# A Novel Evolutionary Algorithm for Designing Robust Analog Filters
## 1 Introduction  
Topologically open-ended computational design by genetic programming (GP) has been used for engineering design innovation, with many success stories in a variety of domains including analog circuits, digital circuits, molecular design, and mechatronic systems [1, 2]. This approach uses genetic programming as an open-ended search method for functional design innovation--achieving a specified behavior without pre-specifying the design topology--and has achieved considerable success. However, in practical engineering design, there is another criterion in addition to functional specifications that should be considered during the design process. Robustness, as the ability of a system to maintain function even with changes in internal structure (including variations in parameters from nominal values) or external environment [3], is also critical to engineering design decisions. Engineering design, in reality, does not normally take into account every uncertainty or variation to which the engineered artifacts are subject to, such as manufacturing variation, degradation or non-uniformity of material properties, environmental changes, and changing operating conditions. We are interested in the following two kinds of system robustness: One is the system robustness with respect to perturbation in the parameters of the system, which has been well studied in the traditional robust design community [4] and also in evolutionary robust design [5]. The other kind is the system robustness with respect to topological perturbation--for example, accidental removal or failure ofcomponents. Reliable systems, having the least sensitivity of performance to variations or failures in the system components or environmental conditions, are highly desirable. However, there are relatively few studies that explore how a GP-based open-ended topology search may contribute to the design of robust systems such that they can withstand internal or external perturbations. In this paper, we are interested in exploring GP algorithms for the design of robust systems such as analog filters. Specifically, we proposed a GP-based algorithm to facilitate the design of more robust systems with respect to parameter variations or uncertainty of the design variables. A set of systematic experiments are conducted to verify the following hypotheses about robust design using genetic programming: (1) that dynamic systems with high functional performance evolved by GP without considering a robustness criterion during the evolutionary process may have unacceptably low robustness with respect to parameter perturbation, (2) that the robustness of a system is strongly constrained by its topological/functional structure, and that the amount of robustness improvement available through parameter tuning is limited, and (3) that topologically open-ended synthesis by GP allows for the evolution of more robust solutions than traditional robust design approaches with parameter tuning. Evolving robustness has a unique role in GP-based automated design. As most of such computational synthesis approaches depend on software simulators to evaluate the performance of candidate solutions, the quality of the final implementation of the evolved solutions strongly depends on how well the simulator approximates the physical behavior of the physical systems. A related issue arises when the objective function is replaced by a surrogate function (approximation) to speed up simulation [6]. One strategy to ensure effective transfer from evolved solutions to reality is to improve the robustness of the solutions by introducing noise or environmental variation during simulation or fitness evaluation, as proposed by [PERSON] [7] in evolutionary robotics, for example. If the evolved solution is robust to such variations, the performance of the model evolved may sufficiently resemble (such that the model is useful) that of its physical implementation.