This is a study of the evolving design of a composite material with inserts that are free to be configured and distributed through the base material. Several classes of shapes of inserts are considered competitively: parallel plates, staggered plates, forks, chains and diamonds. The architecture evolves in two directions (with two objectives), high thermal conductance and mechanical strength (stiffness). Relative to the base material, the inserts have higher thermal conductivity and lower modulus of elasticity. As a consequence, better architectures emerge from the tradeoff between thermal conductance and strength, for example, chain and diamond shaped inserts. The two-objective performance further improves when the inserts are distributed nonuniformly through the base material, such that the high conductivity inserts are not placed in the regions with the highest stresses.