Preface of the “Symposium on numerical optimization and applications”

[Excerpt] Numerical Optimization and Applications Symposium emphasizes modeling, theory and study of numerical algorithms for optimization. Optimization is an important tool in decision science and in the analysis of physical systems. Furthermore the Optimization plays central role in a tremendous variety of application in the natural sciences, in the sectors of economy, finance, and industry operational research and in the engineering. Because of the wide and growing use of optimization, it is important to develop an understanding of optimization algorithms. Knowledge of the capabilities and limitations of these algorithms leads to a better understanding of their impact on various applications, and points the way to future research on improving and extending optimization algorithms and software. [...](undefined

Assessment of an hybrid multi-objective pattern search filter method

A hybrid multi-objective evolutionary algorithm (MOEA) for solving nonlinear multi-objective opti- mization problems that relies on a pattern search filter method is proposed. The aim is to reduce the computational time involved in solving expensive multi-objective problems by improving a subset of Pareto points. The proposed pattern search filter method relies on two components. Each entry in the filter aims to measure feasibility and optimality. The feasibility and optimality come directly from each single-objective nonlinear program problem that is associated to the multi-objective problem. Experi- ments carried out with a set of nonlinear multi-objective problems show that our pattern search filter approach is effective in reaching improved Pareto points. A comparison with other techniques known in the literature is presented.Fundação para a Ciência e a Tecnologia - Pluriannual Funding Program

Global vs. local nonlinear optimization techniques for human-like movement of an anthropomorphic robot

In this paper a comparison between using global and local optimization techniques for solving the problem of generating human-like arm and hand movements for an anthropomorphic dual arm robot is made. Although the objective function involved in each optimization problem is convex, there is no evidence that the admissible regions of these problems are convex sets. For the sequence of movements for which the numerical tests were done there were no significant differences between the optimal solutions obtained using the global and the local techniques. This suggests that the optimal solution obtained using the local solver is indeed a global solution

Generalized fractional maxwell model : parameter estimation of a viscoelastic material

In this paper, we show how fractional viscoelastic models can be efficient in the modeling of linear viscoelastic behavior, increasing the fitting accuracy of classic generalized viscoelastic models, such as the Generalized Maxwell model. Experimental data (Loss and Storage modulus in the frequency domain) were retrieved from a Dynamic Mechanical Analysis test considering Carbon Fibre Reinforced Polymer samples. The estimated parameters, for the derived fractional viscoelastic models, were obtained through numerical optimization techniques that minimize the difference between model-predicted values and experimental data. An excellent correlation between analytical and experimental results was observed, minimizing numerical instabilities found on a previous work, for the same experimental setup.This work was financed by FEDER funds through COMPETE-Programa Operacional Fatores de Competitividade and by portuguese funds through FCT-Fundação para a Ciência e a Tecnologia within projects PEst-C/MAT/UI0013/ 2011

Parameter estimation of viscoelastic materials : a test case with different optimization strategies

In this work, and based on numerical optimization techniques, constitutive parameters for viscoelastic materials are determined using a inverse problem formulation. The optimization methodology is based on experimental results obtained in the frequency domain, for a CFRP-Carbon Fibre Reinforced Polymer, through DMA-Dynamic Mechanical Analysis. The relaxation modulus of viscoelastic materials is given by a summation of decaying exponentiating functions, known as Prony series. Prony series, in time domain, are normally used to determine constitutive parameters for viscoelastic materials. In this paper, using the Fourier transform of the time domain Prony series, a nonlinear constrained least square problem based on Prony series representations of storage and loss modulus, for the considered material, is analyzed. A case study considering the estimation of 2N viscoelastic parameters, N = 1,2, ···11, is taken as a benchmark. The nonlinear constrained least square problems are solved using global and local optimization solvers. The computational results as well as the main conclusion are shown

A modified fractional zener model to describe the behaviour of a carbon fibre reinforced polymer

In this work a modified conventional Fractional Zener Model is deduced and applied to estimate the viscoelastic constitutive parameters of a Carbon Fibre Reinforced Polymer. The accuracy of this modified model was studied against conventional Fractional Zener model and Fractional Maxwell model, considering experimental data in the frequency domain. The set of parameters was found by solving a nonlinear constrained least square problem based on the variation of the storage and loss moduli with frequency.This work was financed by FEDER funds through COMPETE (Operational Programme Thematic Factors of Competitiveness) and by portuguese funds through FCT (Foundation for Science and Technology) within the project PEst-C/MAT/UI0013/ 2011

Practical implementation of an interior point nonmonotone line search filter method

Versão não definitiva do artigoHere we present a primal-dual interior point nonmonotone line search filter method for nonlinear programming. The filter relies on three measures, the feasibility, the centrality and the optimality presented in the optimality conditions, considers relaxed acceptability criteria for the step size and includes a feasibility restoration phase. The evaluation of the method is until now made on small problems and a comparison is provided with a merit function approach

Practical evaluation of an interior point three-D filter line search method using engineering design problems

We present a primal-dual interior point method for nonlinear optimization that relies on a line search filter strategy to allow convergence from poor starting points. The filter technique has already been adapted to interior point methods in different ways. Our filter relies on three components. Each entry in the filter includes the feasibility measure, the centrality measure and the barrier objective function value as the optimality measure. Numerical experiments carried out with a set of engineering design problems show that our filter approach is effective in reaching the solution. A comparison with other well-known methods is also reported

Incorporating a four-dimensional filter line search method into an interior point framework

Here we incorporate a four-dimensional filter line search method into an infeasible primal-dual interior point framework for nonlinear programming. Each entry in the filter has four components measuring dual feasibility, complementarity, primal feasibility and optimality. Three measures arise directly from the first order optimality conditions of the problem and the fourth is the objective function, so that convergence to a stationary point that is a minimizer is guaranteed. The primary assessment of the method has been done with a well-known collection of small problems

Nonlinear optimization for human-like movements of a high degree of freedom robotics arm-hand system

The design of autonomous robots, able to closely cooperate with human users in shared tasks, provides many new challenges for robotics research. Compared to industrial applications, robots working in human environments will need to have human-like abilities in their cognitive and motor behaviors. Here we present a model for generating trajectories of a high degree of freedom robotics arm-hand system that reflects optimality principles of human motor control. The process of finding a human-like trajectory among all possible solutions is formalized as a large-scale nonlinear optimization problem. We compare numerically three existing solvers, IPOPT, KNITRO and SNOPT, in terms of their real-time performance in different reach-to-grasp problems that are part of a human-robot interaction task. The results show that the SQP methods obtain better results than the IP methods. SNOPT finds optimal solutions for all tested problems in competitive computational times, thus being the one that best serves our purpose.Eliana Costa e Silva was supported by FCT (grant: SFRH/BD/23821/2005). The resources and equipment were financed by FCT and UM through project "Anthropomorphic robotic systems: control based on the processing principles of the human and other primates motor system and potential applications in service robotics and biomedical engineering" (Ref. CONC-REEQ/17/2001) and by EC through project "JAST: Joint-Action Science and Technology" (Ref. IST- 2-003747-IP).We thank the Mobile and Anthropomorphic Robotics Laboratory at University of Minho for constant good work environment. Finally, we would like to thank Carl Laird and Andreas Wachter for making available IPOPT, and AMPL for making available an unrestricted 30 days trial version of AMPL, KNITRO and SNOPT executables