Efficient Non-domination Level Update Method for Steady-State Evolutionary Multi-objective Optimization

Non-dominated sorting, which divides a population into several non-domination levels, is a basic step in many evolutionary multi-objective optimization 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, non-dominated sorting 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 nondomination level update method to reduce the cost for maintaining the non-domination level structure in steady-state evolutionary multi-objective optimization. Rather than perform the non-dominated sorting from scratch, our method only updates the nondomination levels of a limited number of solutions by extracting the knowledge from the current non-domination level structure. Notice that our non-domination level 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 nondominated sorting methods, our proposed method avoids a significant amount of unnecessary comparisons, not only in synthetic data sets, but also in real optimization scenarios. Index Terms Pareto dominance, non-domination level, non-dominated sorting, computational complexity, steady-state evolutionary multiobjective optimization