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A NORMALIZED CIRCLE INTERSECTION METHOD FOR BI-OBJECTIVE OPTIMIZATION PROGRAMMING

机译:双目标优化规划的归一化圆交算法

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摘要

Multi-objective optimization (MOO) problems are encountered in many applications and a number of approaches have been proposed to deal with this kind of problems. Despite the computational efforts, the quality of the Pareto front is also a considerable issue. An evenly distributed Pareto front is desirable for developing analytical expressions. In this paper, a brand new approach called Normalized Circle Intersection (NCI) is proposed, which is able to efficiently generate a Pareto front with evenly-distributed Pareto points for bi-objective problems, no matter the feasible boundary is convex or not. Firstly, the anchor points are computed using an existing sequential MOO (SMOO) approach. Then in the normalized objective space, a circle with a radius of r centering at one of the anchor points or the latest obtained Pareto point is drawn. The intersection of the circle and the feasible boundary, which exists for sure, can be determined whether it is a Pareto point or not. For a convex or concave feasible boundary, the intersection is exactly the Pareto point to be found, while for a non-convex boundary the intersection can provide useful information for searching the true Pareto point even if it self is not a Pareto point. A novel MOO formulation is proposed for NCI correspondingly. Four examples, including two numerical and two engineering examples, are provided to demonstrate the applicability of the proposed method. Comparison of the computational results with WS, NNC and SMOO shows the effectiveness of the proposed method.
机译:在许多应用程序中会遇到多目标优化(MOO)问题,并且已经提出了许多方法来处理此类问题。尽管进行了计算工作,但帕累托阵线的质量也是一个相当大的问题。均匀分布的Pareto前沿是开发解析表达式所需要的。在本文中,提出了一种全新的方法,称为归一化圆交(NCI),该方法可以有效地生成具有双目标问题的Pareto点均匀分布的Pareto前沿,而不管可行边界是凸的还是非凸的。首先,使用现有的顺序MOO(SMOO)方法来计算锚点。然后,在归一化的目标空间中,绘制一个以r为半径,以锚点或最新获得的帕累托点之一为中心的圆。可以确定圆和可行边界的交点,确定它是否是帕累托点。对于凸或凹可行边界,相交恰好是要找到的帕累托点,而对于非凸边界,相交可以为搜索真实帕累托点提供有用的信息,即使它本身不是帕累托点也是如此。相应地为NCI提出了一种新颖的MOO配方。提供了四个示例,包括两个数值示例和两个工程示例,以证明所提出方法的适用性。将计算结果与WS,NNC和SMOO进行比较,表明了该方法的有效性。

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