Planar antenna arrays based on certain categories of aperiodic tilings have been shown to exhibit several useful properties, including a wide bandwidth void of grating lobes, relatively low sidelobe levels, and sparse element distributions. While these arrays possess beneficial properties, their performance is basically limited by the corresponding set of prototiles that make up the tiling, i.e. the arrays tend to lack design flexibility. A design technique was recently introduced that circumvents this limitation of these arrays by incorporating additional parameters into the basic tiling generation process. With only a small number of parameters it is possible to greatly vary the geometry, and consequently the radiation properties, of aperiodic tiling arrays. This technique has been combined with a genetic algorithm (GA) to generate planar arrays with bandwidths up to 22:1. With successful single-objective optimizations carried out, a natural extension of this technique is to expand its application to multiobjective designs. In this paper examples will be presented for arrays that were optimized to achieve two design objectives: a desired number of elements within a given aperture and minimum sidelobes at a specified frequency. The conventional GA that was utilized in the single-objective optimizations was replaced by a Multiple Objective Genetic Algorithm (MOGA), which is much more adept at handing such a design problem. Optimized array examples with bandwidths up to 7.35:1 and a targeted number of elements will be presented.