A generalized stochastic goal programming model

In this paper we show how one can get stochastic solutions of Stochastic Multi-objective Problem (SMOP) using goal programming models. In literature it is well known that one can reduce a SMOP to deterministic equivalent problems and reduce the analysis of a stochastic problem to a collection of deterministic problems. The first sections of this paper will be devoted to the introduction of deterministic equivalent problems when the feasible set is a random set and we show how to solve them using goal programming technique. In the second part we try to go more in depth on notion of SMOP solution and we suppose that it has to be a random variable. We will present stochastic goal programming model for finding stochastic solutions of SMOP. Our approach requires more computational time than the one based on deterministic equivalent problems due to the fact that several optimization programs (which depend on the number of experiments to be run) needed to be solved. On the other hand, since in our approach we suppose that a SMOP solution is a random variable, according to the Central Limit Theorem the larger will be the sample size and the more precise will be the estimation of the statistical moments of a SMOP solution. The developed model will be illustrated through numerical examples.     

Image restoration and edge detection by topological asymptotic expansion

A new method for edge detection and image restoration is proposed. This method is based on topological gradient approach. Experimental results obtained on noisy images illustrate the capabilities of this promising method in image processing. To cite this article: L.J. Belaid et al., C. R. Acad. Sci. Paris, Ser. I 342 (2006).     

Financial portfolio management through the goal programming model: Current state-of-the-art

Since Markowitz (1952) formulated the portfolio selection problem, many researchers have developed models aggregating simultaneously several conflicting attributes such as: the return on investment, risk and liquidity. The portfolio manager generally seeks the best combination of stocks/assets that meets his/her investment objectives. The Goal Programming (GP) model is widely applied to finance and portfolio management. The aim of this paper is to present the different variants of the GP model that have been applied to the financial portfolio selection problem from the 1970s to nowadays.     

Numerical analysis for factorial data analysis. Part I: Numerical software — the package INDA for microcomputers

A large collection of factorial data analysis methods can be characterized by the following matrices: X , the k x n matrix of data, and A, B the symmetric positive definite matrices of size n, k which represent the chosen norms of ?ⁿ, ?^k, respectively. All methods amount to computing the largest eigenvalues of U = XAX^TB or the largest singular values of E = B^1/2XA^1/2 . In Part I of this paper we begin by a geometrical and probabilistic interpretation of the various methods, showing how U and E are defined in each case. We then define the computational kernel for factorial data analysis. We conclude by devising the numerical aspects of software implementation for this kernel on microcomputers and presenting the package INDA.     

Submaximal and door compactifications

In this paper, a characterization is given for compact door spaces. We, also, deal with spaces X such that a compactification K(X) of X is submaximal or door.Let X be a topological space and K(X) be a compactification of X.We prove, here, that K(X) is submaximal if and only if for each dense subset D of X, the following properties hold:

(i)

D is co-finite in K(X);

(ii)

for each x∈K(X)?D, {x} is closed.

If X is a noncompact space, then we show that K(X) is a door space if and only if X is a discrete space and K(X) is the one-point compactification of X.     

Surface characteristics analysis of nitrocarburized (Tenifer) and carbonitrided industrial steel AISI 02 types

Generally, tool steels for cold work are obtained by rolling and forging processes. They are treated to have a structure conferring to the material a high toughness limit in terms of wear resistance and endurance. The objective of this study is the thermochemical heat treatment of industrial steel blades made of AISI 02 types, intended for polymer crushing. The effects of nitrocarburizing (Tenifer) and gaseous carbonitriding processes on surface characteristics are considered. These surface treatments increase the usefulness of properties, that is, fatigue strength, wear and corrosion resistance of this microalloyed steel. The influence of treatment duration and the thickness of the layers on surface properties are investigated. The analysis and characterization are carried out using physical analysis [optical microscopy, scanning electron microscopy, X‐ray diffraction and glow discharge optical emission spectroscopy (GDOES) techniques] and mechanical measurements (microhardness, weight loss and residual stresses) of treated material. The results are intended to contribute in defining and optimizing the adequate choice of treatments for this type of steel in industrial conditions. Copyright © 2008 John Wiley & Sons, Ltd.     

Scheduling batches in flowshop with limited buffers in the shampoo industry

In this paper we address the problem of planning a temporary storage area in a real production system. This temporary storage area is composed of parallel temporary storage units with distinct capacities. The storage operation of a job, also called a batch, has to answer time restrictions such as release dates, due dates, restricted family dependent setup times and time lags, and also a space constraint which is the capacity of the temporary storage unit. The goal is to schedule the batches on the storage units in order to minimize the total setup times and the maximum lateness. First, we model the problem on a single storage unit as a two-machine flowshop problem with a limited buffer capacity and we show that it is NP-hard. We also show that the particular case in which no lateness is allowed is solvable in polynomial time under special conditions on the buffer capacity, both for single or parallel temporary storage units. Next we provide three heuristics: a greedy algorithm, a hybrid heuristic based on Ant Colony Optimization and Simulated Annealing and finally a dedicated heuristic. The latter strongly exploits the structural properties shown in this paper. We provide experimental results which highlight the efficiency of the dedicated heuristic in comparison with the two other heuristics.     

H-spectral spaces

Let X be a T₀-space, we say that X is H-spectral if its T₀-compactification is spectral. This paper deal with topological properties of H-spectral spaces. In the case of T₁-spaces the T₀-compactification coincides with the Wallman compactification. We give necessary and sufficient condition on the T₁-space X in order to get its Wallman compactification spectral.