Optical logic gates play a crucial role in all-optical signal processing systems. Traditional methods of designing logic gates require manual adjustment of structural parameters. In this paper, we utilize a genetic algorithm for inverse design, and the optical AND, OR, and NOT logic gates are achieved on a silicon platform at the working wavelength of 1.55 μm. The total area of the logic gates is fixed at 2.2 μm × 2.2 μm, convenient to be integrated with other functional devices, the optimized structural parameters are acquired for different logic gates and the contrast ratios of the OR, AND, and NOT gates are 8.55, 5.32, and 4.14 dB, respectively. The design is characterized by a compact structure, high contrast, and a high degree of freedom, offering a valuable reference for photonic integrated circuits. •A compact optical logic gate with rectangular air hole array is designed and high performance is achieved.•The optimization efficiency was enhanced by GA, and optical logic gates were achieved with ultra-small size.•The influence of air hole’s variation to device’s performance was studied, and it guided the actual fabrication.