  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 model's 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.
