A challenge in designing self-assembling building blocks is to ensure the target state is both thermodynamically stable and kinetically accessible. These two objectives are known to be typically in competition, but it is not known how to simultaneously optimize them. We consider this problem through the lens of multi-objective optimization theory: we develop a genetic algorithm to compute the Pareto fronts characterizing the tradeoff between equilibrium probability and folding rate, for a model system of small polymers of colloids with tunable short-ranged interaction energies. We use a coarse-grained model for the particles dynamics that allows us to efficiently search over parameters, for systems small enough to be enumerated. For most target states there is a tradeoff when the number of types of particles is small, with medium-weak bonds favouring fast folding, and strong bonds favouring high equilibrium probability. The tradeoff disappears when the number of particle types reaches a value $m_*$, that is usually much less than the total number of particles. This general approach of computing Pareto fronts allows one to identify the minimum number of design parameters to avoid a thermodynamic-kinetic tradeoff. However, we argue, by contrasting our coarse-grained models predictions with those of Brownian dynamics simulations, that particles with short-ranged isotropic interactions should generically have a tradeoff, and avoiding it in larger systems will require orientation-dependent interactions.
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