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A bio-inspired artificial immune system is developed to track dynamically the Pareto fronts of timevarying 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.

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An immune optimization algorithm, based on the model of biological immune system, is proposed to solve multiobjective optimization problems with multimodal nonlinear constraints. First, the initial population is divided into feasible nondominated population and infeasible/dominated population. The feasible nondominated individuals focus on exploring the nondominated front through clone and hypermutation based on a proposed affinity design approach, while the infeasible/dominated individuals are exploited and improved via the simulated binary crossover and polynomial mutation operations. And then, to accelerate the convergence of the proposed algorithm, a transformation technique is applied to the combined population of the above two offspring populations. Finally, a crowded-comparison strategy is used to create the next generation population. In numerical experiments, a series of benchmark constrained multiobjective optimization problems are considered to evaluate the performance of the proposed algorithm and it is also compared to several state-of-art algorithms in terms of the inverted generational distance and hypervolume indicators. The results indicate that the new method achieves competitive performance and even statistically significant better results than previous algorithms do on most of the benchmark suite.