A visualisation method for Pareto Front approximations in many-objective optimisation

Visualisation of Pareto Front (PF) approximations of many-objective optimisation problems (MaOP) is critical in understanding and solving a MaOP. Research is ongoing on developing effective visualisation methods with desired properties, such as simultaneously revealing dominance relations, PF shape, and the diversity of approximations. State-of-the-art visualisation methods in the literature often retain some of the preferred properties, but there are still shortfalls to address others. A new visualisation method is proposed in this paper, which covers the majority of the desired properties for visualisation methods. The proposed method is based on displaying PF approximations via projections on a reference vector versus distances to the same reference vector. The reference vector is created using nominal Ideal and Nadir points of existing nondominated PF approximation sets. MaF benchmark problems are used to demonstrate the effectiveness; results show that the proposed method exhibits a more balanced performance than the state-of-the-art in capturing desired visualisation properties.