Configuring ship locks using a product platform based on DSM methods

Rijkswaterstaat (RWS), the executive branch of the Dutch Ministry of Infrastructure and Water Management, has announced that a significant number of ship locks in the Netherlands are due for renovation during the coming decades. The renovation of ship locks allows RWS to reconsider current existing preferences for lock design and to investigate options to develop a product platform for locks. This paper presents a method for the development of such a platform, based on the functions of a lock and the component alternatives to provide that function. By applying design structure matrix (DSM) modeling and value analysis methods, a ranked set of feasible lock configurations can be obtained that meets the specific requirements for a particular lock location while trading against the desired commonality in the family of locks. Preferred configuration attributes are to be incorporated in a product platform for locks to support RWS with the planned lock renovations

On the equivalence of optimality criterion and sequential approximate optimization methods in the classical 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 proposed by Bends¿e, 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 =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

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. © 2009 Springer-Verlag