IEEE Trans Neural Netw Learn Syst. 2015 Oct;26(10):2500-20. doi: 10.1109/TNNLS.2015.2388511. Epub 2015 Jan 30.
This paper develops a neural network architecture and a new processing method for solving in real time, the nonlinear equality constrained multiobjective optimization problem (NECMOP), where several nonlinear objective functions must be optimized in a conflicting situation. In this processing method, the NECMOP is converted to an equivalent scalar optimization problem (SOP). The SOP is then decomposed into several-separable subproblems processable in parallel and in a reasonable time by multiplexing switched capacitor circuits. The approach which we propose makes use of a decomposition-coordination principle that allows nonlinearity to be treated at a local level and where coordination is achieved through the use of Lagrange multipliers. The modularity and the regularity of the neural networks architecture herein proposed make it suitable for very large scale integration implementation. An application to the resolution of a physical problem is given to show that the approach used here possesses some advantages of the point of algorithmic view, and provides processes of resolution often simpler than the usual techniques.
本文提出了一种神经网络结构和一种新的处理方法，用于实时求解非线性等式约束多目标优化问题（NECMOP），其中必须在冲突情况下优化多个非线性目标函数。在这种处理方法中，将 NECMOP 转换为等效的标量优化问题（SOP）。然后，通过复用开关电容电路，将 SOP 分解为几个可并行处理且在合理时间内处理的可分离子问题。我们提出的方法利用了分解-协调原理，该原理允许在局部级别处理非线性，并且通过使用拉格朗日乘子来实现协调。所提出的神经网络结构的模块化和规则性使其适合大规模集成实现。通过应用于解决物理问题，表明这里使用的方法在算法观点上具有一些优势，并提供了通常比常用技术更简单的求解过程。
