Three-way decision-making based on index threshold acquisition

Currently, the fact that the equilibrium between diversity and convergence deteriorates as the count of objectives rises is now a significant barrier in the multi-objective optimisation problem. Additionally, conventional techniques for determining three-way decision thresholds rely on real-valued state-based cost loss functions that cannot handle intricate real-world scenarios. The three decisions of the index threshold are used to design a new environment-selecting technique and a multi-objective optimisation algorithm (MaOEA-TWD-IT) in this paper to address the aforementioned issues. In more detail, the convergence threshold and diversity threshold are first obtained using the index thresholds acquisition method, and then the solutions owning better diversity and convergence are chosen based on three decision-making techniques. By assessing the smallest distance between individuals and other solutions, the diversity of solutions is revealed. The solutions' convergence is quantified with the distance between the solutions and the ideal solution. Finally, the MaOEA-TWD-IT method suggested in our study also performs excellently and is able to successfully equilibrium population diversity and convergence, according to experimental results.