Various preference-based multi-objective evolutionary algorithms have been developed to help a decision-maker search for his/her preferred solutions to multi-objective problems. In most of the existing approaches the decision-maker preferences are formulated either by mathematical expressions such as the utility function or simply by numerical values such as aspiration levels and weights. However, in some sense a decision-maker may find it easier to specify preferences visually by drawing rather than using numbers. This paper introduces such a method, namely, the brushing technique. Using this technique the decision-maker can specify his/her preferences easily by drawing in the objective space. Combining the brushing technique with one existing algorithm PICEA-g, we present a novel approach named iPICEA-g for an interactive decision-making. The performance of iPICEA-g is tested on a set of benchmark problems and is shown to be good. 
The iPICEA-g: a new hybrid evolutionary multi-criteria decision making approach using the brushing technique