solve approximately the subproblem by an iterative method with the Barzilai–Borwein steplength. Some extensions to the noisy problems and nuclear norm regularized least‐square problems are also discussed. Numerical experiments and comparisons with the state‐of‐the‐art method FPCA show that the proposed method is effective and promising. Copyright © 2011 John Wiley & Sons, Ltd.     

Dynamical models of molecular chains and efficient integration algorithms

Chains of point masses and chains of rigid bodies are used to model biological polymers. To investigate their dynamics we propose a method which allows an efficient realization of the constraints jointly with a simple and accurate integration of the free rigid body motion. The method is quite effective to evolute the geodesic flow of a rigid body chain and the global performance depends on the computational complexity of the algorithms used to compute the interaction forces. Our approach is suitable to describe a chain of rigid bodies immersed in a thermal bath. In the method we propose, the constraints are realized by hard springs whose elastic constant is set to maximize the energy dissipation rate of a Runge–Kutta integrator scheme. Moreover the use of local Lagrangian coordinates is introduced using the possibility of a continuous change of chart, such that the distance from the coordinate singularities is the highest possible. For a chain of point masses the numerical results are checked with another method where the constraints are exactly realized by means of Lagrangian coordinates. When the chain is subject to regular interactions potentials plus a thermal bath the exact and approximate constraints realization provide comparable results.     

Flight control system synthesis using eigenstructure assignment

The central topic of this paper is the establishment of an efficient practical synthesis procedure for modern flight control systems. Unlike the classical design methodology (Bode plots, Nichols plot, etc.) and optimal control techniques, the present approach provides the designer a direct approach for the synthesis of desired control laws. Although the setting is the now familiar state space, the actual design is performed relative to classical specifications (i.e., modes and mode distribution) by placing closed-loop eigenvalues and eigenvectors at some desired locations (regions) within the state space. The new method can handle output feedback configurations, subject to controller structural constraints. Complete theoretical background and a realistic numerical example are provided.     

Measuring Lineup Difficulty By Matching Distance Metrics With Subject Choices in Crowd-Sourced Data

Graphics play a crucial role in statistical analysis and data mining. Being able to quantify structure in data that is visible in plots, and how people read the structure from plots is an ongoing challenge. The lineup protocol provides a formal framework for data plots, making inference possible. The data plot is treated like a test statistic, and lineup protocol acts like a comparison with the sampling distribution of the nulls. This article describes metrics for describing structure in data plots and evaluates them in relation to the choices that human readers made during several large Amazon Turk studies using lineups. The metrics that were more specific to the plot types tended to better match subject choices, than generic metrics. The process that we followed to evaluate metrics will be useful for general development of numerically measuring structure in plots, and also in future experiments on lineups for choosing blocks of pictures. Supplementary materials for this article are available online.     

Penalized sample average approximation methods for stochastic programs in economic and secure dispatch of a power system

In this paper, we develop a stochastic programming model for economic dispatch of a power system with operational reliability and risk control constraints. By defining a severity-index function, we propose to use conditional value-at-risk (CVaR) for measuring the reliability and risk control of the system. The economic dispatch is subsequently formulated as a stochastic program with CVaR constraint. To solve the stochastic optimization model, we propose a penalized sample average approximation (SAA) scheme which incorporates specific features of smoothing technique and level function method. Under some moderate conditions, we demonstrate that with probability approaching to 1 at an exponential rate with the increase of sample size, the optimal solution of the smoothing SAA problem converges to its true counterpart. Numerical tests have been carried out for a standard IEEE-30 DC power system.     

Stochastic Programming with Multivariate Second Order Stochastic Dominance Constraints with Applications in Portfolio Optimization

In this paper we study optimization problems with multivariate stochastic dominance constraints where the underlying functions are not necessarily linear. These problems are important in multicriterion decision making, since each component of vectors can be interpreted as the uncertain outcome of a given criterion. We propose a penalization scheme for the multivariate second order stochastic dominance constraints. We solve the penalized problem by the level function methods, and a modified cutting plane method and compare them to the cutting surface method proposed in the literature. The proposed numerical schemes are applied to a generic budget allocation problem and a real world portfolio optimization problem.     

Managing the spread of alfalfa stem nematodes (Ditylenchus dipsaci): The relationship between crop rotation periods and pest reemergence

Alfalfa is a critical cash/rotation crop in the western region of the United States, where it is common to find crops affected by the alfalfa stem nematode (ASN) (Ditylenchus dipsaci). Understanding the spread dynamics associated with this pest would allow growers to design better management programs and farming practices. This understanding is of particular importance given that there are no nematicides available against ASNs and control strategies largely rely on crop rotation to nonhost crops or by planting resistant varieties of alfalfa. In this paper, we present a basic host‐parasite model that describes the spread of the ASN on alfalfa crops. With this discrete time model, we are able to portray a relationship between the length of crop rotation periods and the time at which the density of nematode‐infested plants becomes larger than that of nematode‐free ones in the postrotation alfalfa. The numerical results obtained are consistent with farming practice observations, suggesting that the model could play a role in the evaluation of management strategies.     

New lower bounds for the three-dimensional finite bin packing problem

The three-dimensional finite bin packing problem (3BP) consists of determining the minimum number of large identical three-dimensional rectangular boxes, bins, that are required for allocating without overlapping a given set of three-dimensional rectangular items. The items are allocated into a bin with their edges always parallel or orthogonal to the bin edges. The problem is strongly NP-hard and finds many practical applications. We propose new lower bounds for the problem where the items have a fixed orientation and then we extend these bounds to the more general problem where for each item the subset of rotations by 90° allowed is specified. The proposed lower bounds have been evaluated on different test problems derived from the literature. Computational results show the effectiveness of the new lower bounds.     

Membrane triangles with corner drilling freedoms—I. The EFF element

This paper is the first of a three-part series that studies the formulation of 3-node, 9-dof membrane elements with normal-to-element-plane rotations (the so-called drilling freedoms) within the context of parametrized variational principles. These principles supply a unified basis for several advanced element-construction techniques; in particular: the free formulation (FF), the extended free formulation (EFF) and the assumed natural deviatoric strain (ANDES) formulation. In Part I we construct an element of this type using the EFF. This derivation illustrates the basic steps in the application of that formulation to the construction of high-performance, rank-sufficient, nonconforming elements with corner rotations. The element is initially given the twelve degress of freedom of the linear strain triangle (LST), which allows the displacement expansion to be a complete quadratic in each component. The expansion basis contains the six linear basic functions and six energy-orthogonal quadratic higher-order functions. Three degrees of freedom, defined as the midpoint deviations from linearity along the triangle-median directions, are eliminated by kinematic constraints. The remaining hierarchical midpoint freedoms are transformed to corner rotations. The performance of the resulting element is evaluated in Part III.     

带组约束可靠性网络最优化问题的精确算法

本文提出了一种求解带组约束串-并网络系统最优冗余问题的精确算法.该算法利用拉格朗日松驰和Dantzig-Wolfe分解法得到问题的上界,并结合动态规划求解子问题.算法采用一种有效的切割和剖分方法,以逐步缩小对偶间隙和保证收敛性.数值结果表明该算法对于求解带组约束可靠性最优化问题是很有效的.