Jianjun Hu and Erik Goodman
Genetic Algorithm Research & Application Group (GARAGe), Michigan State University
Abstract Traditional robust design constitutes only one step in the detailed design stage, where parameters of a design solution are tuned to improve the robustness of the system. This chapter proposes that robust design should start from the conceptual design stage and genetic programming-based open-ended topology search can be used for automated synthesis of robust systems. Combined with a bond graph-based dynamic system synthesis methodology, an improved sustainable genetic programming technique - quick hierarchical fair competition (QHFC)- is used to evolve robust high-pass analog filters. It is shown that topological innovation by genetic programming can be used to improve the robustness of evolved design solutions with respect to both parameter perturbations and topology faults.
Keywords: sustainable genetic programming, automated synthesis,dynamic systems, robust design, bond graphs, analog filter
1. Introduction
Topologically open-ended computational synthesis by genetic programming (GP) has been used as an effective approach for engineering design innova-tions, with many success stories in a variety of domains (Koza et al., 2003) including analog circuits , digital circuits, molecular design, and mechatronic systems (Seo et al., 2003a), etc. Much of the existing research focuses on em-ploying genetic programming as a topologically open-ended search method to do functional design innovation – achieving a specified behavior without pre-specifying the design topology. In this chapter, we are interested in exploring more thoroughly how genetic-programming-based open-ended design synthe-sis can improve another dimension of engineering design: the robustness of the systems designed. Specifically, we examine whether topological innovation
by genetic programming can facilitate design of robust dynamic systems with respect to environmental noise, variation in design parameters, and structural failures in the system.
Robustness, as the ability of a system to maintain function even with changes in internal structure or external environment (Carlson and Doyle, 2002, Jen, 2001), is critical to engineering design decisions. Engineering design systems, in reality, do not normally take into account all the types of uncertainties or variations to which the engineered artifacts are subjected, such as manufacturing variation, degradation or non-uniformity of material properties, environmental changes, and changing operating conditions. However, reliable systems, having the least sensitivity of performance to variations in the system components or environmental conditions, are highly desirable. Evolving robustness can also contribute to genetic-programming-based design synthesis by increasing the robustness of the evolved solutions, which make them easier to implement physically despite the discrepancy between the simulator and real-world model (Jakobi et al., 1995).
Our hypothesis here is that control factors (design variables) as used in the robust design framework in (Chen et al., 1996) should not be limited to chang-ing the dimensions (or sizchang-ing) and other numeric parameters of the systems. As any given function of a dynamic system can be implemented in various ways, we believe that the topological or the functional design in the conceptual design phase may have a significant role in determining the robustness of the design solutions with respect to both topology variation as well as parameter pertur-bation in terms of traditional robust design. Actually, Ferrer i Cancho et al.
(Ferrer i Cancho et al., 2001) gave an analysis of topological patterns in electric circuits and their relationship with the properties of the system behavior. There is already a body of research on how the structure of a system affects its func-tional robustness.For example, Balling and Sobieszczanski-Sobieski (Balling and Sobieszczanski-Sobieski, 1996) discussed how the coupling structure of the system may affect robust parameter design. But a systematic methodology and investigation of robust design of dynamic systems based on topologically open-ended search by genetic programming is still lacking.
2. Related Work
Robust design, originally proposed by Taguchi (Tay and Taguchi, 1993), has been intensively investigated in the engineering design community since the 1980s and remains an important topic (Zhu, 2001). In robust design, a designer seeks to determine the control parameter settings that produce desirable values of the performance mean, while at the same time minimizing the variance of the performance (Tay and Taguchi, 1993).
Many aspects of traditional robust design such as performance sensitivity dis-tribution have been investigated intensively (Zhu, 2001, Du and Chen, 2000).
However, most of these robust design studies assume that there already exists a design solution for a system and the task of robust design is to determine its robust operating parameters with respect to various kinds of variations. The relation of how topological or functional structure of a system affects its robust-ness is often not treated. One reason why these issues are unresolved is that the prevailing approach for system design is a top-down procedure from functional design to detailed design, and robust design is applied only in the detailed design stage. Topologically open-ended synthesis by genetic programming provides a way to move robust design forward to the conceptual/functional design stage and thus consider design for robustness from the very beginning, which will augment the current practice of design for robustness in parametric design.
Application of evolutionary computation to robust design has been investi-gated since the early 1990s (Forouraghi, 2000) and can be classified into three categories. The first type of work applies evolutionary algorithms to parametric design for robustness, following the track of robust design in traditional engi-neering. Tsutsui et al. (Tsutsui and Ghosh, 1997) proposed to use noise on the design variables in the calculation of fitness values to evolve robust solu-tions. This approach was later applied to parametric robust design of MEMS by Ma and Antonsson (Ma and Antonsson, 2001). The second type of research on evolving robustness focuses on evolving robust solutions in a noisy environment (Hammel and Back, 1994). In these problems, the variation in the environment leads to uncertainty in the fitness function evaluation and the true fitness of a can-didate solution needs to be evaluated based on sampling multiple environment configurations. In the evolutionary robotics area, for example, Lee et al. (Lee et al., 1997) evolved robust mobile robot controllers by training them in mul-tiple trials of simulation, using genetic programming and a genetic algorithm, respectively. The active area of evolving robust systems is evolvable hardware (Thompson and Layzell, 2000). Most of these approaches employ genetic al-gorithms or evolution strategies as the search procedures. Very recent work is the evolution of robust digital circuits (Miller and Hartmann, 2001, Hartmann et al., 2002a). In this work, Miller, Hartmann, and their collaborators examine the feasibility of evolving robust digital circuits using a type of “messy gate.”
Hartmann et al.(Hartmann et al., 2002b) investigated how evolution may ex-ploit non-perfect digital gates to achieve fault tolerance, including tolerance to output noise and gate failure. However, the noise introduced to improve robust-ness is not applied to parametric values of the components, but to the analog outputs of the messy gates, and an evolution strategy is used as the open-ended topology search tool. This method is thus not as instructive as might be desired in exploring effects of alternative topologies.
3. Analog Filter Synthesis by Bond Graphs and Sustainable Genetic Programming
Dynamic systems in this chapter are represented as bond graphs (Karnopp et al., 2000). A strongly typed genetic programming tool, enhanced with the sustainable evolutionary computation model, the Hierarchical Fair Competition (HFC) model (Hu and Goodman, 2002), is used for topologically open-ended search. In this section, bond graphs, the bond graph synthesis approach by genetic programming and the HFC-GP algorithm (Hu and Goodman, 2002) are introduced briefly.