Several limitations such as high cost, different longitudinal expansion coefficient of glass and metal, and the need for a complex tracking system in parabolic collectors have led to the design and construction of new systems in solar technology. Fresnel collectors are such systems that in the first place, reduced the cost of the system by replacing flat mirrors instead of parabolic mirrors which are costly to build. Of course, the efficiency of parabolic collectors is more than Fresnel collectors. Fresnel collectors usually use one or more tubes to receive radiation. In this study, a design has been proposed to increase the efficiency of these collectors by increasing the radiation flux. Placing several absorbent tubes in a cavity will cause many of the beams that were previously out of reach, now hit the tubes and their energy been absorbed. In this study, the defining parameters for designing a Fresnel collector with a cavity have been identified. Then, optimal state of these parameters has been investigated to achieve the highest amount of collision rays to the absorbent tubes and also to increase the uniformity of the distribution of collision beams between the adsorbent tubes by employing multi-objective genetic algorithm in MATLAB. Among the designs presented by this algorithm, a design with optical efficiency 83.46% is chosen while the uniformity of the distribution of the collision rays between the adsorbent tubes is appropriate in this design. Keywords: Solar energy, Fresnel collector, Absorbent tubes, Cavity, Solar power plants, Genetic algorithm