In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and t...In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.展开更多
This paper presents a new approach to solve mixed-variable unit commitment(UC) problems with non-smooth cost functions based on a generalized pattern search filter(GPS-filter) algorithm. A GPS-filter algorithm does no...This paper presents a new approach to solve mixed-variable unit commitment(UC) problems with non-smooth cost functions based on a generalized pattern search filter(GPS-filter) algorithm. A GPS-filter algorithm does not require any information about the gradient of the objective function while searching for an optimum solution. At the same time, it is available for solving mixed-variable optimization problems, which is very suitable for UC. A new suitable discrete neighborhood structure with UC characteristics is proposed to improve GPS-filter efficiently. A lot of multiple units' states are fixed before search; hence, the polling search of discrete variable is efficient for a few uncertain units. Numerical experiments are included to demonstrate the proposed approach's ability to handle the highly nonlinear, discontinuous, non-smooth cost functions and mixed variables of the UC problem.展开更多
基金the National Natural Science Foundation of China (60274016)the Project of Scientific Research in Hight Education Bureau Liaoning Province (2023901018).
文摘In this paper, we introduce the concept of fuzzifying topological linear space and discuss the structures and properties of the balanced neighborhood system of zero element. We also give the algebraic properties and the topological properties of fuzzifying convex set in the fuzzifying topological linear space.
基金Project Supported by National Natural Science Foundation of China(51277034,51377027)
文摘This paper presents a new approach to solve mixed-variable unit commitment(UC) problems with non-smooth cost functions based on a generalized pattern search filter(GPS-filter) algorithm. A GPS-filter algorithm does not require any information about the gradient of the objective function while searching for an optimum solution. At the same time, it is available for solving mixed-variable optimization problems, which is very suitable for UC. A new suitable discrete neighborhood structure with UC characteristics is proposed to improve GPS-filter efficiently. A lot of multiple units' states are fixed before search; hence, the polling search of discrete variable is efficient for a few uncertain units. Numerical experiments are included to demonstrate the proposed approach's ability to handle the highly nonlinear, discontinuous, non-smooth cost functions and mixed variables of the UC problem.
