Danger theory based artificial immune system solving dynamic constrained single-objective optimization

In this paper, we propose an artificial immune system (AIS) based on the danger theory in immunology for solving dynamic nonlinear constrained single-objective optimization problems with time-dependent design spaces. Such proposed AIS executes orderly three modules—danger detection, immune evolution and memory update. The first module identifies whether there are changes in the optimization environment and decides the environmental level, which helps for creating the initial population in the environment and promoting the process of solution search. The second module runs a loop of optimization, in which three sub-populations each with a dynamic size seek simultaneously the location of the optimal solution along different directions through co-evolution. The last module stores and updates the memory cells which help the first module decide the environmental level. This optimization system is an on-line and adaptive one with the characteristics of simplicity, modularization and co-evolution. The numerical experiments and the results acquired by the nonparametric statistic procedures, based on 22 benchmark problems and an engineering problem, show that the proposed approach performs globally well over the compared algorithms and is of potential use for many kinds of dynamic optimization problems.