Context. The diluted aperture synthesis is one of the most promising ways of obtaining direct images with an angular resolution in the milliarcsecond range. By applying apodization techniques to a hypertelescope, it is possible to discriminate between objects with a high contrast in intensity with a reasonable number of telescopes (<10). Aims. To reach such performances, we attempt to develop a co-phasing system capable of stabilizing the optical path differences with an accuracy better than λ/100 RMS. Methods. We propose a method based on a joint use of a sub-aperture piston phase-diversity technique and a genetic algorithm to co-phase a laboratory prototype called a temporal hypertelescope (THT). First, we simulated the behavior of this instrument and inferred the related statistical properties of our co-phasing method. In a second step, we implemented this co-phasing system on our THT prototype. Results. We obtain an experimental stabilization of the optical path differences of about λ/300 RMS over 1000 s. Thanks to this result, we are able to acquire an image of a high-contrast binary system. We also validate that the instrument accurately estimates the object characteristics, i.e. 25 μrad for the angular separation and ΔH = 9.1 magnitude difference between the main star and its companion.