Cartesian genetic programming (CGP) represents the most efficient method for the evolution of digital circuits. Despite many successful applications, however, CGP suffers from limited scalability, especially when used for evolutionary circuit design, i.e. design of circuits from a randomly initialized population. Considering the multiplier design problem, for example, the 5\(\times\)5-bit multiplier represents the most complex circuit designed by the evolution from scratch. The efficiency of CGP highly depends on the performance of the point mutation operator, however, this operator is purely stochastic. This contrasts with the recent developments in genetic programming (GP), where advanced informed approaches such as semantic-aware operators are incorporated to improve the search space exploration capability of GP. In this paper, we propose a semantically-oriented mutation operator (\(\mathrm {SOMO}^k\)) suitable for the evolutionary design of combinational circuits. In contrast to standard point mutation modifying the values of the mutated genes randomly, the proposed operator uses semantics to determine the best value for each mutated gene. Compared to the common CGP and its variants, the proposed method converges on common Boolean benchmarks substantially faster while keeping the phenotype size relatively small. The successfully evolved instances presented in this paper include 10-bit parity, 10 + 10-bit adder and 5\(\times\)5-bit multiplier. The most complex circuits were evolved in less than one hour with a single-thread implementation running on a common CPU.

笛卡尔遗传编程（CGP）代表了数字电路进化的最有效方法。然而，尽管有许多成功的应用，但 CGP 的可扩展性有限，尤其是当用于进化电路设计时，即从随机初始化的群体设计电路时。考虑乘法器设计问题，例如，5 \(\times\)5位乘法器代表了从零开始进化设计的最复杂的电路。CGP 的效率很大程度上取决于点变异算子的性能，然而，这个算子是纯随机的。这与遗传编程 (GP) 的最新发展形成鲜明对比，在遗传编程 (GP) 中，结合了语义感知运算符等先进的知情方法来提高 GP 的搜索空间探索能力。在本文中，我们提出了一个面向语义的变异算子（\(\mathrm {SOMO}^k\)) 适用于组合电路的进化设计。与随机修改突变基因值的标准点突变相比，所提出的算子使用语义来确定每个突变基因的最佳值。与常见的 CGP 及其变体相比，所提出的方法在保持表型大小相对较小的同时，更快地收敛于常见的布尔基准。本文介绍的成功进化实例包括 10 位奇偶校验、10 + 10 位加法器和 5 \(\times\) 5 位乘法器。最复杂的电路是在不到一小时的时间内通过在通用 CPU 上运行的单线程实现而演变的。