This paper describes the use of a genetic algorithm with memory for the design of minimum thickness composite laminates subject to strength, buckling and ply contiguity constraints. A binary tree is used to efficiently store and retrieve information about past designs. This information is used to construct a set of linear approximations to the buckling load in the neighborhood of each member of the population of designs. The approximations are then used to seek nearby improved designs in a procedure called local improvement. The paper demonstrates that this procedure substantially reduces the number of analyses required for the genetic search. The paper also demonstrates that the use of genetic algorithms helps find several alternate designs with similar performance, thus giving the designer a choice of alternatives.