基于深度卷积神经网络的复杂多目标规划问题机器学习方法

Machine learning method for complex multi-objective programming problems based on deep convolutional neural network

针对多目标规划进化算法中测试函数的Pareto最优解集模式单一、种群多样性与算法收敛速度相互牵制等问题,设计了一种基于深度卷积神经网络的复杂多目标规划问题的机器学习方法:在原像空间中,提出“部分精英集的Gauss采样+部分拉丁超立方采样”的混合采样新方法,其中部分样本以精英集中的Pareto最优解为中心进行Gauss采样以保证所获Pareto最优前沿不差于上一代,部分样本利用拉丁超立方采样以保证样本的多样性;在像空间中,利用基于深度卷积神经网络图像特定边缘提取直接获取Pareto最优前沿。为测试算法求解复杂多目标规划问题的效率和普适性,将5个经典多目标规划问题进行改进(测试模型的最优Pareto解集具有随机性并增加了测试模型维度),利用该算法对5个改进模型进行了仿真试验,结果表明,算法对求解复杂多目标规划问题的具有可行性且具有较高的计算效率。

A machine learning method for complex multi-objective programming problems based on deep convolutional neural network was designed to solve the problems of single Pareto optimal solution set mode of test function and mutual constraint between population diversity and algorithm convergence speed in multi-objective programming evolutionary algorithm.In the preimage space, a new hybrid sampling method of “partial elite set Gauss sampling+partial Latin hypercube sampling” was proposed.Gauss sampling of some samples was centered on the Pareto optimal solution of elite sets to ensure that the Pareto optimal front obtained was not worse than that of the previous generation.Some samples were sampled by Latin hypercube sampling to ensure the diversity of samples.In the image space, the Pareto optimal front was directly obtained by extracting the specific edge of the image based on the deep convolutional neural network.In order to test the efficiency and universality of the algorithm for solving complex multi-objective programming problems, five classic multi-objective programming problems were improved(The optimal Pareto solution set of the test model was random, and the dimension of the test model was increased).Finally, five improved models were simulated by using the algorithm in this paper.The experimental results show that the algorithm is feasible and has high computational efficiency for complex multi-objective programming problems.