BwF and eVar in CGP to improve digital circuit synthesis of complex non-linear designs

Cartesian Genetic Programming (CGP) is regularly applied to synthesize and realize digital circuits for small arithmetic and digital-logic functions. CGP benefits in obtaining hardware-efficient circuits through its heuristic search-space exploration, which is hard to reach in a rule-based synthesis process. However, the traditional CGP configuration has limitations in evolving large and complex circuits, requiring a large number of generations. High computation time and energy requirements hinder its usage from evolving complex digital circuits. This paper investigates and demonstrates the desired modifications to existing CGP in the form of Binary Weighted Fitness (BwF) and exponentially varying mutation rate (eVar) to evolve functionally correct solutions extremely fast. The benefits are demonstrated for the basic non-linear power functions and are validated for usage in activation functions which are otherwise difficult to realize. Additionally, 12 different CGP configurations with changes in mutation scheme and evolutionary strategy were also investigated for the power functions. A comparison with the benefits of BwF and eVar adopted CGP over the traditional CGP methods is presented and discussed.

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Power function circuits :

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Power 2 (x^2) :

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Circuit photos

HDL files

Power 3 (x^3) :

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Circuit photos

HDL files

Power 4 (x^4) :

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Circuit photos

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Error metrics used in this work :

Round to floor Quantization Scheme example :

Resources :

CGP:

https://www.cartesiangp.com/

https://link.springer.com/book/10.1007/978-3-642-17310-3#about

Logic synthesis basics:

https://en.wikipedia.org/wiki/Logic_synthesis

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