Immune normalized-normal-constraint method and its application
免疫标准化正规化约束方法及其应用

To accelerate the solving process of the multi-objective optimization problems by using the normalizednormal-constraint (referred to as NNC) method, we propose an immune algorithm called the IA NNC method by combining the immune algorithm with the NNC method. It uses the clonal-selection algorithm to solve the single-objective optimization problem by the NNC method; and extracts vaccines from the single-objective optimization process corresponding to the nearby points on the utopia plane. These vaccines are inoculated to the initial antibody population by using the vaccineinoculation technique of the immune algorithm. By the combination of the above two methods, the IA NNC algorithm generates the Pareto solution-set more rapidly. Furthermore, the convergence of IA NNC method is analyzed. Finally, the IA NNC method is applied to optimize the multi-objective scheduling for the tandem cold rolling; it generates the Pareto solution-set for the rolling schedules with less time consumption compared with the genetic algorithm-based NNC method.