For the car sequencing（CS） problem, the draw-backs of the ＂sliding windows＂ technique used in the objective function have not been rectified, and no high quality initial solution has been acquired to accelerate th...For the car sequencing（CS） problem, the draw-backs of the ＂sliding windows＂ technique used in the objective function have not been rectified, and no high quality initial solution has been acquired to accelerate the improvement of the solution quality. Firstly, the objective function is improved to solve the double and bias counting of violations broadly discussed. Then, a new method combining heuristic with constraint propagation is proposed which constructs initial solutions under a parallel framework. Based on constraint propagation, three filtering rules are designed to intersecting with three greedy functions, so the variable domain is narrowed in the process of the construction. The parallel framework is served to show its robustness in terms of the quality of the solution since it greatly increases the performance of obtaining the best solution. In the computational experiments, 109 instances of 3 sets from the CSPLib＇ s benchmarks are used to test the performance of the proposed method. Experiment results show that the proposed method outperforms others in acquiring the best-known results for 85 best-known results of 109 are obtained with only one construction. The proposed research provides an avenue to remedy the deficiencies of ＂sliding windows＂ technique and construct high quality initial solutions.展开更多
Kernel learning forward backward stochastic differential equations(FBSDE)filter is an iterative and adaptive meshfree approach to solve the non-linear filtering problem.It builds from forward backward SDE for Fokker-P...Kernel learning forward backward stochastic differential equations(FBSDE)filter is an iterative and adaptive meshfree approach to solve the non-linear filtering problem.It builds from forward backward SDE for Fokker-Planker equation,which defines evolving density for the state variable,and employs kernel density estimation(KDE)to approximate density.This algo-rithm has shown more superior performance than mainstream particle filter method,in both convergence speed and efficiency of solving high dimension problems.However,this method has only been shown to converge empirically.In this paper,we present a rigorous analysis to demonstrate its local and global convergence,and provide theoretical support for its empirical results.展开更多
基金Supported by National Natural Science Foundation of China(Grant Nos.51435009,71302085)Zhejiang Provincial Natural Science Foundation of China(Grant No.LQ14E080002)K.C.Wong Magna Fund in Ningbo University
文摘For the car sequencing（CS） problem, the draw-backs of the ＂sliding windows＂ technique used in the objective function have not been rectified, and no high quality initial solution has been acquired to accelerate the improvement of the solution quality. Firstly, the objective function is improved to solve the double and bias counting of violations broadly discussed. Then, a new method combining heuristic with constraint propagation is proposed which constructs initial solutions under a parallel framework. Based on constraint propagation, three filtering rules are designed to intersecting with three greedy functions, so the variable domain is narrowed in the process of the construction. The parallel framework is served to show its robustness in terms of the quality of the solution since it greatly increases the performance of obtaining the best solution. In the computational experiments, 109 instances of 3 sets from the CSPLib＇ s benchmarks are used to test the performance of the proposed method. Experiment results show that the proposed method outperforms others in acquiring the best-known results for 85 best-known results of 109 are obtained with only one construction. The proposed research provides an avenue to remedy the deficiencies of ＂sliding windows＂ technique and construct high quality initial solutions.
基金supported by the U.S.National Science Foundation through Project DMS-2142672by the U.S.Department of Energy,Office of Science,Office of Advanced Scientific Computing Research,Applied Mathematics Program under Grant DE-SC0022297.
文摘Kernel learning forward backward stochastic differential equations(FBSDE)filter is an iterative and adaptive meshfree approach to solve the non-linear filtering problem.It builds from forward backward SDE for Fokker-Planker equation,which defines evolving density for the state variable,and employs kernel density estimation(KDE)to approximate density.This algo-rithm has shown more superior performance than mainstream particle filter method,in both convergence speed and efficiency of solving high dimension problems.However,this method has only been shown to converge empirically.In this paper,we present a rigorous analysis to demonstrate its local and global convergence,and provide theoretical support for its empirical results.
