A Robust Method of Choosing a Unique Solution within Pareto Front

Abstract

This paper proposes a simple and effective approach for identifying and selecting a single set of optimal values of the variables that compose the models subjected to the process improvement, throughout an iterative manner, without the designer’s intervention. The proposed algorithm is set to identify the extreme values of Pareto Front, to which 100% is assigned to the best values obtained for studied functions, and 0% to the lowest ones. Related to these maximum/minimum values, the other items from the front receive a percentage which is equivalent to their size. The next steps involve adding up these percentages for each set of values in particular, and then focusing over the three largest sums. The last step in choosing the solution is weighing the percentages obtained, after processing the data considering the homogeneity given by the standard deviation function, because it assumes that there are no criteria for the ranking of the objective functions, so that none of them can be maximized or minimized to the detriment of the others. The preferred solution is the one that has the standard deviation’s lowest value of the three sums selected. The algorithm NSGA-II and Comsol Multiphysics program were used to identify the edge points.