There are a large number of engineering optimization problems in real world, whose input-output relationships are vague and indistinct. Here, they are called black box function optimization problem (BBFOP). Then, inspired by the mechanism of neuroendocrine system regulating immune system, BP neural network modified immune optimization algorithm (NN-MIA) is proposed. NN-MIA consists of two phases: the first phase is training BP neural network with expected precision to confirm input-output relationship and the other phase is immune optimization phase, whose aim is to search global optima. BP neural network fitting without expected fitting precision could be replaced with polynomial fitting or other fitting methods within expected fitting precision. Experimental simulation confirms global optimization capability of MIA and the practical application of BBFOP optimization method.

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A novel multi-population coevolution immune optimization algorithm (MCIA) is proposed to solve numerical and engineering optimization problem in real world. MCIA is inspired by the mechanism that how neuroendocrine system affects T cells and B cells in immune system to eliminate the danger and the main idea of MCIA is to promote three populations, population B, population T and assistant population A, to coevolution through self-adjusted clone operator, the applied dislocation arithmetic crossover, cloud self-adapting mutation operator and local search operator to produce lymphocyte with high affinity. Self-adjusted clone operator and selecting elite elements in the memory population enable the search space be broadened and compressed, cloud self-adapting mutation operator characterized with randomness, stable topotaxis and local search technique enable global and local search be integrated to find the global optima with high population diversity. Therefore, several operators enable MCIA enjoy the capability of broadening the elite search space, boosting the global and local search around elites in search space. The performance comparisons of MCIA with three known immune algorithms and other three optimization algorithms in optimizing twelve benchmark functions indicate that MCIA is an effective algorithm for solving global optimization problems with high precision, good robustness and low time complexity.

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