Méthode adaptée de programmation quadratique convexe: Théorie et applications

International audienceLe but de ce travail est d'implémenter une méthode adaptée de programmation quadratique convexe en variables bornées et d'effectuer ensuite des calculs numériques pour prouver son efficacité. Une étude comparative est ensuite menée où les résultats numériques de la méthode seront comparés avec ceux d'une méthode classique (Méthode d'Activation de Contraintes), en terme du nombre d'itérations et du temps d'exécution

An iterative method for finding the efficient frontier for a cardinality constrained portfolio assets selection

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Exact method for generating efficient solutions to constrained portfolio assets selection

International audienceThe problem of portfolio selection is one of the most popular areas in Finance. In this work, we will rely on the theory of Harry Markowitz, and the works of Ralph Steuer] for a quad-lin bi-objective mixed integer model. Next, we will propose an exact method for its resolution based on the conjugate gradient, and the cutting efficiency of Chergui et al. as well as new exploration strategy of problems generated in the branches. The proposed algorithm will also be applied to different cardinality constraint conditions, for different market indices

An exact method for multiple objective mixed-integer linear programming problem

International audienceIn this article, we present an exact method to find all efficient solutions of the multi-objective mixed-integer linear programming problem (MOMILP). Based on the branching process and by using an efficient cut to find at each iteration a new efficient solution (if it exists), the proposed algorithm is able to identify all the efficient solutions of the MOMILP problem in a finite number of iterations

Finding the Boundary Nodes of a Euclidean Graph: Algorithms and Applications

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An empirical study to find the optimal number of security in portfolio selection problem

International audiencePortfolio selection problem is one of the most important issues in finance. It had a lot of enthusiasm from the scientific community these last decades specially after the work of the father of modern portfolio theory Harry Markowitz. The aim of this work is to find the optimal number of securities in portfolio selection problem, to get the best efficient frontier. A statistical study is conducted on a different markets. We consider issues of selection of securities under cardinality constraints, as a mixed model bi-objective variable we will solve afterwards with an exact method. Experiments are performed with major market indices, such as the Hang Seng, DAX100, FTSE 100, S&P 100, Nikkei, S&P 500 and Nasdaq

Boundaries and Hulls of Euclidean Graphs: From Theory to Practice

International audienceBoundaries and Hulls of Euclidean Graphs: From Theory to Practice presents concepts and algorithms for finding convex, concave and polygon hulls of Euclidean graphs. It also includes some implementations, determining and comparing their complexities. Since the implementation is application-dependent, either centralized or distributed, some basic concepts of the centralized and distributed versions are reviewed. Theoreticians will find a presentation of different algorithms together with an evaluation of their complexity and their utilities, as well as their field of application. Practitioners will find some practical and real-world situations in which the presented algorithms can be used

Exact method for solving bi-objective cardinality constrained portfolio selection problem

International audienceIn finance, the portfolio optimization problem made a significant progress after Markowitz’s seminal who develop the modern portfolio theory, which stipulates that a portfolio selection problem consists of minimizing the risk represented by the variance and maximizing the ex- pected return. In this work, a bi-objective mixed integer quadratic model is presented, holding notice of real world constraints, which are the constraints on number of selected assets, called "cardinality constraints". For its resolution, we propose an exact method based on the steepest gradient and a new exploration strategy of problems generated at each step. The main idea of this method is to compute the maximum point by considering exclusively the return function obtained by solving a Mixed Integer Linear problem (MILP). Then, after adding a cut effe- ciency that takes into account the risk function, the augmented problem must be solved until finding the minimum of the risk function. This proposed method is validate using some major market indices, such as the Hang Seng, DAX100, FTSE 100, S&P 100, Nikkei, S&P 500 and Nasdaq and by using real data sets involving up to 2196 assets. The results show that this method finds Pareto optimal solutions in a reasonable time

Embedding decision-maker's preferences in the multi-objective Tabu search method for scheduling problems

International audienceThe integration of the decision maker's preferences in the optimization process of a multi-objective problem is a currently prominent research topic. In this work, we consider the scheduling problem of a flexible shop with multiple objectives, where the makespan, the total machining time and the maximum workload all have to be minimized. We assume that the decision maker can express multiple aspiration levels for each of the three objectives, as well as additional information that allows us to construct a preference model. This model corresponds to a SRMP (Simple Ranking using Multiple Profiles) model which we propose to integrate in a new Tabu search based approach. The SRMP model serves to order the neighboring solutions and thus help in implementing the descent phase, while the aspiration levels are also used to filter out neighboring solutions without needing to decode them beforehand. The proposal is compared to a state-of-the-art Tabu search algorithm on benchmark instances. Preliminary results show that our approach is quicker to find better solutions from the perspective of the decision maker

Integrating preferences within multiobjective flexible job shop scheduling

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