Composite materials offer the unique advantage of allowing customization of their properties based on their load. However, the optimization of composite laminate properties can often be challenging, often leading to quasi-isotropic designs or the use of industry guidelines. This paper presents a novel method for optimizing of a composite cylinder under axial compression. It introduces an innovative approach by merging a tailored differential evolution algorithm with a deep neural network. The key modification is in the method of constraint implementation. The initial population and trial vectors are constrained to balanced laminates using a while loop, effectively shrinking the design space and reducing computational requirements. The advantage of the customization is reflected in the faster convergence of the optimization as well as a much more accurate deep neural network model. It also enabled the differential evolution to escape the local maxima. Using the deep neural network to evaluate candidate solutions, further reduces the computational costs. The technique is validated using linear buckling analysis and applied to design an inter-tank truss structure. The optimization resulted in a drop in the mass of the truss structure from 5.28 to 4.87 kg. The study establishes a general optimization method applicable to various composite cylinders, including short and long, thin and thick cylinders, and honeycomb core sandwiched composite structures.