In the following experiments, we try to evolve a robust analog filter that can tolerate the failure of its components and has graceful performance degradation.
The running parameters are the same as stated in the beginning of this section.
Remember that because a significant portion of the topologically perturbed systems are causally ill-posed and can not be simulated with our simulator, the final fitness of the solutions (and the resulting conclusion) is much less reliable than that in the previous subsection. Topology perturbation during evolution is applied by removing a uniformly chosen number (between 1 and 5) of compo-nents from each candidate solution for 10 samplings. The evolved filter, in bond graph form, is shown in Figure 9-7 and the performance degradation levels are illustrated in Figure 9-6 (b).
Comparing Figure 9-6 (b) with Figure 9-4 (b), it is clear that a more fault-tolerant filter has been evolved. Removing 3 faulty components, the robust solution can still achieve 65% of the fitness of the original solution on average, while the non-robust filter can only achieve 39% of the fitness of the original solution. Another interesting observation is that the fault-tolerant filter in Figure 9-7 tends to be much more complex than the robust solution evolved in the previous subsection. This can be explained like this: more complex structures can have more redundancy, which serves as means for providing fault-tolerance.
The lower degree of symmetry of this solution compared to that of Figure 9-5 seems to also contribute to its tolerance of component removal. It is clear that different perturbation patterns lead to different topological structures of the robust solutions.
Figure 9-7. Evolved fault-tolerant filter represented as bond graph. Component sizing values are omitted for simplicity.
6. Conclusions and Future Work
This chapter proposes to exploit open-ended topology search capability of genetic programming for robust design of dynamic systems. We believe that topological or functional innovation in the conceptual design stage can improve the robustness of (the functionality of) the systems. Specifically, we apply an improved version of sustainable genetic programming-QHFC and a bond graph-based modular set approach to automated synthesis of robust dynamic systems.
We find that our sustainable genetic programming enables us to find more robust analog filters with respect to the variations in their parameters and component faults.
Evolving robustness is a rich research theme and there are several interesting topics to be further investigated. First, we find that selection pressure for ro-bustness w.r.t. parameter perturbation and component faults leads to different topological patterns. It would be interesting to investigate how simultaneous requirements for both types of robustness would affect topological structures.
Another related study would be to examine how perturbation pattern would affect structures. For example, one could study how the evolutionary system responds differentially to component removal by an absolute number of or by a percentage of components. Next, our experiments suggest that symmetry or scale-free topology may have a role in system robustness. More experiments are needed to confirm this. Future work will also explore the tradeoffs between improving robustness by parameter search and by topological innovation will be studied and methods to control it will be developed.
Acknowledgments
The authors wish to thank Rick Riolo, Julian Miller, and Jason Lohn for their constructive review suggestions and also other GPTP04 participants for stimu-lating discussions. This work was partially funded by NSF grant DMI0084934.
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