Development of Parallel Multiobjective Genetic algorithm for Designing Flexible Systems

在柔性系统中，目标对象的值可以在设计变量数量少、变化小的情况下发生变化。提出了多目标优化问题中设计变量对Pareto最优解的柔性概念。以下步骤是评估设计变量对帕累托最优解的灵活性的方法。1）制定多目标问题。这个问题是解决所有的设计变量。在这种情况下，没有设计变量值是固定的。2）导出的帕累托最优解与特定目标函数的值一起沿着。3）从排列的帕累托最优解中确定五个点。五个点之间的距离应该是相同的。4）在每个点上，一个设计变量被改变。在这种情况下，其他解的值是固定的。假定设计变量的范围。在此条件下，重新进行多目标优化，得到新的Pareto最优解。这些新的Pareto最优解沿着确定，等于该点的柔度。5）推导出所有设计变量和所有五个点的柔度，由此推导出设计变量对Pareto最优解的柔度。将所提出的方法应用于柴油机燃料排放调度问题，证实了帕累托最优解可以得到只有设计变量的灵活性高。

In flexible system, values of target object can be changed with small number and little change of design variables. In this research, the concept of the flexibility of design variables to Pareto-optimal solutions in Multi-Objective Optimization problems was proposed. The following procedure is a method for evaluation of the flexibility of design variables to the Pareto-optimal solutions.1) Formulate the multi-objective problem. This problem is solved using all the design variables. In this case, no design variable values are fixed.2) The derived Pareto-optimal solutions are sorted along with the value of a certain object function.3) Five points are determined from the sorted Pareto optimal solutions. The distances between the five points should be the same.4) In each point, one of the design variables is changed. In this case, the values of the other solutions are fixed. The range of the design variable is assumed. In this condition, the multi-objective optimization is performed again and the new Pareto-optimal solutions are derived. These new Pareto-optimal solutions determined along with the changes in the parameter are equal to the flexibilities of this point.5) The flexibilities of all design variables and all five points are derived.From this procedure, the flexibility of the design variable to the Pareto-optimal solution is derived. The proposed method was applied to diesel engine fuel emission scheduling problems and it is confirmed that the Pareto-optimal solutions can be derived with only the design variables whose flexibilities are high.