Two New Filled Functions Based On Differential Dynamic Systems

In this paper, we propose two new dynamic filled function algorithms which are based on differential dynamic systems. The algorithms are applied to constrained global optimization problems. We propose two filled functions and show their properties under the given assumptions. Inspired by the idea of Kennedy and Chua, we construct two differential dynamic systems and discuss the stability of them. The main idea of the algorithms is that in concept of two-phase method, the objective function and the filled function are respectively combined with a differential dynamic system to get global minima. In the first stage, we use the objective function and its constraints to construct a differential system. By solving the equation, we get a local minima point. In the second stage, we construct a filled function at current local minima point and the differential dynamic system with the filled function. By solving the equation, we get a new local minima point which is taken as the initial point for the differential system in the first stage of next round. This process will be repeated until the global minima point is found. Besides, we show that the local minima point in the second stage is proven to be at low level set.The algorithms are designed and the numerical experiments are presented. The numerical results have proven that the algorithms are effective.