Differential evolution （DE） has become a very popular and effective global optimization algorithm in the area of evolutionary computation. In spite of many advantages such as conceptual simplicity, high efficiency a...Differential evolution （DE） has become a very popular and effective global optimization algorithm in the area of evolutionary computation. In spite of many advantages such as conceptual simplicity, high efficiency and ease of use, DE has two main components, i.e., mutation scheme and parameter control, which significantly influence its performance. In this paper we intend to improve the performance of DE by using carefully considered strategies for both of the two components. We first design an adaptive mutation scheme, which adaptively makes use of the bias of superior individuals when generating new solutions. Although introducing such a bias is not a new idea, existing methods often use heuristic rules to control the bias. They can hardly maintain the appropriate balance between exploration and exploitation during the search process, because the preferred bias is often problem and evolution-stage dependent. Instead of using any fixed rule, a novel strategy is adopted in the new adaptive mutation scheme to adjust the bias dynamically based on the identified local fitness landscape captured by the current population. As for the other component, i.e., parameter control, we propose a mechanism by using the Levy probability distribution to adaptively control the scale factor F of DE. For every mutation in each generation, an Fi is produced from one of four different Levy distributions according to their historical performance. With the adaptive mutation scheme and parameter control using Levy distribution as the main components, we present a new DE variant called Levy DE （LDE）. Experimental studies were carried out on a broad range of benchmark functions in global numerical optimization. The results show that LDE is very competitive, and both of the two main components have contributed to its overall performance. The scalability of LDE is also discussed by conducting experiments on some selected benchmark functions with dimensions from 30 to 200.展开更多
In this paper, we study a mathematical model of electron beam focusing system. We prove the existence of periodic solutions to the model using homotopy method.
基金the National Natural Science Foundation of China under Grant Nos. 71071106 and 70801062
文摘Differential evolution （DE） has become a very popular and effective global optimization algorithm in the area of evolutionary computation. In spite of many advantages such as conceptual simplicity, high efficiency and ease of use, DE has two main components, i.e., mutation scheme and parameter control, which significantly influence its performance. In this paper we intend to improve the performance of DE by using carefully considered strategies for both of the two components. We first design an adaptive mutation scheme, which adaptively makes use of the bias of superior individuals when generating new solutions. Although introducing such a bias is not a new idea, existing methods often use heuristic rules to control the bias. They can hardly maintain the appropriate balance between exploration and exploitation during the search process, because the preferred bias is often problem and evolution-stage dependent. Instead of using any fixed rule, a novel strategy is adopted in the new adaptive mutation scheme to adjust the bias dynamically based on the identified local fitness landscape captured by the current population. As for the other component, i.e., parameter control, we propose a mechanism by using the Levy probability distribution to adaptively control the scale factor F of DE. For every mutation in each generation, an Fi is produced from one of four different Levy distributions according to their historical performance. With the adaptive mutation scheme and parameter control using Levy distribution as the main components, we present a new DE variant called Levy DE （LDE）. Experimental studies were carried out on a broad range of benchmark functions in global numerical optimization. The results show that LDE is very competitive, and both of the two main components have contributed to its overall performance. The scalability of LDE is also discussed by conducting experiments on some selected benchmark functions with dimensions from 30 to 200.
基金supported by the Fundamental Research Funds for the Central Universities of China (2010LKSX07)the Science Foundation of China University of Mining and Technology (0K4066)
文摘In this paper, we study a mathematical model of electron beam focusing system. We prove the existence of periodic solutions to the model using homotopy method.
