In this paper, we propose a novel hybrid multi-objective immune algorithm with adaptive differential evolution, named ADE-MOIA, in which the introduction of differential evolution (DE) into multi-objective immune algorithm (MOIA) combines their respective advantages and thus enhances the robustness to solve various kinds of MOPs. In ADE-MOIA, in order to effectively cooperate DE with MOIA, we present a novel adaptive DE operator, which includes a suitable parent selection strategy and a novel adaptive parameter control approach. When performing DE operation, two parents are respectively picked from the current evolved and dominated population in order to provide a correct evolutionary direction. Moreover, based on the evolutionary progress and the success rate of offspring, the crossover rate and scaling factor in DE operator are adaptively varied for each individual. The proposed adaptive DE operator is able to improve both of the convergence speed and population diversity, which are validated by the experimental studies. When comparing ADE-MOIA with several nature-inspired heuristic algorithms, such as NSGA-II, SPEA2, AbYSS, MOEA/D-DE, MIMO and D<sup>2</sup>MOPSO, simulations show that ADE-MOIA performs better on most of 21 well-known benchmark problems.
Lin, Q., Zhu, Q., Huang, P., Chen, J., Ming, Z., & Yu, J. (2015). A novel hybrid multi-objective immune algorithm with adaptive differential evolution. Computers and Operations Research, 62, 95–111. https://doi.org/10.1016/j.cor.2015.04.003