Analysis of the maximum level policy in a production-distribution system

We consider a production-distribution system, where a facility produces one commodity which is distributed to a set of retailers by a fleet of vehicles. Each retailer defines a maximum level of the inventory. The production policy, the retailers replenishment policies and the transportation policy have to be determined so as to minimize the total system cost. The overall cost is composed by fixed and variable production costs at the facility, inventory costs at both facility and retailers and routing costs. We study two different types of replenishment policies. The well-known order-up to level (OU) policy, where the quantity shipped to each retailer is such that the level of its inventory reaches the maximum level, and the maximum level (ML) policy, where the quantity shipped to each retailer is such that the inventory is not greater than the maximum level. We first show that when the transportation is outsourced, the problem with OU policy is NP-hard, whereas there exists a class of instances where the problem with ML policy can be solved in polynomial time. We also show the worst-case performance of the OU policy with respect to the more flexible ML policy. Then, we focus on the ML policy and the design of a hybrid heuristic. We also present an exact algorithm for the solution of the problem with one vehicle. Results of computational experiments carried out on small size instances show that the heuristic can produce high quality solutions in a very short amount of time. Results obtained on a large set of randomly generated problem instances are also shown, aimed at comparing the two policies.     

An algebraic characterization of the optimum of regularized kernel methods

The representer theorem for kernel methods states that the solution of the associated variational problem can be expressed as the linear combination of a finite number of kernel functions. However, for non-smooth loss functions, the analytic characterization of the coefficients poses nontrivial problems. Standard approaches resort to constrained optimization reformulations which, in general, lack a closed-form solution. Herein, by a proper change of variable, it is shown that, for any convex loss function, the coefficients satisfy a system of algebraic equations in a fixed-point form, which may be directly obtained from the primal formulation. The algebraic characterization is specialized to regression and classification methods and the fixed-point equations are explicitly characterized for many loss functions of practical interest. The consequences of the main result are then investigated along two directions. First, the existence of an unconstrained smooth reformulation of the original non-smooth problem is proven. Second, in the context of SURE (Stein’s Unbiased Risk Estimation), a general formula for the degrees of freedom of kernel regression methods is derived.     

Command governor for constrained switched systems with scheduled model transition dwell times

In this paper, a switched control architecture for constrained control systems is presented. The strategy is based on command governor ideas that are here specialized to ‘optimally’ schedule switching events on the plant dynamics for improving control performance at the expense of low computational burdens. The significance of the method mainly lies in its capability to avoid constraints violation and loss of stability regardless of any configuration change occurrence in the plant/constraint structure. To this end, the concept of model transition dwell time is used within the proposed control framework to formally define the minimum time necessary to enable a switching event under guaranteed conditions on the overall stability and constraint fulfilment. Simulation results on a simple linear system and on a Cessna 182 aircraft model show the effectiveness of the proposed strategy. Copyright © 2017 John Wiley & Sons, Ltd.     

Comparison of three SeaWiFS atmospheric correction algorithms for turbid waters using AERONET-OC measurements

The use of satellites to monitor the color of the ocean requires effective removal of the atmospheric signal. This can be performed by extrapolating the aerosol optical properties in the visible from the near-infrared (NIR) spectral region assuming that the seawater is totally absorbant in this latter part of the spectrum. However, the non-negligible water-leaving radiance in the NIR which is characteristic of turbid waters may lead to an overestimate of the atmospheric radiance in the whole visible spectrum with increasing severity at shorter wavelengths. This may result in significant errors, if not complete failure, of various algorithms for the retrieval of chlorophyll-a concentration, inherent optical properties and biogeochemical parameters of surface waters.This paper presents results of an inter-comparison study of three methods that compensate for NIR water-leaving radiances and that are based on very different hypothesis: 1) the standard SeaWiFS algorithm (Stumpf et al., 2003; Bailey et al., 2010) based on a bio-optical model and an iterative process; 2) the algorithm developed by Ruddick et al. (2000) based on the spatial homogeneity of the NIR ratios of the aerosol and water-leaving radiances; and 3) the algorithm of Kuchinke et al. (2009) based on a fully coupled atmosphere-ocean spectral optimization inversion. They are compared using normalized water-leaving radiance nL_w in the visible. The reference source for comparison is ground-based measurements from three AERONET-Ocean Color sites, one in the Adriatic Sea and two in the East Coast of USA.Based on the matchup exercise, the best overall estimates of the nL_w are obtained with the latest SeaWiFS standard algorithm version with relative error varying from 14.97% to 35.27% for λ = 490 nm and λ = 670 nm respectively. The least accurate estimates are given by the algorithm of Ruddick, the relative errors being between 16.36% and 42.92% for λ = 490 nm and λ = 412 nm, respectively. The algorithm of Kuchinke appears to be the most accurate algorithm at 412 nm (30.02%), 510 (15.54%) and 670 nm (32.32%) using its default optimization and bio-optical model coefficient settings.Similar conclusions are obtained for the aerosol optical properties (aerosol optical thickness τ(865) and the Ångström exponent, α(510, 865)). Those parameters are retrieved more accurately with the SeaWiFS standard algorithm (relative error of 33% and 54.15% for τ(865) and α(510, 865)).A detailed analysis of the hypotheses of the methods is given for explaining the differences between the algorithms. The determination of the aerosol parameters is critical for the algorithm of Ruddick et al. (2000) while the bio-optical model is critical for the algorithm of Stumpf et al. (2003) utilized in the standard SeaWiFS atmospheric correction and both aerosol and bio-optical model for the coupled atmospheric-ocean algorithm of Kuchinke. The Kuchinke algorithm presents model aerosol-size distributions that differ from real aerosol-size distribution pertaining to the measurements. In conclusion, the results show that for the given atmospheric and oceanic conditions of this study, the SeaWiFS atmospheric correction algorithm is most appropriate for estimating the marine and aerosol parameters in the given turbid waters regions.     

Finite element analysis with uncertain probabilities

This paper presents a general method for the finite element analysis of linear mechanical systems by taking into account probability density functions whose parameters are affected by fuzziness. Within this framework, the standard perturbation-based stochastic finite element method is relaxed in order to incorporate uncertain probabilities in static, dynamic and modal analyses. General formulae are provided for assessing the (fuzzy) structural reliability and several typologies of optimization problems (reliability-based design, robust design, robust/reliability-based design) are formalized. In doing this the credibility theory is extensively used to extract qualified crisp data from the available set of fuzzy results, so that standard optimizers can be adopted to solve the most important design problems. It is shown that the proposed methodology is a general and versatile tool for finite element analyses because it is able to consider, both, probabilistic and non-probabilistic sources of uncertainties, such as randomness, vagueness, ambiguity and imprecision.     

Edge and line oriented contour detection: State of the art

We present an overview of various edge and line oriented approaches to contour detection that have been proposed in the last two decades. By edge and line oriented we mean methods that do not rely on segmentation. Distinction is made between edges and contours. Contour detectors are divided in local and global operators. The former are mainly based on differential analysis, statistical approaches, phase congruency, rank order filters, and combinations thereof. The latter include computation of contour saliency, perceptual grouping, relaxation labeling and active contours. Important aspects are covered, such as preprocessing aimed to suppress texture and noise, multiresolution techniques, connections between computational models and properties of the human visual system, and use of shape priors. An overview of procedures and metrics for quantitative performance evaluation is also presented. Our main conclusion is that contour detection has reached high degree of sophistication, taking into account multimodal contour definition (by luminance, color or texture changes), mechanisms for reducing the contour masking influence of noise and texture, perceptual grouping, multiscale aspects and high-level vision information.