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薛贵文, 张茂军. 基于单纯形法的多目标优化复合算法[J]. 桂林电子科技大学学报, 2022, 42(2): 117-121.
引用本文: 薛贵文, 张茂军. 基于单纯形法的多目标优化复合算法[J]. 桂林电子科技大学学报, 2022, 42(2): 117-121.
XUE Guiwen, ZHANG Maojun. Multi-objective optimization compound algorithm based on simplex algorithm[J]. Journal of Guilin University of Electronic Technology, 2022, 42(2): 117-121.
Citation: XUE Guiwen, ZHANG Maojun. Multi-objective optimization compound algorithm based on simplex algorithm[J]. Journal of Guilin University of Electronic Technology, 2022, 42(2): 117-121.

基于单纯形法的多目标优化复合算法

Multi-objective optimization compound algorithm based on simplex algorithm

  • 摘要: 对于多目标优化问题, 以往的优化方法中因有人为参与的部分最终会导致最优解产生一定误差, 在处理多目标优化问题各类方法中, 将多目标线性加权为单目标的方法使用较为普遍, 而线性加权的权重选取过程中, 人为参与的部分较多, 且干预性较强, 对于最终的优化结果存在一定的误差影响。因此, 为了减少人为参与过程并降低误差, 对线性加权的过程进行改进, 并将单纯形法融入多目标优化的处理过程中, 提出了一种基于单纯形法的多目标优化复合型算法。通过算法选取单纯形初始点及权重, 代替人为选取的方法, 从而减少主观判断对最优解的影响, 并通过算法处理目标函数, 从而降低误差, 同时也能够通过单纯形法的多次迭代计算出最优解。数值算例验证了算法的有效性。

     

    Abstract: For multi-objective optimization problems, in the previous optimization methods, human participation will eventually lead to a certain error in the optimal solution. Among the various methods for dealing with multi-objective optimization problems, the method of linearly weighting multi-objectives into single-objectives is more commonly used. In the process of linear weighting weight selection, there are more parts of human involvement and strong intervention. The optimization result has a certain error influence. In order to reduce human participation in the process and reduce errors, the linear weighting process is improved, and the simplex method is integrated into the multi-objective optimization process, and a multi-objective optimization compound algorithm based on the simplex method is proposed. A composite algorithm based on the simplex method is proposed. The simplex initial point and weight are selected by algorithm, instead of manual selection, so as to reduce the influence of subjective judgment on the optimal solution, and the objective function is processed by algorithm to reduce errors. Numerical examples verify the effectiveness of the algorithm.

     

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