Data Mining and Knowledge Discovery Handbook, 2 Edition part 42. Knowledge Discovery demonstrates intelligent computing at its best, and is the most desirable and interesting end-product of Information Technology. To be able to discover and to extract knowledge from data is a task that many researchers and practitioners are endeavoring to accomplish. There is a lot of hidden knowledge waiting to be discovered – this is the challenge created by today’s abundance of data. Data Mining and Knowledge Discovery Handbook, 2nd Edition organizes the most current concepts, theories, standards, methodologies, trends, challenges and applications of data mining (DM) and knowledge discovery. | 390 Alex A. Freitas the quality of a product and minimize its manufacturing cost in a factory. In the context of data mining a typical example is in the data preprocessing task of attribute selection to minimize the error rate of a classifier trained with the selected attributes and to minimize the number of selected attributes. The conventional approach to cope with such multi-objective optimization problems using evolutionary algorithms is to convert the problem into a singleoptimization problem. This is typically done by using a weighted formula in the fitness function where each objective has an associated weight reflecting its relative importance. For instance in the above example of two-objective attribute selection the fitness function could be defined as say 2 3 classification-error 1 3 Num-ber_of_selected_attributes . However this conventional approach has several problems. First it mixes non-commensurable objectives classification error and number of selected attributes in the previous example into the same formula. This has at least the disadvantage that the value returned by the fitness function is not meaningful to the user. Second note that different weights will lead to different selected attributes since different weights represent different trade-offs between the two conflicting objectives. Unfortunately the weights are usually defined in an ad-hoc fashion. Hence when the EA returns the best attribute subset to the user the user is presented with a solution that represents just one possible trade-off between the objectives. The user misses the opportunity to analyze different trade-offs. Of course we could address this problem by running the EA multiple times with different weights for the objectives in each run and return the multiple solutions to the user. However this would be very inefficient and we would still have the problems of deciding which weights should be used in each run how many runs we should perform and so how many solutions should
