Flexibility of design variables to pareto-optimal solutions in multi objective optimization problems

In this paper, we propose the concept of the flexibility of design variables to Pareto-optimal solutions in Multi-Objective Optimization problems. In addition, we introduce a method for measurement of the flexibility of design variables to Pareto-optimal solutions. Increases in the number of design variables usually result in a wide variety of optimum solutions. However, when the flexibilities of some design variables are small, the contributions of these design variables are also very small. This means that the same Pareto-optimal solutions can be derived without these parameters. Therefore, it is very important to find the flexibility of the design variables to the Pareto-optimal solutions. To find the flexibility, the values of one of the design variables are changed, while those of the remaining parameters are fixed. In this procedure, it is very important to determine the fixed values. We describe these procedures to determine the flexibility of the design variable to the Pareto-optimal solutions. Finally, we illustrate using the diesel engine fuel emission scheduling problem that the Paretooptimal solutions can be derived with only the design variables whose flexibilities are high.