A critical review of multi-objective optimization in data mining

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Abstract
This paper addresses the problem of how to evaluate the quality of a model built from the data in a multi-objective optimization scenario, where two or more quality criteria must be simultaneously optimized. A typical example is a scenario where one wants to maximize both the accuracy and the simplicity of a classification model or a candidate attribute subset in attribute selection. One reviews three very different approaches to cope with this problem, namely: (a) transforming the original multi-objective problem into a single-objective problem by using a weighted formula; (b) the lexicographical approach, where the objectives are ranked in order of priority; and (c) the Pareto approach, which consists of finding as many non-dominated solutions as possible and returning the set of non-dominated solutions to the user. One also presents a critical review of the case for and against each of these approaches. The general conclusions are that the weighted formula approach -- which is by far the most used in the data mining literature -- is to a large extent an ad-hoc approach for multi-objective optimization, whereas the lexicographic and the Pareto approach are more principled approaches, and therefore deserve more attention from the data mining community.

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