We generalize the notion of λ-superstrings, presented in a previous paper, to the notion of weighted λ-superstrings. This generalization entails an important improvement in the applications to vaccine designs, as it allows epitopes to be weighted by their immunogenicities. Motivated by these potential applications of constructing short weighted λ-superstrings to vaccine design, we approach this problem in two ways. First, we formalize the problem as a combinatorial optimization problem (in fact, as two polynomially equivalent problems) and develop an integer programming (IP) formulation for solving it optimally. Second, we describe a model that also takes into account good pairwise alignments of the obtained superstring with the input strings, and present a genetic algorithm that solves the problem approximately. We apply both algorithms to a set of 169 strings corresponding to the Nef protein taken from patiens infected with HIV-1. In the IP-based algorithm, we take the epitopes and the estimation of the immunogenicities from databases of experimental epitopes. In the genetic algorithm we take as candidate epitopes all 9-mers present in the 169 strings and estimate their immunogenicities using a public bioinformatics tool. Finally, we used several bioinformatic tools to evaluate the properties of the candidates generated by our method, which indicated that we can score high immunogenic λ-superstrings that at the same time present similar conformations to the Nef virus proteins.