Performance Comparison of Constrained Multi-objective Evolutionary Algorithms on Artificial and Real-world Benchmarking Problems

Real-world multi-objective optimization problems usually have multiple constraints. To solve constrained multi-objective optimization problems (CMOPs), researchers have proposed various constrained multi-objective evolutionary algorithms (CMOEAs). These CMOEAs explicitly or implicitly assume that there are large infeasible regions in the objective space between the initial population and the constrained Pareto front (CPF), and that the CPF is close to the unconstrained Pareto front (UPF). Thus, some special techniques, such as the push-and-pull strategy and the coevolution strategy, are used to traverse large infeasible regions to find the UPF. However, it is unclear whether these characteristics also exist in real-world CMOPs, and the state-of-the-art algorithms performing well on artificial CMOPs also work well on real-world CMOPs. This paper first compares the performance of fifteen CMOEAs on artificial and real-world CMOPs. It is observed that performance comparison results on real-world CMOPs are clearly different from those on artificial CMOPs. This observation shows the importance of using real-world CMOPs in benchmarking studies. Next, the comparison results are analyzed by using the difference between artificial and real-world CMOPs. It is observed that most of the examined real-world CMOPs do not have large infeasible regions near the CPFs, and the CPFs of some real-world CMOPs are not close to the UPFs. It is also observed that feasible solutions of some real-world CMOPs are difficult to obtain, and NSGA-II performs better than recently-proposed CMOEAs on these difficult real-world problems. This observation suggests the necessity of strong search ability to find feasible solutions for real-world applications.