Allocating fixed costs and common revenue via data envelopment analysis

An issue of considerable importance involves the allocation of fixed costs or common revenue among a set of competing entities in an equitable way. Based on the data envelopment analysis (DEA) theory, this paper proposes new methods for (i) allocating fixed costs to decision making units (DMUs) and (ii) distributing common revenue among DMUs, in such a way that the relative efficiencies of all DMUs remain unchanged and the allocations should reflect the relative efficiencies and the input-output scales of individual DMUs. To illustrate our methods, numerical results for an example are described in this paper.     

Determination of open boundary conditions for computational fluid dynamics (CFD) from interior observations

An optimization approach for the determination of open boundary conditions for Computational Fluid Dynamics is introduced, whereas the error between the solution σ and interior observations ω is minimized. The numerical weather prediction (NWP) model ALADIN–Austria provides data of wind speed and wind direction at virtual weather stations within the area of interest. Also, data from real weather stations and other sources can be incorporated into the model, respectively. In this work, the optimization method is applied to the constant density Navier–Stokes Equations. Thereby, for stabilizing the ill-posed pseudo inverse problem several regularization methods are reviewed. Further, numerical studies are carried out to identify the supreme regularization method for the presented application. Finally, the algorithm is applied to the micro- and meso-scale flow over the Grimming mountain, Austria. The results are compared with real weather station data and show suitable correlation with the measurements.     

Introducing a modified gradient vector method for optimization of accident prediction non-linear functions

In this paper, a new optimization method has been proposed for accident prediction non-linear models. This has been achieved by eliminating the Hessian matrix from the equation of optimal pace length in the gradient vector method. One advantage is that it is independent of the starting point in optimization processes and it provides convergence at the highest top as well. This method has been tested on an accident prediction model and its preference over the gradient vector method has been proven.     

一类偏积分-微分方程中的反问题

对一类偏积分-微分方程中参数校准的反问题进行研究.在弱解的框架下,原问题可转化为含具体正则化项的最优化问题.文中证明了该最优化问题的解的存在性和稳定性,并考察了最优解存在的一阶必要条件.另外,证明了当正则化参数足够大时,该最优化问题关于参数a的凸性性质.基于偏积分-微分方程反问题的研究对于金融市场中的模型校准问题具有重要的意义.     

The statistical overlap theory of chromatography using power law (fractal) statistics

The chromatographic dimensionality was recently proposed as a measure of retention time spacing based on a power law (fractal) distribution. Using this model, a statistical overlap theory (SOT) for chromatographic peaks is developed that estimates the number of peak maxima as a function of the chromatographic dimension, saturation and scale. Power law models exhibit a threshold region whereby below a critical saturation value no loss of peak maxima due to peak fusion occurs as saturation increases. At moderate saturation, behavior is similar to the random (Poisson) peak model. At still higher saturation, the power law model shows loss of peaks nearly independent of the scale and dimension of the model. The physicochemical meaning of the power law scale parameter is discussed and shown to be equal to the Boltzmann-weighted free energy of transfer over the scale limits. The scale is discussed. Small scale range (small β) is shown to generate more uniform chromatograms. Large scale range chromatograms (large β) are shown to give occasional large excursions of retention times; this is a property of power laws where "wild" behavior is noted to occasionally occur. Both cases are shown to be useful depending on the chromatographic saturation. A scale-invariant model of the SOT shows very simple relationships between the fraction of peak maxima and the saturation, peak width and number of theoretical plates. These equations provide much insight into separations which follow power law statistics.     

Optimization of preparative chromatographic separation of multiple rare earth elements

This work presents a method to optimize multi-product chromatographic systems with multiple objective functions. The system studied is a neodymium, samarium, europium, gadolinium mixture separated in an ion exchange chromatography step. A homogeneous Langmuir Mobile Phase Modified model is calibrated to fit the experiments, and then used to perform the optimization task. For the optimization a multi-objective Differential Evolution algorithm was used, with weighting based on relative value of the components to find optimal operation points along the Pareto front. The objectives of the Pareto front are weighted productivity and weighted yield with purity as an equality constraint. A prioritizing scheme based on relative values is applied for determining the pooling order. A simple rule of thumb for pooling strategy selection is presented. The multi-objective optimization gives a Pareto front which shows the rule of thumb, as a gap in one of the objective functions.     

Optimization of the collocation inversion method for the linear viscoelastic homogenization

The effective behaviour of linear viscoelastic heterogeneous material can be derived from the correspondence principle and the inversion of the obtained symbolic homogenized behavior. Various numerical methods were proposed to carry out this inversion. The collocation method, widely used, within this framework rests on a discretization of the characteristic spectrum in a sum of discrete lines for which it is necessary to determine the intensities and the positions by the minimization of the difference between the exact temporal function and its approximation. The classical method is based on a priori choice of the lines positions and on the optimization of their intensities. It is shown here that the combined optimization of the positions and the (positive) intensities lead to a minimization problem under constraints. In the simple case of an incompressible isotropic two-phase material, the assessment of the effective relaxation function with a continuum spectra or made up of discrete lines proves that the proposed method improves the predictions of the classical approach.     

基于层次分析法的隧道综合地质预报优化

隧道综合地质预报是解决隧道施工期地质问题、降低施工风险的一项重要技术手段。鉴于目前综合预报多为简单的数量上的综合,为更加有效地利用综合预报技术,首先归纳地质分析辨识常见不良地质体的方法,通过地质分析法初步判定隧道掌子面前方可能存在的地质异常,并结合层次分析法的基本思路,将影响预报手段的指标量化,即赋予预报方法权重,建立二级综合评价指标体系,研究不同预报方法对特定工程地质条件的适用性,以选择几种最优预报方法。主要研究结论如下:利用地质分析法定性、层次分析法定量的方法优选预报手段,减少了综合超前地质预报中物探手段选择的随意性,并据此建立综合预报体系。最后将该体系应用于紫荆山隧道F2断层的预报中,成功预报了ZK221+960处地下暗河,避免了施工事故的发生,取得了一定的经济效益,证明了通过层次分析法来优化综合预报方法的可行性。     

A self-optimizing inverse analysis method for estimation of cyclic elasto-plasticity model parameters

In this paper, a novel inverse analysis methodology call a Self-Optimizing Inverse Method (Self-OPTIM) has been presented, which inversely estimates cyclic elasto-plastic constitutive model parameters using global forces and displacement on the same partial boundaries and full-(or partial-) field displacement data. A novelty of the methodology is that it automatically self-estimates material parameters by updating “full-field” reference stresses and strains through two parallel nonlinear finite element simulations. Although a well-known classical cyclic plasticity model is chosen in this paper, it must be emphasized that the proposed Self-OPTIM method is a model-independent method, which means that any advanced model can be naturally integrated with the proposed methodology. Thus, using numerically generated test data of low-carbon steel specimens (AISI 1010), the proposed Self-OPTIM method has been verified showing its successful performance to estimate nonlinear isotropic and kinematic hardening parameters, yield stress, Young’s modulus and Poisson ratio. The effects of experimental noises from CCD camera and measurement errors of the boundary forces are also investigated for the Self-OPTIM method.     

Optimization of control setting and size of shunt capacitors on distribution feeders

Loads on electric utility systems have two components: active power (measured in kilowatts) and reactive power (measured in kilovars). Active power has to be generated at the power plant, whereas reactive power can be provided by either power plants or capacitors. It is a well-known fact that shunt power capacitors are the most economical source to meet the reactive power requirements of inductive loads and transmission lines operating at a lagging power factor.This paper describes new contributions to the problem of optimization of size and control setting of shunt capacitors on distribution feeders, so that the losses along the feeder are minimized. The variation of the KVAR of the load on the feeder with the distance from the substation is assumed to be linear. The parameters of this function are estimated from the available KVAR loading on the feeder first by using least-square techniques and then by using least-absolute-value parameter estimation techniques. The results obtained are compared with that obtained if the current profile is assumed to be uniformly distributed on the feeder. Our results show that the optimum size of the capacitor bank as well as its optimum location depend on the parameters of the model used for the load. Also, our results show a large saving in the size of the capacitor banks used with a considerable per-unit-loss reduction along the feeder.This work was supported by the National Science and Engineering Research Council of Canada, Grant No. A4146. The first author acknowledges the help received from Engineer Samy Soliman for reviewing all the mathematical expressions in this paper.