In the past, one or several antibodies with the highest affinities were used as memory cells by a traditional immune algorithm. This method often retained a relatively similar antibody population, which made many important immune information lost and might decrease the diversity of memory cells. However, the diversity might determine the future evolutionary direction of the antibody population and was used to avoid the precocity of the local optimum. Therefore, it is necessary to improve the immune algorithm to save enough immune information and ensure the diversity of memory cell information. Thus, the traditional immune algorithm was improved to keep certain distances among memorized antibodies and select the antibodies with high affinities (not only the highest ones) as the memory cells.

The theory of information entropy or the Euclid distance between two antibody coding strings were commonly used as the antibody similarity judgment methods. However, these methods only judged the genes with the same gene positions in an antibody, and couldn’t represent the relative positional relationship of the gene arrangement. Therefore, the traditional methods were not good at judging the similarity among the antibody-solutions of the path optimization problem. In the improved immune algorithm, in consideration of the relative position, it was judged whether or not the antibodies were similar according to whether or not the length of the same gene fragment between the antibodies exceeded the threshold.

With the real number coding, the dynamic vaccine extraction and vaccination strategy were proposed, in order to form a vaccine library by dynamically extracting excellent gene fragments as vaccines in a memory cell bank of excellent antibodies. Then, in the process of immune gene manipulation, the vaccine was vaccinated with a certain probability and combined with the cross mutation procedure to update the antibodies with poor affinities. In a better way, this improved strategy retained the excellent genes and expanded the search space of the algorithm to increase the search ability of the algorithm, while maintaining the diversity of the algorithm and avoiding the possibility that the algorithm falls into any local optimum.

Vaccines were utilized to activate the production of useful antibodies, which were useful in eliminating viruses and defending against invasions into the body in time. The extraction of the vaccine in the traditional immune algorithm was based on the basic feature extraction from the prior knowledge of the target problem and the valid information extraction from the genes of the best individuals in the process of population evolution. The acquisition of the vaccine ensured that the antibody retained excellent characteristics during the mutation process, so the proportion of the antibody genes were effectively optimized and the antibodies evolved rapidly.

In the improved immune algorithm, m antibodies (m < N, N represents the number of memory antibodies in the memory antibody group) were randomly selected from the memory antibody group M(t), and the common gene fragment of m antibodies was recorded as one vaccine in the vaccine library V(t), which retained the excellent gene fragment of the memory antibody. With the evolution of the population, dynamic updating of the vaccine library for vaccine extraction better preserved the excellent antibody gene and accelerated the convergence speed of the immune algorithm.

In the traditional immune algorithm, the vaccination operation was before the cross-variation operation, and the partial antibodies were randomly vaccinated. However, when the vaccine immunization operation was insufficient, the loss of diversity was accelerated and the premature convergence of the traditional immune algorithm occurred. Moreover, the traditional crossover operator randomly selected the intersection position, and this operation might destroy the structures of other excellent genes, after a large number of crossover operations. This operation might generate a large number of infeasible offspring individuals, which resulted in the premature convergence or redundant iteration of the traditional immune algorithm. In the improved immune algorithm, unsuitable antibodies were vaccinated by the probability-based crossover operation to optimize the antibody population. This improved crossover operation better retained the excellent genes and accelerated the optimal-solution searching of the immune algorithm. By combining the mutation operation, the diversity of the improved immune algorithm was guaranteed, and the prematurity of the local optimum was prevented in the searching procedure of the improved immune algorithm.

In the traditional immune algorithm, the vaccination operation was performed by random injection, which was not conducive to the optimization of antibodies, because the location of random injections might easily destroy the sequences of the original antibodies. Since each vaccine itself already contained the location information, the location information was injected by the improved immune algorithm at the time of vaccination, so that the positions of the injected vaccines were more reasonable and useful.

Like the traveling salesman problem, the shortest path optimization problem in the deep immune learning of gene network was represented in Figure 2. Given n relative nodes in the gene network graph, the shortest path was found to generate new pathway for reactivating the immune response against such non-self as tumors, as described mathematically below.

min f = ∑ i = 1 n − 1 d ( c i , c i + 1 ) + d ( c n , c 1 ) (1)

Here, s t . c i ∈ C , C = { c 1 , c 2 , c 3 , … , c n } , i = 1 , 2 , 3 , … , n , C denoted the node collection, c_i represented the number of the node.

In order to evaluate the merits of individuals, the affinity was calculated below.

a f f ( b ) = 75.6 × L × n / l e n g t h ( b ) (2)

Here, L denoted the side length of the smallest square containing all nodes, n denoted the number of nodes, and l e n g t h ( b ) denoted the path length corresponding to the antibody.

In the improved immune algorithm, suitable distance between one memory antibody and another was kept, and the suitable antibody with the highest fitness was saved as the memory cell. For example, among the antibody populations, the antibody A with the highest retention affinity was a memory cell. Afterwards, the antibody B with the second highest affinity was compared with the comparative antibody A. When the same gene fragment of A and B exceeded the certain

threshold, which was defined as 80% of the length of the antibody, the antibodies A and B were regarded as similar, and the antibody B wasn’t recorded as a memory cell. Otherwise, the antibody B was saved as a memory cell. Furthermore, the antibody C with the third highest affinity in the antibody group was compared with the remaining memory antibodies to determine whether there was a same gene fragment exceeding the threshold. If there was not any same gene fragment exceeding the threshold, the memory antibody group was added. By analogy, a memory antibody population M(t) of N memory antibodies was generated.

In the improved immune algorithm, the two parts of the antibody population were processed by two steps of immunological manipulation.

1) The partial neighborhood search strategy was used for the high affinity anterior NP/4 antibodies in the optimization.

If a large number of random cross-mutation operations were performed on antibodies with high affinity, the orders of the excellent genes in these antibodies would be destroyed, which lead to the premature convergence or redundant iteration of the algorithm and then failed in finding the optimal solution. The local neighborhood search strategy was useful for better preserving the good genes, which was helpful to further accelerate the convergence of the improved immune algorithm and shorten the running time of searching the optimal solution. This operation was designed to generate a new local domain progeny individual by adopting a right neighbor gene exchange method for each gene in the antibody. For example, the antibody S = (1, 6, 5, 4, 2, 3) exchanged gene 1 with its right domain gene to generate a new individual S’ = (6, 1, 5, 4, 2, 3).Therefore, the local neighborhood searching operation generated some local neighborhood progeny individuals, and selected the neighbor individuals with the greatest fitness to compare with the matrix. Afterwards, the higher affinity was used to update the matrix.

2) The proposed dynamic vaccine strategy was employed for 3NP/4 antibodies with worse affinity in the antibody population.

In the cloned antibody, the vaccine was optimized by the probability of Pv to optimize the antibody. And the search space was expanded by a random multiple-point two-point crossover operation to ensure the diversity of the population and to find better antibodies. The vaccination was performed according to the position of the first gene of the vaccine in the original antibody, and the part of the original antibody that conflicted with the vaccine was deleted. The specific operation flow chart is shown in Figure 3.

The immune selection operation was designed according to the natural selection mechanism, by retaining excellent antibodies and optimizing the population. In the improved immune algorithm, two parts of the immune gene operations were compared with each other.