AN ANALYSIS AND AN ORGANIZATION OF OPTIMIZATION METHODS USING COUPLED NONLINEAR DYNAMICS

本文从理论上分析了由非线性动力学驱动的多搜索点实现优化的耦合非线性动力学优化方法。此外，我们还研究了一种用非线性动力学方法组织的优化方法。因此，我们从理论上解释了将耦合动力学引入优化方法的有效性。针对约束优化问题和多目标问题，提出了耦合非线性动力学优化方法。此外，我们还提出了一种梯度动力学与惯性耦合的优化方法。这些成果有助于利用耦合非线性动力学组织优化方法。

In this study, we theoretically analyzed the optimization methods using coupled nonlinear dynamics in which multiple search points driven by nonlinear dynamics implement optimization. Furthermore, we studied an organization of the optimization method using nonlinear dynamics. In consequence, we theoretically explain effectiveness of the introduction of coupled dynamics to the optimization method. Furthermore, we proposed optimization methods using coupled nonlinear dynamics for constrained optimization problems and multi-objective problems. In addition, we proposed an optimization method using coupled gradient dynamics with inertia. These fruits contribute to organize the optimization methods using coupled nonlinear dynamics.