A population-based artificial immune system for numerical optimization

Many immue-inspired algorithms are based on the abstractions of one or several immunology theories, such as clonal selection, negative selection, positive selection, rather than the whole process of immune response to solve computational problems. In order to build a general computational framework by simulating immune response process, this paper introduces a model for population-based artificial immune systems, termed as PAIS, and applies it to numerical optimization problems. PAIS models the dynamic process of human immune response as a quaternion (G, I, R, Al), where G denotes exterior stimulus or antigen, I denotes the set of valid antibodies, R denotes the set of reaction rules describing the interactions between antibodies, and Al denotes the dynamic algorithm describing how the reaction rules are applied to antibody population. Some general descriptions of reaction rules including the set of clonal selection rules and the set of immune memory rules are introduced in PAIS. Based on these reaction rules, a dynamic algorithm, termed as PAISA, is designed for numerical optimization. In order to validate the performance of PAISA, nine benchmark functions with 20–10,000 dimensions and a practical optimization problem, optimal approximation of linear systems are solved by PAISA, successively. The experimental results indicate that PAISA has high performance in optimizing some benchmark functions and practical optimization problems.