Visualization of the Non-Dominated Solutions in Many-Objective Optimization
Minghui Xiong, Wei Xiong, Ping Jian · 2019
The high dimensionality of many-objective optimization makes it difficult to represent the relationships between objectives and solutions of such problems. The overlapping and visual confusion problems occur when mapping high-dimensional solution sets to two-dimensional planes in the conventional parallel coordinate plots, which adds difficulty for decision maker choosing a preference solution. This paper introduces a visualization method for many-objective optimization non-dominated solution sets based on fuzzy theory and electromagnetic field clustering. The fuzzy theory is used to classify the non-dominated solution set, and each rating grade denotes the preference degree of decision maker. Visual clustering is conducted by electromagnetic field clustering, the solutions in the same cluster attract each other while solutions between clusters are mutually exclusive. The distribution structure of preference solution is highlighted through brightness gradient enhancement to optimize the visual perception. The experimental results show that the visualization plot of the proposed method is more clear and intuitive than the original plot, which is convenient for decision makers to discover the pattern of solution sets and make final decisions.