Particle swarm and simulated annealing for multi-local optimization

Particle swarm and simulated annealing optimization algorithms proved to be valid in finding a global optimum in the bound constrained optimization context. However, their original versions can only detect one global optimum even if the problem has more than one solution. In this paper we propose modifications to both algorithms. In the particle swarm optimization algorithm we introduce gradient information to enable the computation of all the global and local optima. The simulated annealing algorithm is combined with a stretching technique to be able to compute all global optima. The numerical experiments carried out with a set of well-known test problems illustrate the effectiveness of the proposed algorithms.Work partially supported by FCT grant POCTI/MAT/58957/ 2004 and by the Algoritmi research center

Solving nonlinear equations by a tabu search strategy

Solving systems of nonlinear equations is a problem of particular importance since they emerge through the mathematical modeling of real problems that arise naturally in many branches of engineering and in the physical sciences. The problem can be naturally reformulated as a global optimization problem. In this paper, we show that a metaheuristic, called Directed Tabu Search (DTS) [16], is able to converge to the solutions of a set of problems for which the fsolve function of MATLAB® failed to converge. We also show the effect of the dimension of the problem in the performance of the DTS.Fundação para a Ciência e a Tecnologia (FCT

Optimizing radial basis functions by D.C. programming and its use in direct search for global derivative-free optimization

In this paper we address the global optimization of functions subject to bound and linear constraints without using derivatives of the objective function. We investigate the use of derivative-free models based on radial basis functions (RBFs) in the search step of direct-search methods of directional type. We also study the application of algorithms based on difference of convex (d.c.) functions programming to solve the resulting subproblems which consist of the minimization of the RBF models subject to simple bounds on the variables. Extensive numerical results are reported with a test set of bound and linearly constrained problems

La gestion des groupes de variables en recherche directe

RÉSUMÉ La Recherche par Coordonnées (CS), la Recherche par Motifs Généralisée (GPS) et la Recherche Directe sur Treillis Adaptatif (MADS) sont des exemples d’algorithmes robustes en optimisation non lin´eaire et non lisse. Afin d’améliorer la solution courante, ces méthodes utilisent des directions d’exploration qui affectent soit une seule variable à la fois (CS), soit plusieurs variables à la fois (GPS et MADS). Nous nous proposons ici de formaliser et généraliser ces approches, à travers le concept de “groupes” de variables : chaque groupe, gérée par l’algorithme de manière ´evolutive, génère des points d’essai en ne modifiant que les variables le concernant. Cela permet la construction d’un voisinage particulier potentiellement fructueux : dans le cas de variables de positionnement par exemple, cela permet de d´eplacer des objets ou des collections d’objets de manière individuelle. On utilise pour cette étude le logiciel NOMAD développé par Le Digabel (2009), qui est une implémentation écrite en C++ des tout derniers algorithmes de ce type, à savoir BIMADS et ORTHOMADS, respectivement introduits par Audet et al. (2008d) et Abramson et al. (2009b). Ces méthodes sont conçues pour l’optimisation de boîtes noires : les évaluations des fonctions relatives aux objectifs et contraintes sont le résultat d’un processus opaque, typiquement un code informatique. Par conséquent, ces fonctions peuvent ˆetre non lisses, non linéaires, non convexes ou discontinues, avec possiblement des domaines de d´efinition très fragmentés. Nous souhaitons également nous atteler à la résolution de problématiques concrètes liées à ce type d’optimisation : nous traiterons en particulier le cas d’un problème de localisation de balises à rayonnement gamma, sur des cartes en deux dimensions à domaines réalisables très fragmentés. Ce projet, mené en collaboration avec l’Institut de recherche d’HYDROQUE BEC (IREQ), vise à améliorer la pr´ecision de l’estimation du manteau neigeux et de l’équivalent Eau-Neige, afin de gérer les prévisions hydriques tout au long de l’année, et plus particulièrement aux moments critiques tels que la fonte des neiges printanière.----------Abstract Coordinate Search (CS), Generalized Pattern Search (GPS) and Mesh Adaptive Direct Search (MADS) are examples of robust algorithms for nonsmooth nonlinear optimization. To improve the current solution, these methods use exploratory directions that affect either a single variable at a time (CS), or several variables at once (GPS and MADS). We will formalize and generalize these approaches, through the concept of “groups” of variables : each group, managed by the algorithm dynamically, generates trial points by only changing the variables concerning them. This allows the construction of a particular and potentially fruitful neighborhood : for example, in the case of positioning variables, the algorithm can move objects or collections of objects sequentially. We use for this research the software NOMAD developed by Le Digabel (2009), which is an C++ implementation of the very latest MADS algorithms, namely BIMADS and ORTHOMADS, respectively introduced by Audet et al. (2008d) and Abramson et al. (2009b). These methods are designed for blackbox optimization : the evaluations of the objective and constraint functions are the result of an opaque process, typically a computer code. Therefore, these functions may be nonsmooth, non-linear, non-convex or discontinuous, with possibly highly fragmented domains. We aim to solve practical issues linked to this type of optimization : we will focus on the case of a gamma-monitoring beacons location problem, on two-dimensional maps with very fragmented domains. This project, in collaboration with the Research Institute of HYDRO-QUEBEC (IREQ), aims to improve the snowpack estimate accuracy in order to manage the hydrological forecast throughout the year, especially at critical times such as spring snowmelt

A Metaheuristic-Based Simulation Optimization Framework For Supply Chain Inventory Management Under Uncertainty

The need for inventory control models for practical real-world applications is growing with the global expansion of supply chains. The widely used traditional optimization procedures usually require an explicit mathematical model formulated based on some assumptions. The validity of such models and approaches for real world applications depend greatly upon whether the assumptions made match closely with the reality. The use of meta-heuristics, as opposed to a traditional method, does not require such assumptions and has allowed more realistic modeling of the inventory control system and its solution. In this dissertation, a metaheuristic-based simulation optimization framework is developed for supply chain inventory management under uncertainty. In the proposed framework, any effective metaheuristic can be employed to serve as the optimizer to intelligently search the solution space, using an appropriate simulation inventory model as the evaluation module. To be realistic and practical, the proposed framework supports inventory decision-making under supply-side and demand-side uncertainty in a supply chain. The supply-side uncertainty specifically considered includes quality imperfection. As far as demand-side uncertainty is concerned, the new framework does not make any assumption on demand distribution and can process any demand time series. This salient feature enables users to have the flexibility to evaluate data of practical relevance. In addition, other realistic factors, such as capacity constraints, limited shelf life of products and type-compatible substitutions are also considered and studied by the new framework. The proposed framework has been applied to single-vendor multi-buyer supply chains with the single vendor facing the direct impact of quality deviation and capacity constraint from its supplier and the buyers facing demand uncertainty. In addition, it has been extended to the supply chain inventory management of highly perishable products. Blood products with limited shelf life and ABO compatibility have been examined in detail. It is expected that the proposed framework can be easily adapted to different supply chain systems, including healthcare organizations. Computational results have shown that the proposed framework can effectively assess the impacts of different realistic factors on the performance of a supply chain from different angles, and to determine the optimal inventory policies accordingly

Sélection et réglage de paramètres pour l'optimisation de logiciels d'ordonnancement industriel

L’utilisation d’un logiciel d’ordonnancement industriel fait intervenir une multitude de paramètres dont le réglage influence fortement la qualité des résultats. A l’heure actuelle, ce réglage est effectué de façon manuelle, après un travail souvent fastidieux au cours de l’installation initiale du logiciel’ De plus, une fois spécifiées, les valeurs de ces paramètres sont rarement remises en cause par les utilisateurs, du fait de leur manque d’expérience et du nombre important de paramètres à ajuster. L’idée que nous développons ici consiste à utiliser des métaheuristiques pour automatiser cette tâche. Deux problèmes seront abordés : la sélection des paramètres pertinents et leur réglage en fonction des exigences de l’utilisateur. Nous proposons de résoudre ces deux problèmes de façon simultanée, en introduisant des stratégies de sélection au sein des métaheuristiques. Cette approche est appliquée au logiciel d’ordonnancement Ortems® et validée sur plusieurs cas industriels. ABSTRACT : The use of scheduling software requires to set-up a number of parameters that have a direct influence on the schedule quality. Nowadays, this set-up is obtained manually after an extensive effort during initial software installation. Moreover, this set-up is rarely called into question by users, due to their lack of experience and to the high number of parameters involved. It is suggested in this thesis the use of metaheuristics to automate this task. Two problems are considered: selection of relevant parameters and their tuning according to user requirements. We suggest here an approach to solve these problems simultaneously, based on the combination of metaheuristics with some parameter selection strategies. An implementation framework has been developed and tested on an industrial scheduler, named Ortems®. The first results of the use of this framework on real industrial databases are described and commented