Nanoparticle-based drug delivery is a promising method to increase the therapeutic index of anti-cancer agents with low median toxic dose. The delivery efficiency, corresponding to the fraction of the injected nanoparticles that adhere to the tumor site, depends on nanoparticle size \(a\) and aspect ratio \(AR\). Currently, values for these variables are chosen empirically, and may not yield optimal targeted drug delivery. This study applies rigorous optimization to the design of nanoparticles. A preliminary investigation revealed that delivery efficiency increases monotonically with \(a\) and \(AR\). However, maximizing \(a\) and \(AR\) results in non-uniform drug distribution, which impairs tumor regression. Therefore, a multi-objective optimization problem (MO) is formulated to quantify the trade-off between nanoparticles accumulation and distribution. The MO is solved using the derivative-free Mesh Adaptive Direct Search algorithm. Theoretically, the Pareto-optimal set consists of an infinite number of mathematically equivalent solutions to the MO problem. However, interesting design solutions can be identified subjectively, e.g., the ellipsoid with a major axis of 720 nm and an aspect ratio of 7.45, as the solution closest to the utopia point. The MO problem formulation is then extended to optimize nanoparticle biochemical properties, in particular ligand-receptor binding affinity and ligand density. Optimizing physical and chemical properties simultaneously results in optimal designs with reduced nanoparticle sizes, thus enhanced cellular uptake. The presented study provides an insight on nanoparticle structures that have potential for producing desirable drug delivery.