Asymmetric distances to improve n-dimensional Pareto fronts graphical analysis

作者：Blasco Xavier^*; Reynoso Meza Gilberto; Sanchez Perez Enrique A; Sanchez Perez Juan V

来源：Information Sciences, 2016, 340: 228-249.

DOI：10.1016/j.ins.2015.12.039

• Multi-criteria decision-making
• Asymmetric distance
• Multi-objective optimization
• Decision-making tools
• n-dimensional Pareto front
• n-dimensional Pareto front visualization

Visualization tools and techniques to analyze n-dimensional Pareto fronts are valuable for designers and decision makers in order to analyze straightness and drawbacks among design alternatives. Their usefulness is twofold: on the one hand, they provide a practical framework to the decision maker in order to select the preferable solution to be implemented; on the other hand, they may improve the decision maker's design insight, i.e. increasing the designer's knowledge on the multi-objective problem at hand. In this work, an order based asymmetric topology for finite dimensional spaces is introduced. This asymmetric topology, associated to what we called asymmetric distance, provides a theoretical and interpretable framework to analyze design alternatives for n-dimensional Pareto fronts. The use of this asymmetric distance will allow a new way to gather dominance and relative distance together. This property can be exploited inside interactive visualization tools. Additionally, a composed norm based on asymmetric distance has been developed. The composed norm allows a fast visualization of designer preferences hypercubes when Level Diagram visualization is used for multidimensional Pareto front analysis. All these proposals are evaluated and validated through different engineering benchmarks; the presented results show the usefulness of this asymmetric topology to improve visualization interpretability.

• 出版日期2016-5-1