Multiobjective optimization of viscoelastic laminated sandwich structures using the Direct MultiSearch method

A multiobjective approach for optimization of passive damping for vibration reduction in sandwich structures is presented in this paper. Constrained optimization is conducted for maximization of modal loss factors and minimization of weight of sandwich beams and plates with elastic laminated constraining layers and a viscoelastic core, with layer thickness and material and laminate layer ply orientation angles as design variables. The problem is solved using the Direct MultiSearch (DMS) solver for derivative-free multiobjective optimization and solutions are compared with alternative ones obtained using genetic algorithms.

Reply to: Comments on “Particle Swarm Optimization with Fractional-Order Velocity”

We agree with Ling-Yun et al. [5] and Zhang and Duan comments [2] about the typing error in equation (9) of the manuscript [8]. The correct formula was initially proposed in [6, 7]. The formula adopted in our algorithms discussed in our papers [1, 3, 4, 8] is, in fact, the following: ...

Constrained Consumption Shifting Management in the Distributed Energy Resources Scheduling Considering Demand Response

Demand response concept has been gaining increasing importance while the success of several recent implementations makes this resource benefits unquestionable. This happens in a power systems operation environment that also considers an intensive use of distributed generation. However, more adequate approaches and models are needed in order to address the small size consumers and producers aggregation, while taking into account these resources goals. The present paper focuses on the demand response programs and distributed generation resources management by a Virtual Power Player that optimally aims to minimize its operation costs taking the consumption shifting constraints into account. The impact of the consumption shifting in the distributed generation resources schedule is also considered. The methodology is applied to three scenarios based on 218 consumers and 4 types of distributed generation, in a time frame of 96 periods.

Testing Nelder-Mead Based Repulsion Algorithms for Multiple Roots of Nonlinear Systems via a Two-Level Factorial Design of Experiments

This paper addresses the challenging task of computing multiple roots of a system of nonlinear equations. A repulsion algorithm that invokes the Nelder-Mead (N-M) local search method and uses a penalty-type merit function based on the error function, known as 'erf', is presented. In the N-M algorithm context, different strategies are proposed to enhance the quality of the solutions and improve the overall efficiency. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm. The main goal of this paper is to use a two-level factorial design of experiments to analyze the statistical significance of the observed differences in selected performance criteria produced when testing different strategies in the N-M based repulsion algorithm.

A filter algorithm: comparison with NLP solvers

The purpose of this work is to present an algorithm to solve nonlinear constrained optimization problems, using the filter method with the inexact restoration (IR) approach. In the IR approach two independent phases are performed in each iteration—the feasibility and the optimality phases. The first one directs the iterative process into the feasible region, i.e. finds one point with less constraints violation. The optimality phase starts from this point and its goal is to optimize the objective function into the satisfied constraints space. To evaluate the solution approximations in each iteration a scheme based on the filter method is used in both phases of the algorithm. This method replaces the merit functions that are based on penalty schemes, avoiding the related difficulties such as the penalty parameter estimation and the non-differentiability of some of them. The filter method is implemented in the context of the line search globalization technique. A set of more than two hundred AMPL test problems is solved. The algorithm developed is compared with LOQO and NPSOL software packages.

Linear amplification with multiple nonlinear devices

Dissertação para obtenção do Grau de Mestre em Engenharia Electrotécnica e Computadores

Project scheduling and cost minimization with multiple availability constrained resources under stochastic conditions

The authors propose a mathematical model to minimize the project total cost where there are multiple resources constrained by maximum availability. They assume the resources as renewable and the activities can use any subset of resources requiring any quantity from a limited real interval. The stochastic nature is inferred by means of a stochastic work content defined per resource within an activity and following a known distribution and the total cost is the sum of the resource allocation cost with the tardiness cost or earliness bonus in case the project finishes after or before the due date, respectively. The model was computationally implemented relying upon an interchange of two global optimization metaheuristics – the electromagnetism-like mechanism and the evolutionary strategies. Two experiments were conducted testing the implementation to projects with single and multiple resources, and with or without maximum availability constraints. The set of collected results shows good behavior in general and provide a tool to further assist project manager decision making in the planning phase.

A musculoskeletal shoulder model based on pseudo-inverse and null-space optimization.

The goal of the present work was assess the feasibility of using a pseudo-inverse and null-space optimization approach in the modeling of the shoulder biomechanics. The method was applied to a simplified musculoskeletal shoulder model. The mechanical system consisted in the arm, and the external forces were the arm weight, 6 scapulo-humeral muscles and the reaction at the glenohumeral joint, which was considered as a spherical joint. The muscle wrapping was considered around the humeral head assumed spherical. The dynamical equations were solved in a Lagrangian approach. The mathematical redundancy of the mechanical system was solved in two steps: a pseudo-inverse optimization to minimize the square of the muscle stress and a null-space optimization to restrict the muscle force to physiological limits. Several movements were simulated. The mathematical and numerical aspects of the constrained redundancy problem were efficiently solved by the proposed method. The prediction of muscle moment arms was consistent with cadaveric measurements and the joint reaction force was consistent with in vivo measurements. This preliminary work demonstrated that the developed algorithm has a great potential for more complex musculoskeletal modeling of the shoulder joint. In particular it could be further applied to a non-spherical joint model, allowing for the natural translation of the humeral head in the glenoid fossa.

Fuzzy coding in constrained ordinations

Canonical correspondence analysis and redundancy analysis are two methods of constrained ordination regularly used in the analysis of ecological data when several response variables (for example, species abundances) are related linearly to several explanatory variables (for example, environmental variables, spatial positions of samples). In this report I demonstrate the advantages of the fuzzy coding of explanatory variables: first, nonlinear relationships can be diagnosed; second, more variance in the responses can be explained; and third, in the presence of categorical explanatory variables (for example, years, regions) the interpretation of the resulting triplot ordination is unified because all explanatory variables are measured at a categorical level.

Analyzing Carbon Trade Permits in Optimization Framework

The threats caused by global warming motivate different stake holders to deal with and control them. This Master's thesis focuses on analyzing carbon trade permits in optimization framework. The studied model determines optimal emission and uncertainty levels which minimize the total cost. Research questions are formulated and answered by using different optimization tools. The model is developed and calibrated by using available consistent data in the area of carbon emission technology and control. Data and some basic modeling assumptions were extracted from reports and existing literatures. The data collected from the countries in the Kyoto treaty are used to estimate the cost functions. Theory and methods of constrained optimization are briefly presented. A two-level optimization problem (individual and between the parties) is analyzed by using several optimization methods. The combined cost optimization between the parties leads into multivariate model and calls for advanced techniques. Lagrangian, Sequential Quadratic Programming and Differential Evolution (DE) algorithm are referred to. The role of inherent measurement uncertainty in the monitoring of emissions is discussed. We briefly investigate an approach where emission uncertainty would be described in stochastic framework. MATLAB software has been used to provide visualizations including the relationship between decision variables and objective function values. Interpretations in the context of carbon trading were briefly presented. Suggestions for future work are given in stochastic modeling, emission trading and coupled analysis of energy prices and carbon permits.

MCMC Analysis for Optimization of Stochastic Models

In any decision making under uncertainties, the goal is mostly to minimize the expected cost. The minimization of cost under uncertainties is usually done by optimization. For simple models, the optimization can easily be done using deterministic methods.However, many models practically contain some complex and varying parameters that can not easily be taken into account using usual deterministic methods of optimization. Thus, it is very important to look for other methods that can be used to get insight into such models. MCMC method is one of the practical methods that can be used for optimization of stochastic models under uncertainty. This method is based on simulation that provides a general methodology which can be applied in nonlinear and non-Gaussian state models. MCMC method is very important for practical applications because it is a uni ed estimation procedure which simultaneously estimates both parameters and state variables. MCMC computes the distribution of the state variables and parameters of the given data measurements. MCMC method is faster in terms of computing time when compared to other optimization methods. This thesis discusses the use of Markov chain Monte Carlo (MCMC) methods for optimization of Stochastic models under uncertainties .The thesis begins with a short discussion about Bayesian Inference, MCMC and Stochastic optimization methods. Then an example is given of how MCMC can be applied for maximizing production at a minimum cost in a chemical reaction process. It is observed that this method performs better in optimizing the given cost function with a very high certainty.

Simulation and optimization tools in paper machine concept design

The last decade has shown that the global paper industry needs new processes and products in order to reassert its position in the industry. As the paper markets in Western Europe and North America have stabilized, the competition has tightened. Along with the development of more cost-effective processes and products, new process design methods are also required to break the old molds and create new ideas. This thesis discusses the development of a process design methodology based on simulation and optimization methods. A bi-level optimization problem and a solution procedure for it are formulated and illustrated. Computational models and simulation are used to illustrate the phenomena inside a real process and mathematical optimization is exploited to find out the best process structures and control principles for the process. Dynamic process models are used inside the bi-level optimization problem, which is assumed to be dynamic and multiobjective due to the nature of papermaking processes. The numerical experiments show that the bi-level optimization approach is useful for different kinds of problems related to process design and optimization. Here, the design methodology is applied to a constrained process area of a papermaking line. However, the same methodology is applicable to all types of industrial processes, e.g., the design of biorefiners, because the methodology is totally generalized and can be easily modified.

Contact with friction using the augmented Lagrangian Method: a conditional constrained minimization problem

This work presents a formulation of the contact with friction between elastic bodies. This is a non linear problem due to unilateral constraints (inter-penetration of bodies) and friction. The solution of this problem can be found using optimization concepts, modelling the problem as a constrained minimization problem. The Finite Element Method is used to construct approximation spaces. The minimization problem has the total potential energy of the elastic bodies as the objective function, the non-inter-penetration conditions are represented by inequality constraints, and equality constraints are used to deal with the friction. Due to the presence of two friction conditions (stick and slip), specific equality constraints are present or not according to the current condition. Since the Coulomb friction condition depends on the normal and tangential contact stresses related to the constraints of the problem, it is devised a conditional dependent constrained minimization problem. An Augmented Lagrangian Method for constrained minimization is employed to solve this problem. This method, when applied to a contact problem, presents Lagrange Multipliers which have the physical meaning of contact forces. This fact allows to check the friction condition at each iteration. These concepts make possible to devise a computational scheme which lead to good numerical results.

Particle swarm optimization for two-connected networks with bounded rings

The Two-Connected Network with Bounded Ring (2CNBR) problem is a network design problem addressing the connection of servers to create a survivable network with limited redirections in the event of failures. Particle Swarm Optimization (PSO) is a stochastic population-based optimization technique modeled on the social behaviour of flocking birds or schooling fish. This thesis applies PSO to the 2CNBR problem. As PSO is originally designed to handle a continuous solution space, modification of the algorithm was necessary in order to adapt it for such a highly constrained discrete combinatorial optimization problem. Presented are an indirect transcription scheme for applying PSO to such discrete optimization problems and an oscillating mechanism for averting stagnation.

Staffing Optimization with Chance Constraints in Call Centers

Les centres d’appels sont des éléments clés de presque n’importe quelle grande organisation. Le problème de gestion du travail a reçu beaucoup d’attention dans la littérature. Une formulation typique se base sur des mesures de performance sur un horizon infini, et le problème d’affectation d’agents est habituellement résolu en combinant des méthodes d’optimisation et de simulation. Dans cette thèse, nous considérons un problème d’affection d’agents pour des centres d’appels soumis a des contraintes en probabilité. Nous introduisons une formulation qui exige que les contraintes de qualité de service (QoS) soient satisfaites avec une forte probabilité, et définissons une approximation de ce problème par moyenne échantillonnale dans un cadre de compétences multiples. Nous établissons la convergence de la solution du problème approximatif vers celle du problème initial quand la taille de l’échantillon croit. Pour le cas particulier où tous les agents ont toutes les compétences (un seul groupe d’agents), nous concevons trois méthodes d’optimisation basées sur la simulation pour le problème de moyenne échantillonnale. Étant donné un niveau initial de personnel, nous augmentons le nombre d’agents pour les périodes où les contraintes sont violées, et nous diminuons le nombre d’agents pour les périodes telles que les contraintes soient toujours satisfaites après cette réduction. Des expériences numériques sont menées sur plusieurs modèles de centre d’appels à faible occupation, au cours desquelles les algorithmes donnent de bonnes solutions, i.e. la plupart des contraintes en probabilité sont satisfaites, et nous ne pouvons pas réduire le personnel dans une période donnée sont introduire de violation de contraintes. Un avantage de ces algorithmes, par rapport à d’autres méthodes, est la facilité d’implémentation.