**7. Summary**

This work is devoted to recombination for an NNIA algorithm. We propose three recombinations, inspired by the BSA algorithm crossing operator when adapting input populations.

In the first NNIA+X1 algorithm, the clonal population and an extended active population are concerned, when the extended active population is founded by duplicating individual antibodies.

In the second algorithm, NNIA+X2, recombination is achieved by using the clonal population and itself.

The NNIA+X3 algorithm uses the clonal population and an extended working population, which finds by duplicating individual antibodies and a proportion of random individuals. From this algorithm, a certain degree of mutation is carried out. The results obtained for the benchmark, ZDT, and DTLZ functions show that our proposed algorithm NNIA+X3 can accelerate the speed of convergence and maintain the desirable diversity, especially when solving problems with many local Pareto-optimal fronts. The experimental results of this algorithm to solve the problems of bi-objectives and three-objectives of optimization of 10 bar trellis structure indicate that the proposed NNIA+X3 surpasses the NNIA algorithm in terms of convergence rate and of course of quality of the solution.
