IEEE Trans Neural Netw Learn Syst. 2018 Apr;29(4):981-992. doi: 10.1109/TNNLS.2017.2652478. Epub 2017 Feb 1.
This paper is concerned with multiple-objective distributed optimization. Based on objective weighting and decision space decomposition, a collaborative neurodynamic approach to multiobjective distributed optimization is presented. In the approach, a system of collaborative neural networks is developed to search for Pareto optimal solutions, where each neural network is associated with one objective function and given constraints. Sufficient conditions are derived for ascertaining the convergence to a Pareto optimal solution of the collaborative neurodynamic system. In addition, it is proved that each connected subsystem can generate a Pareto optimal solution when the communication topology is disconnected. Then, a switching-topology-based method is proposed to compute multiple Pareto optimal solutions for discretized approximation of Pareto front. Finally, simulation results are discussed to substantiate the performance of the collaborative neurodynamic approach. A portfolio selection application is also given.
本文研究了多目标分布式优化问题。基于目标加权和决策空间分解，提出了一种协同神经动力学方法来解决多目标分布式优化问题。在该方法中，开发了一个协同神经网络系统来搜索 Pareto 最优解，其中每个神经网络与一个目标函数和给定的约束条件相关联。推导出了充分条件，以确定协同神经动力学系统收敛到 Pareto 最优解。此外，证明了当通信拓扑断开时，每个连通子系统都可以生成一个 Pareto 最优解。然后，提出了一种基于切换拓扑的方法，用于计算 Pareto 前沿的离散逼近的多个 Pareto 最优解。最后，讨论了仿真结果，以验证协同神经动力学方法的性能。还给出了一个投资组合选择应用。
