Generating alphaalpha -dense curves in non-convex sets to solve a class of non-smooth constrained global optimization

This paper deals with the dimensionality reduction approach to study multi-dimensional constrained global optimization problems where the objective function is non-differentiable over a general compact set $D$ of $mathbb{R}^{n}$ and H"{o}lderian. The fundamental principle is to provide explicitly a parametric representation $x_{i}=ell _{i}(t),1leq ileq n$ of $alpha$-dense curve $ell_{alpha }$ in the compact $D$, for $t$ in an interval $mathbb{I}$ of $mathbb{R}$, which allows to convert the initial problem to a one dimensional H"{o}lder unconstrained one. Thus, we can solve the problem by using an efficient algorithm available in the case of functions depending on a single variable. A relation between the parameter $alpha$ of the curve $ell _{alpha }$ and the accuracy of attaining the optimal solution is given. Some concrete $alpha$ dense curves in a non-convex feasible region $D$ are constructed. The numerical results show that the proposed approach is efficient.</p

Estimation of Volatility and Correlation with Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models: An Application to Moroccan Stock Markets

Volatility and correlation are important metrics of risk evaluation for financial markets worldwide. The latter have shown that these tools are varying over time, thus, they require an appropriate estimation models to adequately capture their dynamics. Multivariate GARCH models were developed for this purpose and have known a great success. The purpose of this article is to examine the performance of Multivariate GARCH models to estimate variance covariance matrices in application to ten years of daily stock prices in Moroccan stock markets. The estimation is done through the most widely used Multivariate GARCH models, Dynamic Conditional Correlation (DCC) and Baba, Engle, Kraft and Kroner (BEKK) models. A comparison of estimated results is done using multiple statistical tests and with application to volatility forecast and Value at Risk calculation. The results show that BEKK model performs better than DCC in modeling variance covariance matrices and that both models failed to adequately estimate Value at Risk. Keywords: Volatility, Correlation, Multivariate GARCH, diagonal BEKK, DCC, stock markets, Morocco. JEL Classifications: C3, E44, G

Hybridations d'algorithmes métaheuristiques en optimisation globale et leurs applications

L optimisation des structures est un processus essentiel dans la conception des systèmes mécaniques et électroniques. Cette thèse s intéresse à la résolution des problèmes mono-objectifs et multi-objectifs des structures mécaniques et mécatroniques. En effet, les industriels ne sont pas seulement préoccupés à améliorer les performances mécaniques des pièces qu ils conçoivent, mais ils cherchent aussi à optimiser leurs poids, leurs tailles, ainsi que leurs coûts de production. Pour résoudre ce type de problème, nous avons fait appel à des métaheuristiques robustes qui nous permettent de minimiser le coût de production de la structure mécanique et de maximiser le cycle de vie de la structure. Alors que des méthodes inappropriées de l évolution sont plus difficiles à appliquer à des modèles mécaniques complexes en raison de temps calcul exponentiel. Il est connu que les algorithmes génétiques sont très efficaces pour les problèmes NP-difficiles, mais ils sont très lourds et trop gourmands quant au temps de calcul, d où l idée d hybridation de notre algorithme génétique par l algorithme d optimisation par essaim de particules (PSO) qui est plus rapide par rapport à l algorithme génétique (GA). Dans notre expérimentation, nous avons obtenu une amélioration de la fonction objectif et aussi une grande amélioration de la minimisation de temps de calcul. Cependant, notre hybridation est une idée originale, car elle est différente des travaux existants. Concernant l avantage de l hybridation, il s agit généralement de trois méthodes : l hybridation en série, l hybridation en parallèle et l hybridation par insertion. Nous avons opté pour l hybridation par insertion par ce qu elle est nouvelle et efficace. En effet, les algorithmes génétiques se composent de trois étapes principales : la sélection, le croisement et la mutation. Dans notre cas, nous remplaçons les opérateurs de mutation par l optimisation par essaim de particules. Le but de cette hybridation est de réduire le temps de calcul ainsi que l amélioration la solution optimale.This thesis focuses on solving single objective problems and multiobjective of mechanical and mechatronic structures. The optimization of structures is an essential process in the design of mechanical and electronic systems. Industry are not only concerned to improve the mechanical performance of the parts they design, but they also seek to optimize their weight, size and cost of production. In order to solve this problem we have used Meta heuristic algorithms robust, allowing us to minimize the cost of production of the mechanical structure and maximize the life cycle of the structure. While inappropriate methods of evolution are more difficult to apply to complex mechanical models because of exponential calculation time. It is known that genetic algorithms are very effective for NP-hard problems, but their disadvantage is the time consumption. As they are very heavy and too greedy in the sense of time, hence the idea of hybridization of our genetic algorithm optimization by particle swarm algorithm (PSO), which is faster compared to the genetic algorithm (GA). In our experience, it was noted that we have obtained an improvement of the objective function and also a great improvement for minimizing computation time. However, our hybridization is an original idea, because it is a different and new way of existing work, we explain the advantage of hybridization and are generally three methods : hybridization in series, parallel hybridization or hybridization by insertion. We opted for the insertion hybridization it is new and effective. Indeed, genetic algorithms are three main parts : the selection, crossover and mutation. In our case,we replace the operators of these mutations by particle swarm optimization. The purpose of this hybridization is to reduce the computation time and improve the optimum solution.ROUEN-INSA Madrillet (765752301) / SudocSudocFranceF

A hybrid non-dominated sorting genetic algorithm for a multi-objective demand-side management problem in a smart building

One of the most significant challenges facing optimization models for the demand-side management (DSM) is obtaining feasible solutions in a shorter time. In this paper, the DSM is formulated in a smart building as a linear constrained multi-objective optimization model to schedule both electrical and thermal loads over one day. Two objectives are considered, energy cost and discomfort caused by allowing flexibility of loads within an acceptable comfort range. To solve this problem, an integrative matheuristic is proposed by combining a multi-objective evolutionary algorithm as a master level with an exact solver as a slave level. To cope with the non-triviality of feasible solutions representation and NP-hardness of our optimization model, in this approach discrete decision variables are encoded as partial chromosomes and the continuous decision variables are determined optimally by an exact solver. This matheuristic is relevant for dealing with the constraints of our optimization model. To validate the performance of our approach, a number of simulations are performed and compared with the goal programming under various scenarios of cold and hot weather conditions. It turns out that our approach outperforms the goal programming with respect to some comparison metrics including the hypervolume difference, epsilon indicator, number of the Pareto solutions found, and computational time metrics

Gestion du risque climatique par l'utilisation des produits dérivés d'assurance

Cette thèse s intéresse à la gestion du risque climatique par l utilisation des produits dérivés climatiques. Les travaux réalisés dans le cadre de cette thèse sont une contribution aux aspects statistiques, économétriques et financiers de la modélisation et de l'évaluation des produits dérivés climatiques. Un intérêt particulier a été accordé au contexte marocain aussi bien au niveau du volet qualitatif que quantitatif. En plus des développements théoriques que nous avons apportés (tests statistiques pour vérifier l impact du climat sur l économie, amélioration d un modèle de prévision de la température moyenne quotidienne, confirmation du choix de la température moyenne, au lieu des températures extrêmes, comme sous-jacent pour les contrats basés sur la température, etc.), nous avons proposé des cas de gestion entre opérateurs économiques marocains exerçant des activités sensibles à l aléa climatique avec des profils de risque différents en leur apportant des solutions de couverture basées sur l utilisation de produits dérivés climatiques.This thesis focuses on the weather risk management by using weather derivatives. The work done in this thesis is a contribution to statistics, econometric and financial aspects of the modeling and the evaluation of weather derivatives. Particular attention was paid to the Moroccan context both in a qualitative point of view. In additionto theoretical developments that we have made (statistical tests to verify the impact of weather conditions on the economy, improvement of a model to forecast daily average temperatures, confirming the choice of the average temperature instead of extreme temperatures as the preferred under lying for contracts based on temperature, etc.), we also proposed case studies with Moroccan economic actors carrying out their weather sensitive activities and having different risk profiles and we provide them hedging solutions based on the use of weather derivatives.ROUEN-INSA Madrillet (765752301) / SudocSudocFranceF

Tornado: An Autonomous Chaotic Algorithm for Large Scale Global Optimization

In this paper we propose an autonomous chaotic optimization algorithm, called Tornado, for large scale global optimization problems. The algorithm introduces advanced symmetrization, levelling and fine search strategies for an efficient and effective exploration of the search space and exploitation of the best found solutions. To our knowledge, this is the first accurate and fast autonomous chaotic algorithm solving large scale optimization problems. A panel of various benchmark problems with different properties were used to assess the performance of the proposed chaotic algorithm. The obtained results has shown the scalability of the algorithm in contrast to chaotic optimization algorithms encountered in the literature. Moreover, in comparison with some state-of-the-art meta-heuristics (e.g. evolutionary algorithms, swarm intelligence), the computational results revealed that the proposed Tornado algorithm is an effective and efficient optimization algorithm

A new algorithm for approaching Nash equilibrium and Kalai Smoridinsky solution

International audienceIn the present paper, a new formulation of Nash games is proposed for solving general multi-objective optimization problems. The main idea of this approach is to split the optimization variables which allow us to determine numerically the strategies between two players. The first player minimizes his cost function using the variables of the first table P, the second player, using the second table Q. The original contribution of this work concerns the construction of the two tables of allocations that lead to a Nash equilibrium on the Pareto front. On the other hand, we search P and Q that lead to a solution which is both a Nash equilibrium and a Kalai Smorodinsky solution. For this, we proposed and tried out successfully two algorithms which calculate P, Q and their associated Nash equilibrium, by using some extension of Normal Boundary Intersection approach (NBI)

Multi-agent modeling and simulation of a stock market

The stock market represents complex systems where multiple agents interact. The complexity of the environment in the financial markets in general has encouraged the use of modeling by multi-agent platforms and particularly in the case of the stock market.In this paper, an agent-based simulation model is proposed to study the behavior of the volume of market transactions. The model is based on the case of a single asset and three types of investor agents. Each investor can be a zero intelligent trader, fundamentalist trader or traders using historical information in the decision making process. The goal of the study is to simulate the behavior of a stock market according to the different considered endogenous and exogenous variables

An Immune Multiobjective Optimization with Backtracking Search Algorithm Inspired Recombination

We propose a novel hybrid multiobjective (MO) immune algorithm for tackling continuous MO problems. Similarly to the nondominated neighbor immune algorithm (NNIA), it considers the characteristics of OM problems: based on the fitness values, the best individuals from the test population are selected and recombined to guide the rest of the individuals in the population to the Pareto front. But NNIA uses the simulated binary crossover (SBX), which uses the local search method. In our algorithm, the recombination is essentially inspired by the cross used in the backtracking search algorithm (BSA), but the adaptations are found in the immune algorithm. Thus, three variants are designed in this chapter, resulting in new recombination operators. They are evaluated through 10 benchmark tests. For the most advanced proposed variant, which is designed to have global search ability, results show that an improved convergence and a better diversity of the Pareto front are statistically achieved when compared with a basic immune algorithm having no recombination or to NNIA. Finally, the proposed new algorithm is demonstrated to be successful in approximating the Pareto front of the complex 10 bar truss structure MO problem

A new algorithm for approaching Nash equilibrium and Kalai Smoridinsky solution

In the present paper, a new formulation of Nash games is proposed for solving general multi-objective optimization problems. The main idea of this approach is to split the optimization variables which allow us to determine numerically the strategies between two players. The first player minimizes his cost function using the variables of the first table P, the second player, using the second table Q. The original contribution of this work concerns the construction of the two tables of allocations that lead to a Nash equilibrium on the Pareto front. On the other hand, we search P and Q that lead to a solution which is both a Nash equilibrium and a Kalai Smorodinsky solution. For this, we proposed and tried out successfully two algorithms which calculate P, Q and their associated Nash equilibrium, by using some extension of Normal Boundary Intersection approach (NBI)