A classification of methods for distributed system optimization based on formulation structure

Augmented Lagrangian coordination (ALC) is a provably convergent coordination method for multidisciplinary design optimization (MDO) that is able to treat both linking variables and linking functions (i.e. system-wide objectives and constraints). Contrary to quasi-separable problems with only linking variables, the presence of linking functions may hinder the parallel solution of subproblems and the use of the efficient alternating directions method of multipliers. We show that this unfortunate situation is not the case for MDO problems with block-separable linking constraints. We derive a centralized formulation of ALC for block-separable constraints, which does allow parallel solution of subproblems. Similarly, we derive a distributed coordination variant for which subproblems cannot be solved in parallel, but that still enables the use of the alternating direction method of multipliers. The approach can also be used for other existing MDO coordination strategies such that they can include block-separable linking constraints. This work is funded by MicroNed, grant number 10005898.     

An augmented Lagrangian approach to non-convex SAO using diagonal quadratic approximations

Successful gradient-based sequential approximate optimization (SAO) algorithms in simulation-based optimization typically use convex separable approximations. Convex approximations may however not be very efficient if the true objective function and/or the constraints are concave. Using diagonal quadratic approximations, we show that non-convex approximations may indeed require significantly fewer iterations than their convex counterparts. The nonconvex subproblems are solved using an augmented Lagrangian (AL) strategy, rather than the Falk-dual, which is the norm in SAO based on convex subproblems. The results suggest that transformation of large-scale optimization problems with only a few constraints to a dual form via convexification need sometimes not be required, since this may equally well be done using an AL formulation.     

Approximated approximations for SAO

We propose to replace a number of popular approximations by their diagonal quadratic Taylor series expansions. The resulting separable quadratic approximations are easily convexified, and are well suited for use in dual sequential approximate optimization (SAO) algorithms. Global convergence of the resulting SAO algorithms may be enforced in a natural way using conservatism. The approximated approximation approach is explicitly illustrated for (i) reciprocal and exponential intervening variables, (ii) the intervening variables used in the method of moving asymptotes (MMA), (iii) the intervening variables used in CONLIN, and (iv) the TANA-3 approximations. The use of intermediate responses for use in, for example, truss and frame-like structures, is also discussed. Key advantages of replacing nonlinear approximations by their diagonal quadratic approximations are that these approximated approximations can all be used simultaneously in a single dual statement; the dual does not depend on the form of the original approximations. In addition, in a dual setting, the resulting subproblems yield simple analytical relationships between the primal and dual variables, which is often not the case with the original nonlinear approximations. An important example hereof is the exponential approximation. Although the diagonal quadratic approximations may differ notably from their original counterparts, they typically are quite similar in a sufficiently small search subregion, which relates to the move limits commonly used in SAO anyway.     

Azo disperse dyes for synthetic fibres. 2: Benzimidazole derivatives

Ten variously substituted derivatives ( IIa–j ) of 3′-(benzimidazol-2-yl)-4′-hydroxyazobenzene were prepared. The effects of the nature and orientation of the substituents on the colour and dyeing properties of these dyes on polyester and acrylic fibres were evaluated.     

Corrosion and hydrogen surface embrittlement inhibition of amorphous FeBSiC alloy in molar HCl by diorthoaminodiphenyldisulphane (DOAPD)

The mode of corrosion inhibition of amorphous alloys due to diorthoaminodiphenyldisulphane (DOAPD) in molar HCl is studied through solution analysis and electrochemical steady state and transient measurements. DOAPD acts on the cathodic reaction without changing the mechanism of the hydrogen reduction reaction on the surface of the amorphous alloy electrode. The efficiency of corrosion inhibition depends on both the concentration of DOAPD and the potential of the electrode. The addition of 10^–4 m DOAPD to 1m HCl increases the impedance and decreases the capacity of the double layer. From the comparison of results with those obtained using other organic compounds, it is shown that DOAPD is the best inhibitor. A correlation between the efficiency of corrosion inhibition of DOAPD and its molecular structure is established. A schematic representation of the surface coverage due to different action modes of DOAPD cations is presented. Evidence is revealed for a double rôle of DOAPD in the decrease of corrosion and in hydrogen penetration. The schematic representation proposed explains why the mechanism of hydrogen reduction reaction is the same in the absence and in the presence of DOAPD.     

A quadratic approximation for structural topology optimization

In topology optimization, it is customary to use reciprocal‐like approximations, which result in monotonically decreasing approximate objective functions. In this paper, we demonstrate that efficient quadratic approximations for topology optimization can also be derived, if the approximate Hessian terms are chosen with care. To demonstrate this, we construct a dual SAO algorithm for topology optimization based on a strictly convex, diagonal quadratic approximation to the objective function. Although the approximation is purely quadratic, it does contain essential elements of reciprocal‐like approximations: for self‐adjoint problems, our approximation is identical to the quadratic or second‐order Taylor series approximation to the exponential approximation. We present both a single‐point and a two‐point variant of the new quadratic approximation. Copyright © 2009 John Wiley & Sons, Ltd.     

On the equivalence of optimality criterion and sequential approximate optimization methods in the classical topology layout problem

We study the ‘classical’ topology optimization problem, in which minimum compliance is sought, subject to linear constraints. Using a dual statement, we propose two separable and strictly convex subproblems for use in sequential approximate optimization (SAO) algorithms. Respectively, the subproblems use reciprocal and exponential intermediate variables in approximating the non‐linear compliance objective function. Any number of linear constraints (or linearly approximated constraints) are provided for. The relationships between the primal variables and the dual variables are found in analytical form. For the special case when only a single linear constraint on volume is present, we note that application of the ever‐popular optimality criterion (OC) method to the topology optimization problem, combined with arbitrary values for the heuristic numerical damping factor η proposed by Bendsøe, results in an updating scheme for the design variables that is identical to the application of a rudimentary dual SAO algorithm, in which the subproblems are based on exponential intermediate variables. What is more, we show that the popular choice for the damping factor η=0.5 is identical to the use of SAO with reciprocal intervening variables. Finally, computational experiments reveal that subproblems based on exponential intervening variables result in improved efficiency and accuracy, when compared to SAO subproblems based on reciprocal intermediate variables (and hence, the heuristic topology OC method hitherto used). This is attributed to the fact that a different exponent is computed for each design variable in the two‐point exponential approximation we have used, using gradient information at the previously visited point. Copyright © 2007 John Wiley & Sons, Ltd.     

Innovative Hybrid Reinforcement for Flexural Members

The capacity and ductility of RC slabs are affected by the use of fiber-reinforced polymer (FRP) as their main reinforcement for repair and rehabilitation. The balance between increasing the capacity and reducing the ductility of flexural members reinforced with FRP was always a matter of discussion. In this research, innovative hybrid reinforcement system (HRS) was introduced to provide the required increase in capacity while keeping the ductility within an acceptable range. Ten RC one-way slabs were tested in this investigation. They included a control slab which was reinforced with ordinary steel, while the rest of the slabs were reinforced internally with HRS with nine different profiles. The main variables considered in this study were the type of core or perimeter reinforcement and the number of perimeter reinforcing layers. It was revealed that the use of the innovative HRS resulted in remarkable increases in section ultimate load capacity as well as ductility.     

Design Optimization of Multibody Systems by Sequential Approximation

Design optimization of multibody systems is usually established by a direct coupling of multibody system analysis and mathematical programming algorithms. However, a direct coupling is hindered by the transient and computationally complex behavior of many multibody systems. In structural optimization often approximation concepts are used instead to interface numerical analysis and optimization. This paper shows that such an approach is valuable for the optimization of multibody systems as well. A design optimization tool has been developed for multibody systems that generates a sequence of approximate optimization problems. The approach is illustrated by three examples: an impact absorber, a slider-crank mechanism, and a stress-constrained four-bar mechanism. Furthermore, the consequences for an accurate and efficient accompanying design sensitivity analysis are discussed.