Multi-objective optimization by means of multi-dimensional MLP neural networks
Multi-objective optimization by means of multi-dimensional MLP neural networks
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DOI：
10.14311/nnw.2014.24.002
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发表时间：
2014-02
影响因子：
0.8
通讯作者：
M. Rafei;S. E. Sorkhabi;M. Mosavi
中科院分区：
文献类型：
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作者：
M. Rafei;S. E. Sorkhabi;M. Mosavi
本文提出了一种多层感知器（MLP）神经网络（NN）作为执行两个任务的有效工具：1）多目标优化问题和2）求解非线性方程组。在这两种情况下，涉及的数学函数是连续的和部分有界的。在此之前，这两项任务都是由递归神经网络和进化算法等强大的算法来执行的。在这项研究中，多维结构的输出层的MLP-NN，作为一种创新的方法，利用隐式优化的多变量函数下的网络能量优化机制。为此，输出层中的激活函数被替换为要优化的多变量函数。研究了全局搜索中有效的训练参数。此外，它表明，MLP-NN与适当的动态学习率是能够找到全局最优解。最后，通过一些著名的实验实例，研究了MLP-NN在速度和功耗两个方面的效率。在这些例子中，所提出的方法给出了显着更好的全局最优解相比，其他参考文献，并在其他实验中也表现出完全令人满意的结果。
In this paper, a multi-layer perceptron (MLP) neural network (NN) is put forward as an efficient tool for performing two tasks: 1) optimization of multi-objective problems and 2) solving a non-linear system of equations. In both cases, mathematical functions which are continuous and partially bounded are involved. Previously, these two tasks were performed by recurrent neural networks and also strong algorithms like evolutionary ones. In this study, multi-dimensional structure in the output layer of the MLP-NN, as an innovative method, is utilized to implicitly optimize the multivariate functions under the network energy optimization mechanism. To this end, the activation functions in the output layer are replaced with the multivariate functions intended to be optimized. The effective training parameters in the global search are surveyed. Also, it is demonstrated that the MLP-NN with proper dynamic learning rate is able to find globally optimal solutions. Finally, the efficiency of the MLP-NN in both aspects of speed and power is investigated by some well-known experimental examples. In some of these examples, the proposed method gives explicitly better globally optimal solutions compared to that of the other references and also shows completely satisfactory results in other experiments.