Optimising the laser-welded butt-joints of medium carbon steel using RSM

The optimization capabilities in design-expert software were used to optimise the keyhole parameters (i.e. maximize penetration (P) and minimise the heat input, width of welded zone, (W) and width of heat affected zone (WHAZ)) in CW CO2 laser butt-welding of medium carbon steel. The previous developed mathematical models to predict the keyhole parameters in terms of the process factors namely; laser power (LP), welding speed (S) and focused position (F) were used to optimize the welding process. The goal was to set the process factors at optimum values to reach the desirable weld bead quality and to increase the production rate. Numerical and graphical optimization techniques were used. In fact, two optimization criteria were taken into account. In this investigation optimal solutions were found that would improve the weld quality, increase the productivity and minimize the total operation cost. In addition to that, superimposing the contours for the various response surfaces produced overlay plots

Benchmarking five global optimization approaches for nano-optical shape optimization and parameter reconstruction

Numerical optimization is an important tool in the field of computational physics in general and in nano-optics in specific. It has attracted attention with the increase in complexity of structures that can be realized with nowadays nano-fabrication technologies for which a rational design is no longer feasible. Also, numerical resources are available to enable the computational photonic material design and to identify structures that meet predefined optical properties for specific applications. However, the optimization objective function is in general non-convex and its computation remains resource demanding such that the right choice for the optimization method is crucial to obtain excellent results. Here, we benchmark five global optimization methods for three typical nano-optical optimization problems: \removed{downhill simplex optimization, the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm, particle swarm optimization, differential evolution, and Bayesian optimization} \added{particle swarm optimization, differential evolution, and Bayesian optimization as well as multi-start versions of downhill simplex optimization and the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm}. In the shown examples from the field of shape optimization and parameter reconstruction, Bayesian optimization, mainly known from machine learning applications, obtains significantly better results in a fraction of the run times of the other optimization methods.Comment: 11 pages, 4 figure

Set optimization - a rather short introduction

Recent developments in set optimization are surveyed and extended including various set relations as well as fundamental constructions of a convex analysis for set- and vector-valued functions, and duality for set optimization problems. Extensive sections with bibliographical comments summarize the state of the art. Applications to vector optimization and financial risk measures are discussed along with algorithmic approaches to set optimization problems