A regularity property-driven evolutionary algorithm for multiobjective optimization

When most existing multiobjective evolutionary algorithms tackle continuous multiobjective optimization problems, they pay more attention to the population distribution in the objective space and neglect the potential of high-quality solutions in the decision space. In fact, it has been demonstrated that a good approximation of both Pareto optimal set (PS) and Pareto front (PF) is capable of facilitating decision making, especially when preferences are not clearly defined by the decision-maker. However, since different problems may have different internal structures, achieving trade-offs between exploration and exploitation while accelerating convergence toward the PS and PF remains challenging. To address this issue, we propose an evolutionary algorithm that explicitly exploits the regularity properties of the multiobjective optimization problem in the decision space and the objective space. A feedback loop can be formed directly between two spaces, which aims to approximate the PS and the PF by approximating the PS manifold and the PF manifold, respectively. In addition, the uniform distribution of population is guaranteed by two mutually reinforcing diversity maintenance mechanisms. Our experimental results on a variety of benchmark problems and real -world problems demonstrate that the proposed method performs remarkable on problems with regularities but suffers from some limitations when solving some real-world problems.