Artificial immune system in dynamic environments solving time-varying non-linear constrained multi-objective problems

A bio-inspired artificial immune system is developed to track dynamically the Pareto fronts of time-varying constrained multi-objective problems with changing variable dimensions. It executes in order T-module, B-module, and M-module within a run period. The first module is designed to examine dynamically whether the environment changes or whether a change takes place in the optimization problem, while creating an initial population by means of the history information. Thereafter, the second one is a loop of optimization that searches for the desired non-dominated front of a given environment, in which the evolving population is sorted into several subpopulations. Each of such subpopulations, relying upon the population diversity, suppresses its redundant individuals and evolves the winners. The last one stores temporarily the resultant non-dominated solutions of the environment that assist T-module to create some initial candidates helpful for the coming environment. These dynamic characteristics, along with the comparative experiments guarantee that the artificial immune system can track adaptively the time-varying environment and maintain the diversity of population while being of potential use for complex dynamic constrained multi-objective problems.