We suggest new approaches to reduce the number of fitness function evaluations in genetic algorithms (GAs) applied to multidisciplinary optimization of composite laminates. In the stacking sequence design of laminated structures, the design criteria are classified into two groups, which are layer combination dependent criteria and layer sequence dependent criteria. The memory approach is employed to lessen the number of fitness function evaluations for the identical design individuals that appear during the search. The permutation operator with local learning or random shuffling is applied to the same design individual to improve the fitness for layer sequence dependent criterion, while maintaining the same performance for layer combination dependent criterion. The numerical efficiency of the present method is validated by the sample problem of weight minimization of composite laminated plate under multiple design constraints.