Global Optimization Algorithms in Multidisciplinary DesignOptimization

While Multidisciplinay Design Optimization (MDO) literature focuses mainly on the development of different formulations, through the manipulation of design variables, less attention is generally devoted to the combination of specific MDO formulations with existing nonlinear optimization algorithms. In this paper, the focus is on the application of a Global Optimization (GO) algorithm to an MDO problem. We first introduce and describe some MDO approaches from the literature. Then, we consider our MDO formulation where we deal with the GO box-constrained problem min_{a R We assume that the solution of the latter problem requires the use of a derivative-free methods since the derivatives of f(x) are unavailable and/or the function must be treated as a `black-box'. Within this framework we study some globally convergent modifications of the evolutionary Particle Swarm Optimization (PSO) algorithm, suitably adapted for box-constrained optimization. Finally, we report our numerical experience. Preliminary results are provided for a simple hydroelastic problem. Two different numerical tools are involved: a fluid dynamic solver, to simulate the ow around hydrofoils traveling in proximity of the air-water interface, and a simplified torsion-flexional wing model

Globally convergent hybridization of particle swarm optimization using line search-based derivative-free techniques

The hybrid use of exact and heuristic derivative-free methods for global unconstrained optimization problems is presented. Many real-world problems are modeled by computationally expensive functions, such as problems in simulationbased design of complex engineering systems. Objective-function values are often provided by systems of partial differential equations, solved by computationally expensive black-box tools. The objective-function is likely noisy and its derivatives are not provided. On the one hand, the use of exact optimization methods might be computationally too expensive, especially if asymptotic convergence properties are sought. On the other hand, heuristic methods do not guarantee the stationarity of their final solutions. Nevertheless, heuristic methods are usually able to provide an approximate solution at a reasonable computational cost, and have been widely applied to real-world simulation-based design optimization problems. Herein, an overall hybrid algorithm combining the appealing properties of both exact and heuristic methods is discussed, with focus on Particle Swarm Optimization (PSO) and line search-based derivative-free algorithms. The theoretical properties of the hybrid algorithm are detailed, in terms of limit points stationarity. Numerical results are presented for a test function and for two real-world optimization problems in ship hydrodynamics.The hybrid use of exact and heuristic derivative-free methods for global unconstrained optimization problems is presented. Many real-world problems are modeled by computationally expensive functions, such as problems in simulationbased design of complex engineering systems. Objective-function values are often provided by systems of partial differential equations, solved by computationally expensive black-box tools. The objective-function is likely noisy and its derivatives are often not available. On the one hand, the use of exact optimization methods might be computationally too expensive, especially if asymptotic convergence properties are sought. On the other hand, heuristic methods do not guarantee the stationarity of their final solutions. Nevertheless, heuristic methods are usually able to provide an approximate solution at a reasonable computational cost, and have been widely applied to real-world simulation-based design optimization problems. Herein, an overall hybrid algorithm combining the appealing properties of both exact and heuristic methods is discussed, with focus on Particle Swarm Optimization (PSO) and line search-based derivative-free algorithms. The theoretical properties of the hybrid algorithm are detailed, in terms of limit points stationarity. Numerical results are presented for a specific test function and for two real-world optimization problems in ship hydrodynamics

Assessing written work by determining competence to achieve the module-specific learning outcomes.

This chapter describes lasers and other sources of coherent light that operate in a wide wavelength range. First, the general principles for the generation of coherent continuous-wave and pulsed radiation are treated including the interaction of radiation with matter, the properties of optical resonators and their modes as well as such processes as Q-switching and mode-locking. The general introduction is followed by sections on numerous types of lasers, the emphasis being on todayʼs most important sources of coherent light, in particular on solid-state lasers and several types of gas lasers. An important part of the chapter is devoted to the generation of coherent radiation by nonlinear processes with optical parametric oscillators, difference- and sum-frequency generation, and high-order harmonics. Radiation in the extended ultraviolet (EUV) and x-ray ranges can be generated by free electron lasers (FEL) and advanced x-ray sources. Ultrahigh light intensities up to 1021 W/cm2 open the door to studies of relativistic laser–matter interaction and laser particle acceleration. The chapter closes with a section on laser stabilization