Leung Man-Fai, Wang Jun
IEEE Trans Neural Netw Learn Syst. 2018 Nov;29(11):5738-5748. doi: 10.1109/TNNLS.2018.2806481. Epub 2018 Mar 29.
There are two ultimate goals in multiobjective optimization. The primary goal is to obtain a set of Pareto-optimal solutions while the secondary goal is to obtain evenly distributed solutions to characterize the efficient frontier. In this paper, a collaborative neurodynamic approach to multiobjective optimization is presented to attain both goals of Pareto optimality and solution diversity. The multiple objectives are first scalarized using a weighted Chebyshev function. Multiple projection neural networks are employed to search for Pareto-optimal solutions with the help of a particle swarm optimization (PSO) algorithm in reintialization. To diversify the Pareto-optimal solutions, a holistic approach is proposed by maximizing the hypervolume (HV) using again a PSO algorithm. The experimental results show that the proposed approach outperforms three other state-of-the-art multiobjective algorithms (i.e., HMOEA/D, MOEA/DD, and NSGAIII) most of times on 37 benchmark datasets in terms of HV and inverted generational distance.
多目标优化有两个最终目标。首要目标是获得一组帕累托最优解，而次要目标是获得均匀分布的解以刻画有效前沿。本文提出一种用于多目标优化的协同神经动力学方法，以实现帕累托最优和解决方案多样性这两个目标。首先使用加权切比雪夫函数对多个目标进行标量化。在重新初始化过程中，利用粒子群优化（PSO）算法，通过多个投影神经网络搜索帕累托最优解。为了使帕累托最优解多样化，再次使用PSO算法，通过最大化超体积（HV）提出了一种整体方法。实验结果表明，在37个基准数据集上，所提出的方法在HV和倒置世代距离方面，大多数时候优于其他三种最先进的多目标算法（即HMOEA/D、MOEA/DD和NSGAIII）。
