Real-world optimization problems typically involve multiple objectives to be optimized simultaneously under multiple constraints and with respect to several variables. While multi-objective optimization itself can be a challenging task, equally difficult is the ability to make sense of the obtained solutions. In this two-part paper, we deal with data mining methods that can be applied to extract knowledge about multi-objective optimization problems from the solutions generated during optimization. This knowledge is expected to provide deeper insights about the problem to the decision maker, in addition to assisting the optimization process in future design iterations through an expert system. The current paper surveys several existing data mining methods and classifies them by methodology and type of knowledge discovered. Most of these methods come from the domain of exploratory data analysis and can be applied to any multivariate data. We specifically look at methods that can generate explicit knowledge in a machine-usable form. A framework for knowledge-driven optimization is proposed, which involves both online and offline elements of knowledge discovery. One of the conclusions of this survey is that while there are a number of data mining methods that can deal with data involving continuous variables, only a few ad hoc methods exist that can provide explicit knowledge when the variables involved are of a discrete nature. Part B of this paper proposes new techniques that can be used with such datasets and applies them to discrete variable multi-objective problems related to production systems.

No abstract

No abstract

Evolutionary optimisation of noisy multi-objective problems using confidence-based dynamic resampling. European Journal of Operational AbstractMany real-world optimisation problems approached by evolutionary algorithms are subject to noise. When noise is present, the evolutionary selection process may become unstable and the convergence of the optimisation adversely affected. In this paper, we present a new technique that efficiently deals with noise in multi-objective optimisation. This technique aims at preventing the propagation of inferior solutions in the evolutionary selection due to noisy objective values. This is done by using an iterative resampling procedure that reduces the noise until the likelihood of selecting the correct solution reaches a given confidence level. To achieve an efficient utilisation of resources, the number of samples used per solution varies based on the amount of noise in the present area of the search space. The proposed algorithm is evaluated on the ZDT benchmark problems and two complex real-world problems of manufacturing optimisation. The first realworld problem concerns the optimisation of engine component manufacturing in aviation industry, while the second real-world problem concerns the optimisation of a camshaft machining line in automotive industry. The results from the optimisations indicate that the proposed technique is successful in reducing noise, and it competes successfully with other noise handling techniques.

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.