Success in synthetic biology depends on the efficient construction of robust genetic circuitry. However, even the direct engineering of the simplest genetic elements (switches, logic gates) is a challenge and involves intense lab work. As the complexity of biological circuits grows, it becomes more complicated and less fruitful to rely on the rational design paradigm, because it demands many time-consuming trial-and-error cycles. One of the reasons is the context-dependent behavior of small assembly parts (like BioBricks), which in a complex environment often interact in an unpredictable way. Therefore, the idea of evolutionary engineering (artificial directed in vivo evolution) based on screening and selection of randomized combinatorial genetic circuit libraries became popular. In this article we build on the so-called dual selection technique. We propose a plasmid-based framework using toxin-antitoxin pairs together with the relaxase conjugative protein, enabling an efficient autonomous in vivo evolutionary selection of simple Boolean circuits in bacteria (E. coli was chosen for demonstration). Unlike previously reported protocols, both on and off selection steps can run simultaneously in various cells in the same environment without human intervention; and good circuits not only survive the selection process but are also horizontally transferred by conjugation to the neighbor cells to accelerate the convergence rate of the selection process. Our directed evolution strategy combines a new dual selection method with fluorescence-based screening to increase the robustness of the technique against mutations. As there are more orthogonal toxin-antitoxin pairs in E. coli, the approach is likely to be scalable to more complex functions. In silico experiments based on empirical data confirm the high search and selection capability of the protocol.