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较少、变化较小的情况下改变。提出了多目标优化问题中设计变量对Pareto最优解的灵活性的概念。下面是一种评估设计变量对Pareto最优解的灵活性的方法。1)建立多目标问题的公式。这个问题是使用所有设计变量来解决的。在这种情况下，不固定设计变量的值。2)将派生的Pareto最优解与某一目标函数的值一起排序。3)从排序后的Pareto最优解中确定5个点。五个点之间的距离应相等。4)在每个点上，改变一个设计变量。在这种情况下，其他解决方案的值是固定的。假定设计变量的范围。在这种情况下，再次进行多目标优化，得到新的Pareto最优解。这些随参数变化而确定的新的Pareto最优解等于该点的柔度。5)推导了所有设计变量和全部五点的柔度，由此推导出设计变量对Pareto最优解的柔度。将该方法应用于柴油机燃油排放调度问题，结果表明，只需具有较高灵活性的设计变量即可得到Pareto最优解。

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.