A transformation system for interactive reformulation of design optimization strategies

Abstract

Numerical design optimization algorithms are highly sensitive to the particular formulation of the optimization problems they are given. The formulation of the search space, the objective function and the constraints will generally have a large impact on the duration of the optimization process as well as the quality of the resulting design. Furthermore, the best formulation will vary from one application domain to another, and from one problem to another within a given application domain. Unfortunately, a design engineer may not know the best formulation in advance of attempting to set up and run a design optimization process. In order to attack this problem, we have developed a software environment that supports interactive formulation, testing and reformulation of design optimization strategies. Our system represents optimization strategies in terms of second-order data ow graphs. Reformulations of strategies are implemented a s t r ansformations between data ow graphs. The system permits the user to interactively generate and searc h a s p ace of design optimization strategies, and experimentally evaluate their performance on test problems, in order to nd a strategy that is suitable for his application domain. The system has been implemented in a domain independent fashion, and is being tested in the domain of racing yacht design.

Learning symbolic formulations in design: Syntax, semantics, and knowledge reification

“…Although it is possible to automatically generate a training database in numerical optimization cases (Schwabacher et al, 1998), generating a training database for symbolic cases will be more difficult. Given the specific conditions related to each problem, formulations from the same design domain or even the same problem in different settings can have widely differing mathematical forms (Ellman et al, 1998). Thus, it is difficult to define the learning characteristics and problem representation form for a training database in any general sense.…”

“…The development of artificial intelligence (AI) algorithms to automate design problem reformulation tasks is an enduring challenge in design automation. Existing methods either require dependence upon high levels of embedded knowledge engineering in the form of rules, heuristics, grammars, or domain/taskspecific procedures (e.g., Ellman et al, 1998;Gelsey et al, 1998;Medland & Mullineux, 2000;Campbell et al, 2003) or require a large database of training cases (e.g., Duffy & Kerr, 1993;Schwabacher et al, 1998). It would be useful to develop a method characterized by the following desirable features: a knowledge-lean method that does not need any significant design domain or task knowledge to be embedded into the system; a training-lean method that can extract design knowledge over one or very few cases; and a simple and computationally efficient method applicable over different design domains, representational forms (analytical, nonanalytical, etc.…”

Multilevel modelling for engineering design optimization

“…In all of the experiments we report in this paper, the flag Do-LineSearchl was set to True so that the LineSearchl routine was invoked after each inner optimization. In experiments on an aircraft design problem and a simpler version of the yacht design problem, we obtained good results without using the LineSearch routine (Ellman et al, 1997).…”

“…We have implemented our multimodel optimization strategies as part of the Design and Modelling/Simulation Associate (DA-MSA) (Ellman et al, 1992(Ellman et al, , 1995(Ellman et al, , 1997. The DA-MSA is a system that supports interactive construction of numerical models for simulation of engineering design artifacts.…”

“…A complete description of the DA-MSA transformation system is beyond the scope of this paper. For additional information, see Ellman et al (1995Ellman et al ( , 1997.…”