Hyper multi-objective evolutionary algorithm for multi-objective optimization problems

Multi-objective optimization problems (MOPs) are very common in practice. To solve MOPs, many kinds of multi-objective evolutionary algorithms (MOEAs) are proposed. However, different MOEAs have different performances for different MOPs. Therefore, it is a time-consuming task to choose a suitable MOEA for a given problem. To pursue a competitive performance for various kinds of MOPs, in this paper, we propose a framework named hyper multi-objective evolutionary algorithm (HMOEA). In this framework, more than one MOEAs are employed, which is more adaptive to different problems. In HMOEA, the population will be randomly divided into several groups. In each group, a selected MOEA will be implemented. Therefore in the framework, the number of groups is equal to the number of the employed MOEAs. The size of each group, namely the size of sub-population in each group, is adjusted according to the corresponding MOEA's performance. If a MOEA performs well, its corresponding group will have a large size group, which means the MOEA obtains more computational resources. On the contrary, if a MOEA has a poor performance in current generation, its corresponding group will obtain only a few individuals. Although a MOEA does not perform very well in current generation, the framework will not abandon this MOEA, but provide it a group that has predefined small size. The reason is that an involvement of different MOEAs will increase the diversity of algorithms in the hyper framework, which is helpful for HMOEA to avoid local optima and also can help HMOEA be adaptive to different phases in the whole optimization process. To compare MOEAs' performances, coverage rate (CR) metric is used to evaluate the quality of MOEA and therefore decides the size of group for each MOEA. In numerical experiments, ZDT benchmarks are employed to test the proposed hyper framework. Several classic MOEAs are also used in comparisons. According to the comparison results, HMOEA can achieve very competitive performances, which demonstrates that the design is feasible and effective to solve MOPs.