Efficient Non-domination Level Update Approach for Steady-State Evolutionary Multiobjective Optimization

Non-dominated sorting, dividing the population into several non-domination levels, is a basic step for many Pareto-based evolutionary multiobjective optimization (EMO) algorithms. Different from the generational scheme, where the selection of next parents is conducted after the generation of a population of offspring, the steady-state scheme updates the parent population whenever a new candidate solution is reproduced. As a consequence, non-dominated sorting can be a computationally expensive part in steady-state EMO algorithmwhen the population size or number of objectives becomes large. In fact, before introducing a new candidate solution, the non-domination level structure of the parent population is already known from the last environmental selection. Thus, conducting non-dominated sorting from scratch, each time, obviously does not take advantages of the existing knowledge and results in a severe waste of computational resources. In view of this, we propose an efficient non-domination level update (ENLU) mechanism for steady-state EMO algorithm. By extracting the knowledge of the non-domination level structure of the parent population, ENLU mechanism only updates the nondomination levels of necessary solutions during the update procedure, including the addition of a new candidate solution into the parent popualtion and the elimination of an inferior solution. Theoretical analysis show the time complexity of ENLU mechanism is O(mN √ N) in the worst-case and O(m) in the best case. Extensive experiments empirically demonstrate that ENLU mechanism is more computationally efficient than the fast non-dominated sorting procedure, as it saves 103 to 104 magnitude of unnecessary dominance comparisons.