A dynamic parallel forecasting model is proposed, which is based on the problem of current forecasting models and their combined model. According to the process of the model, the fuzzy C-means clustering algorithm is ...A dynamic parallel forecasting model is proposed, which is based on the problem of current forecasting models and their combined model. According to the process of the model, the fuzzy C-means clustering algorithm is improved in outliers operation and distance in the clusters and among the clusters. Firstly, the input data sets are optimized and their coherence is ensured, the region scale algorithm is modified and non-isometric multi scale region fuzzy time series model is built. At the same time, the particle swarm optimization algorithm about the particle speed, location and inertia weight value is improved, this method is used to optimize the parameters of support vector machine, construct the combined forecast model, build the dynamic parallel forecast model, and calculate the dynamic weight values and regard the product of the weight value and forecast value to be the final forecast values. At last, the example shows the improved forecast model is effective and accurate.展开更多
Given a connected graph G=（V,E）with a nonnegative cost on each edge in E,a nonnegative prize at each vertex in V,and a target set V′V,the Prize Collecting Steiner Tree（PCST）problem is to find a tree T in G interc...Given a connected graph G=（V,E）with a nonnegative cost on each edge in E,a nonnegative prize at each vertex in V,and a target set V′V,the Prize Collecting Steiner Tree（PCST）problem is to find a tree T in G interconnecting all vertices of V′such that the total cost on edges in T minus the total prize at vertices in T is minimized.The PCST problem appears frequently in practice of operations research.While the problem is NP-hard in general,it is polynomial-time solvable when graphs G are restricted to series-parallel graphs.In this paper,we study the PCST problem with interval costs and prizes,where edge e could be included in T by paying cost xe∈[c e,c＋e]while taking risk（c＋e xe）/（c＋e c e）of malfunction at e,and vertex v could be asked for giving a prize yv∈[p v,p＋v]for its inclusion in T while taking risk（yv p v）/（p＋v p v）of refusal by v.We establish two risk models for the PCST problem with interval data.Under given budget upper bound on constructing tree T,one model aims at minimizing the maximum risk over edges and vertices in T and the other aims at minimizing the sum of risks over edges and vertices in T.We propose strongly polynomial-time algorithms solving these problems on series-parallel graphs to optimality.Our study shows that the risk models proposed have advantages over the existing robust optimization model,which often yields NP-hard problems even if the original optimization problems are polynomial-time solvable.展开更多
基金supported by the National Defense Preliminary Research Program of China(A157167)the National Defense Fundamental of China(9140A19030314JB35275)
文摘A dynamic parallel forecasting model is proposed, which is based on the problem of current forecasting models and their combined model. According to the process of the model, the fuzzy C-means clustering algorithm is improved in outliers operation and distance in the clusters and among the clusters. Firstly, the input data sets are optimized and their coherence is ensured, the region scale algorithm is modified and non-isometric multi scale region fuzzy time series model is built. At the same time, the particle swarm optimization algorithm about the particle speed, location and inertia weight value is improved, this method is used to optimize the parameters of support vector machine, construct the combined forecast model, build the dynamic parallel forecast model, and calculate the dynamic weight values and regard the product of the weight value and forecast value to be the final forecast values. At last, the example shows the improved forecast model is effective and accurate.
基金Supported in part by the National Natural Science Foundation of China under Grant No.11021161 and 10928102973 Program of China under Grant No.2011CB80800+1 种基金Chinese Academy of Sciences under Grant No.kjcx-yw-s7,project grant of"Center for Research and Applications in Plasma Physics and Pulsed Power Technology,PBCT-Chile-ACT 26"Direccio'n de Programas de Investigaci'ón,Universidad de Talca,Chile
文摘Given a connected graph G=（V,E）with a nonnegative cost on each edge in E,a nonnegative prize at each vertex in V,and a target set V′V,the Prize Collecting Steiner Tree（PCST）problem is to find a tree T in G interconnecting all vertices of V′such that the total cost on edges in T minus the total prize at vertices in T is minimized.The PCST problem appears frequently in practice of operations research.While the problem is NP-hard in general,it is polynomial-time solvable when graphs G are restricted to series-parallel graphs.In this paper,we study the PCST problem with interval costs and prizes,where edge e could be included in T by paying cost xe∈[c e,c＋e]while taking risk（c＋e xe）/（c＋e c e）of malfunction at e,and vertex v could be asked for giving a prize yv∈[p v,p＋v]for its inclusion in T while taking risk（yv p v）/（p＋v p v）of refusal by v.We establish two risk models for the PCST problem with interval data.Under given budget upper bound on constructing tree T,one model aims at minimizing the maximum risk over edges and vertices in T and the other aims at minimizing the sum of risks over edges and vertices in T.We propose strongly polynomial-time algorithms solving these problems on series-parallel graphs to optimality.Our study shows that the risk models proposed have advantages over the existing robust optimization model,which often yields NP-hard problems even if the original optimization problems are polynomial-time solvable.
