The first part of this paper served as a comprehensive survey of data mining methods that have been used to extract knowledge from solutions generated during multi-objective optimization. The current paper addresses three major shortcomings of existing methods, namely, lack of interactiveness in the objective space, inability to handle discrete variables and inability to generate explicit knowledge. Four data mining methods are developed that can discover knowledge in the decision space and visualize it in the objective space. These methods are (i) sequential pattern mining, (ii) clustering-based classification trees, (iii) hybrid learning, and (iv) flexible pattern mining. Each method uses a unique learning strategy to generate explicit knowledge in the form of patterns, decision rules and unsupervised rules. The methods are also capable of taking the decision maker's preferences into account to generate knowledge unique to preferred regions of the objective space. Three realistic production systems involving different types of discrete variables are chosen as application studies. A multi-objective optimization problem is formulated for each system and solved using NSGA-II to generate the optimization datasets. Next, all four methods are applied to each dataset. In each application, the methods discover similar knowledge for specified regions of the objective space. Overall, the unsupervised rules generated by flexible pattern mining are found to be the most consistent, whereas the supervised rules from classification trees are the most sensitive to user-preferences.
Bandaru, S., Ng, A. H. C., & Deb, K. (2017). Data mining methods for knowledge discovery in multi-objective optimization: Part B - New developments and applications. Expert Systems with Applications, 70, 119–138. https://doi.org/10.1016/j.eswa.2016.10.016