Development of a Multiobjective Optimization Algorithm Using Data Distribution Characteristics

The weighting method and goal programming require weighting factors or target values to obtain a Pareto optimal solution. However, it is difficult to define these parameters, and a Pareto solution is not guaranteed when the choice of the parameters is incorrect. Recently, the Mahalanobis Taguchi System (MTS) has been introduced to minimize the Mahalanobis distance (MD). However, the MTS method cannot obtain a Pareto optimal solution. We propose a function called the skewed Mahalanobis distance (SMD) to obtain a Pareto optimal solution while retaining the advantages of the MD. The SMD is a new distance scale that multiplies the skewed value of a design point by the MD. The weighting factors are automatically reflected when the SMD is calculated. The SMD always gives a unique Pareto optimal solution. To verify the efficiency of the SMD, we present two numerical examples and show that the SMD can obtain a unique Pareto optimal solution without any additional information.