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Mathematical Problems in Engineering
Volume 2015, Article ID 608325, 11 pages
Research Article

Entropy-Based Weighting for Multiobjective Optimization: An Application on Vertical Turning

1Institute of Production Engineering and Management, Federal University of Itajuba, BPS Avenue 1303, 37500-903 Itajuba, MG, Brazil
2Mahle Metal Leve S/A, Itajuba, MG, Brazil

Received 15 May 2015; Revised 13 July 2015; Accepted 22 July 2015

Academic Editor: Giovanni Falsone

Copyright © 2015 Luiz Célio Souza Rocha et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In practical situations, solving a given problem usually calls for the systematic and simultaneous analysis of more than one objective function. Hence, a worthwhile research question may be posed thus: In multiobjective optimization, what can facilitate for the decision maker choosing the best weighting? Thus, this study attempts to propose a method that can identify the optimal weights involved in a multiobjective formulation. The proposed method uses functions of Entropy and Global Percentage Error as selection criteria of optimal weights. To demonstrate its applicability, this method was employed to optimize the machining process for vertical turning, maximizing the productivity and the life of cutting tool, and minimizing the cost, using as the decision variables feed rate and rotation of the cutting tool. The proposed optimization goals were achieved with feed rate = 0.37 mm/rev and rotation = 250 rpm. Thus, the main contributions of this study are the proposal of a structured method, differentiated in relation to the techniques found in the literature, of identifying optimal weights for multiobjective problems and the possibility of viewing the optimal result on the Pareto frontier of the problem. This viewing possibility is very relevant information for the more efficient management of processes.