In Nature, biological materials such as nacre, bone, and dentin display an enhanced mechanical strength due to their structure characterized by hard inclusions embedded in a soft matrix. This structure has inspired the design of artificial materials with optimized properties. Thus, for given the mechanical properties of matrix and inclusions, it is fundamental to understand how the global observables, essentially strength, and ultimate strain are determined by the geometrical parameters of the inclusions. In this paper, we address this question by extending the two-dimensional random fuse model, which has been widely used to extract statistical properties of fracture processes, to the case of staggered stiff inclusions. We thus investigate numerically how emergent mechanical properties can be optimized by tuning geometrical dimensions and the arrangement of the inclusions. To do this, we adopt an optimization procedure based on an evolutionary algorithm to efficiently explore the parameter space and to determine the most favorable geometrical features of the inclusions for improved strength or ductility, or both. Various lattice sizes and volume fractions are considered. Depending on inclusion sizes and aspect ratios, composite strength or ultimate strain can be maximized, with the Pareto front for simultaneous optimization of the two being interpolated by a simple power law. Characteristic exponents for damage avalanche distributions are found to vary with respect to homogeneous structures, indicating increased fracture ductility simply due to optimized geometrical features. Our study indicates the possibility through structural optimization of creating staggered composites that allow significant advantages in terms of weight reduction and fuel consumption in automotive applications.