Discrete, gradient, and hybrid optimization methods are applied to the challenge of discovering molecules with optimized properties. The cost and performance of the approaches were studied using a tight-binding model to maximize the static first electronic hyperpolarizability of molecules. Our analysis shows that discrete branch and bound methods provide robust strategies for inverse chemical design involving diverse chemical structures. Based on the linear combination of atomic potentials, a hybrid discrete-gradient optimization strategy significantly improves the performance of the gradient methods. The hybrid method performs better than dead-end elimination and competes with branch and bound and genetic algorithms. The branch and bound methods for these model Hamiltonians are more cost effective than genetic algorithms for moderate-sized molecular optimization.