Composite materials nowadays find their place in many fields due to their high functionality in production and applications. In particular, there have been a growing interest in the use of Carbon Nanotubes (CNTs) as composite reinforcement material in order to impart high performance properties. In this thesis 16-ply, symmetric and balanced, CNT-fiber-reinforced composite laminate was studied for minimum weight design. As a novelty, different minimum weight design approaches were presented and compared as two different problems within the context of buckling problem based on the classical laminate theory. Single- and multi-objective genetic algorithms were used, a proposed simulated annealing algorithm adapted to integer-problems was tested as well. The effective material properties of the laminate were determined by using fiber micromechanical and Halpin-Tsai models simultaneously for epoxy, glass materials that were used as matrix, fibers, respectively, in addition to CNTs. Critical buckling load factor to weight ratio was considered as design efficiency criterion used in evaluation. In the first problem, the maximization of the critical buckling load as a single-objective problem with the discrete fiber angles as design variables. In this problem, the CNT and fiber contents were considered as functionally distributed in each ply. In the second problem, critical buckling load factor and weight were taken as two objectives, in which weight fraction of CNTs and volume fraction of fibers in addition to discrete fiber angles were taken as design variables. Finally, it was demonstrated how distribution of CNTs and fibers influence the design efficiency, and that multi-objective approach provides higher design efficiency in comparison with the single-objective alternative.