Efficient Nondomination Level Update Method for Steady-State Evolutionary Multiobjective Optimization

Nondominated sorting (NDS), which divides a population into several nondomination levels (NDLs), is a basic step in many evolutionary multiobjective optimization (EMO) algorithms. It has been widely studied in a generational evolution model, where the environmental selection is performed after generating a whole population of offspring. However, in a steady-state evolution model, where a population is updated right after the generation of a new candidate, the NDS can be extremely time consuming. This is especially severe when the number of objectives and population size become large. In this paper, we propose an efficient NDL update method to reduce the cost for maintaining the NDL structure in steady-state EMO. Instead of performing the NDS from scratch, our method only updates the NDLs of a limited number of solutions by extracting the knowledge from the current NDL structure. Notice that our NDL update method is performed twice at each iteration. One is after the reproduction, the other is after the environmental selection. Extensive experiments fully demonstrate that, comparing to the other five state-of-the-art NDS methods, our proposed method avoids a significant amount of unnecessary comparisons, not only in the synthetic data sets, but also in some real optimization scenarios. Last but not least, we find that our proposed method is also useful for the generational evolution model.