Blending is an important unit operation in process industry. Blending scheduling is nonlinear optimiza- tion problem with constraints. It is difficult to obtain optimum solution by other general optimization methods. ...Blending is an important unit operation in process industry. Blending scheduling is nonlinear optimiza- tion problem with constraints. It is difficult to obtain optimum solution by other general optimization methods. Particle swarm optimization (PSO) algorithm is developed for nonlinear optimization problems with both contin- uous and discrete variables. In order to obtain a global optimum solution quickly, PSO algorithm is applied to solve the problem of blending scheduling under uncertainty. The calculation results based on an example of gasoline blending agree satisfactory with the ideal values, which illustrates that the PSO algorithm is valid and effective in solving the blending scheduling problem.展开更多
The single machine parallel batch problem with job compatibility is considered to minimize makespan, where the job compatibility constraints are represented by a graph G. This problem is proved to be NP-hard. And when...The single machine parallel batch problem with job compatibility is considered to minimize makespan, where the job compatibility constraints are represented by a graph G. This problem is proved to be NP-hard. And when the graph G is limited to be a general bipartite, a complete bipartite and a complete m-partite graph, these problems are solved in polynomial time respectively.展开更多
The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty fu...The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming. Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the quadratic objective penalty function, an algorithm is developed to l^nd an optimal solution to the original bilevel programming, and its convergence proved under some conditions. Furthermore, under the assumption of convexity at function without lower level problems is defined and lower level problems, a quadratic objective penalty is proved equal to the original bilevel programming.展开更多
In this paper,the improved canonical quantization method of the self dual field is given in order to overcome linear combination problem about the second class constraint and the first class constraint number maximiza...In this paper,the improved canonical quantization method of the self dual field is given in order to overcome linear combination problem about the second class constraint and the first class constraint number maximization problem in the Dirac method.In the improved canonical quantization method,there are no artificial linear combination and the first class constraint number maximization problems,at the same time,the stability of the system is considered.Therefore,the improved canonical quantization method is more natural and easier accepted by people than the usual Dirac method.We use the improved canonical quantization method to realize the canonical quantization of the self dual field,which has relation with string theory successfully and the results are equal to the results by using the Dirac method.展开更多
For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a sm...For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.展开更多
基金Supported by the National 863 Project (No. 2003AA412010) and the National 973 Program of China (No. 2002CB312201)
文摘Blending is an important unit operation in process industry. Blending scheduling is nonlinear optimiza- tion problem with constraints. It is difficult to obtain optimum solution by other general optimization methods. Particle swarm optimization (PSO) algorithm is developed for nonlinear optimization problems with both contin- uous and discrete variables. In order to obtain a global optimum solution quickly, PSO algorithm is applied to solve the problem of blending scheduling under uncertainty. The calculation results based on an example of gasoline blending agree satisfactory with the ideal values, which illustrates that the PSO algorithm is valid and effective in solving the blending scheduling problem.
文摘The single machine parallel batch problem with job compatibility is considered to minimize makespan, where the job compatibility constraints are represented by a graph G. This problem is proved to be NP-hard. And when the graph G is limited to be a general bipartite, a complete bipartite and a complete m-partite graph, these problems are solved in polynomial time respectively.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271329 and 10971193
文摘The bilevel programming is applied to solve hierarchical intelligence control problems in such fields as industry, agriculture, transportation, military, and so on. This paper presents a quadratic objective penalty function with two penalty parameters for inequality constrained bilevel programming. Under some conditions, the optimal solution to the bilevel programming defined by the quadratic objective penalty function is proved to be an optimal solution to the original bilevel programming. Moreover, based on the quadratic objective penalty function, an algorithm is developed to l^nd an optimal solution to the original bilevel programming, and its convergence proved under some conditions. Furthermore, under the assumption of convexity at function without lower level problems is defined and lower level problems, a quadratic objective penalty is proved equal to the original bilevel programming.
基金Supported by National Natural Science Foundation of China under Grant Nos. 11275017 and 11173028
文摘In this paper,the improved canonical quantization method of the self dual field is given in order to overcome linear combination problem about the second class constraint and the first class constraint number maximization problem in the Dirac method.In the improved canonical quantization method,there are no artificial linear combination and the first class constraint number maximization problems,at the same time,the stability of the system is considered.Therefore,the improved canonical quantization method is more natural and easier accepted by people than the usual Dirac method.We use the improved canonical quantization method to realize the canonical quantization of the self dual field,which has relation with string theory successfully and the results are equal to the results by using the Dirac method.
基金supported by the National Natural Science Foundation of China under Grant Nos.10971118, 10701047 and 10901096the Natural Science Foundation of Shandong Province under Grant Nos. ZR2009AL019 and BS2010SF010
文摘For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.
