BioSystems 87 (2007) 224–232 The genotypic complexity of evolved fault-tolerant and noise-robust circuits Morten Hartmann ∗ , Pauline C. Haddow, Per Kristian Lehre Complex Adaptive Organically-Inspired Systems Group (CAOS), Department of Computer Science, The Norwegian University of Science and Technology (NTNU), Norway Received 28 February 2005; received in revised form 8 July 2006; accepted 15 July 2006 Abstract Noise and component failure is an increasingly difficult problem in modern electronic design. Bio-inspired techniques is one approach that is applied in an effort to solve such issues, motivated by the strong robustness and adaptivity often observed in nature. Circuits investigated herein are designed to be tolerant to faults or robust to noise, using an evolutionary algorithm. A major challenge is to improve the scalability of the approach. Earlier results have indicated that the evolved circuits may be suited for the application of artificial development, an approach to indirect mapping from genotype to phenotype that may improve scalability. Those observations were based on the genotypic complexity of evolved circuits. Herein, we measure the genotypic complexity of circuits evolved for tolerance to faults or noise, in order to uncover how that tolerance affects the complexity of the circuits. The complexity is analysed and discussed with regards to how it relates to the potential benefits to the evolutionary process of introducing an indirect genotype–phenotype mapping such as artificial development. © 2006 Elsevier Ireland Ltd. All rights reserved. Keywords: Complexity; Fault-tolerance; EHW; Noise; Robust; Evolution 1. Introduction The need for fault and noise tolerance is an important issue in modern electronic design. High density chips increase the possibility of failing components and the complexity of design increases the probability of hu- man errors. Fault acceptance diminishes as the market demands increasingly more reliable systems. The need for fault-tolerant designs and management of noise are stated amongst the long term (2008–2016) grand chal- lenges by the International Technology Roadmap for Semiconductors (ITRS, 2003). Recently, a growing research field has started explor- ing new solutions to these problems, the field of evolv- ∗ Corresponding author. E-mail addresses: mortehar@idi.ntnu.no (M. Hartmann), pauline@idi.ntnu.no (P.C. Haddow), lehre@idi.ntnu.no (P.K. Lehre). able hardware (EHW). The field seeks to apply evolution and other bio-inspired methods to hardware design exploration and optimization. Evolutionary Algorithms (EAs) is one such method, and was used by Hartmann and Haddow (2004) to generate circuits that to some extent are tolerant to faults and robust in handling noise. The approach suffers, like many EAs often do, from the fact that it does not scale well with increased problem size. Increasing the number of elements in the genotype increases the dimensionality of the search space, usually resulting in a problem which is harder to solve. One approach to reducing the search space and thus potentially improving the scalability of EAs is artificial development (AD) (Stanley and Miikkulainen, 2003). Inspired by biological development and the fact that the human genome is exceedingly small compared to fea- tures of a grown human being such as the brain, AD could allow EAs to operate using smaller genotypes. 0303-2647/$ – see front matter © 2006 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.biosystems.2006.09.017